No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
2D Magneto-Optical Trapping of Diatomic Molecules
Abstract
The development of the magneto-optical trap revolutionized the fields of
atomic and quantum physics by providing a simple method for the rapid
production of ultracold, trapped atoms. A similar technique for producing a
diverse set of dense, ultracold diatomic molecular species will likewise
transform the study of strongly interacting quantum systems, precision
measurement, and physical chemistry. We demonstrate one- and two-dimensional
transverse laser cooling and magneto-optical trapping of the polar molecule
yttrium (II) oxide (YO). Using a quasicycling optical transition we observe
transverse Doppler cooling of a YO molecular beam to a temperature of 5 mK,
limited by interaction time. With the addition of an oscillating magnetic
quadrupole field we demonstrate a transverse magneto-optical trap and achieve
temperatures of 2 mK.
... Experimentally, Shuman et al. [8] first achieved transverse laser cooling molecules of SrF using an optical cycling scheme with Doppler and Sisyphus cooling forces. The laser cooling of YO was performed by Hummon et al. [9], while Zhelyazkova et al. [10] demonstrated the longitudinal laser cooling of a supersonic beam of CaF molecules. Several studies have considered a series of diatomic polar molecules and ions, including hydrogen, as promising laser cooling candidates, such as the alkalineearth-metal monohydrides [11] (e.g., BeH, MgH, CaH, SrH, and BaH) and other molecular systems (e.g., CH [12], AlH and AlF [13], BH + and AlH + [14]). ...
... in a closed-loop cycle [43], ii) a short radiative lifetime (in the range of 10 -8 to 10 -5 s), to maximizes the rate of cooling between two vibrational states and consequently produce a strong Doppler force [44][45][46] iii) the absence of an intervening intermediate electronic state in the laser cooling cycle, to limit radiative losses in the cooling scheme. The last criterion applies unless the transition is forbidden/has a minimal probability of occurrence [9,47], or there is a way for the intermediate state to be included in the cooling scheme, as has been recently proposed by Moussa et al. [48]. Level 11 program [49] was used to calculate the Frank-Condon Factor (F.C.F) for transitions between the vibrational levels 0 ≤ v ≤ 5 of the electronic states X 2 Δ 3/2 and (1) 2 Π 1/2 . ...
... A smaller value than what has been recently demonstrated for YO, Table 7 The radiative lifetimes τ, and the vibrational branching ratio of the vibrational transitions between the electronic states X 2 Δ 3/2 -(1) 4 Φ 3/2 of the molecule HfH. and SCO molecules [9,52], where the vibrational branching ratio loss is respectively given by η = 4*10 − 4 and η = 1.44 × 10 − 4 . ...
... [11][12][13][14] Direct laser cooling and trapping of molecules have recently been shown to be effective tools for preparing ultracold molecules. 5,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] An experimental laser-cooling scheme has been established for molecules: 15 molecules are produced by laser ablation and then cooled with cryogenic buffer gas, slowed via radiation pressure from counter-propagating light, captured into a three-dimensional magneto-optical trap (3D MOT), and then transferred to a conservative trap, typically an optical dipole trap (ODT). A variety of diatomic molecules have been slowed 13,[18][19][20] and loaded into 3D MOTs. ...
... 5,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] An experimental laser-cooling scheme has been established for molecules: 15 molecules are produced by laser ablation and then cooled with cryogenic buffer gas, slowed via radiation pressure from counter-propagating light, captured into a three-dimensional magneto-optical trap (3D MOT), and then transferred to a conservative trap, typically an optical dipole trap (ODT). A variety of diatomic molecules have been slowed 13,[18][19][20] and loaded into 3D MOTs. 21,22,24,25,29,[31][32][33][34] The molecular temperature has been reduced to a few µK after sub-Doppler cooling. ...
A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.
... After the realization of transverse laser cooling, two dimensional MOT was demonstrated with YO molecules [35]. A MOT requires a magnetic field whose magnitudes are proportional to the distance from the origin and a pair of counter-propagating lasers with opposite circular polarizations to make space-dependent forces on the molecules. ...
... Authors of Ref. [35] demonstrated two-dimensional magneto-optical force along the beam of YO molecules. The initial transverse temperature of the molecular beam was set to 25 mK by collimating apertures. ...
A recent progress on laser cooling of molecules is summarized. Since the development during the 1980s for atomic species, laser cooling has been the very beginning step to cool and trap atoms for frontier research on quantum simulations, quantum sensing and precision measurements. Despite the complex internal structures of molecules, laser cooling of molecules have been realized with the deepened understanding of molecular structures and interaction between light and molecules. The development of laser technology over the last decades has also been a great aid for the laser cooling of molecules because many lasers are necessary to successfully cool the molecules. A detailed principle and development of laser cooling of molecules as well as the current status of the field are reviewed to give an introduction to the growing field of ultracold molecular physics.
... After the realization of transverse laser cooling, two dimensional MOT was demonstrated with YO molecules [32]. A MOT requires a magnetic field whose magnitudes are proportional to the distance from the origin and a pair of counter-propagating lasers with opposite circular polarizations to make space-dependent forces on the molecules. ...
... Authors of Ref. [32] demonstrated two dimensional magneto-optical force along the beam of YO molecules. The initial transverse temperature of the molecular beam was set to 25 mK by collimating apertures. ...
A recent progress on laser cooling of molecules are summarized. Since the development during 1980s for atomic species, laser cooling has been the very beginning step to cool and trap atoms for frontier research on quantum simulations, quantum sensing and precision measurements. Despite the complex internal structures of molecules, laser cooling of molecules have been realized with the deepened understanding of molecular structures and interaction between light and molecules. The development of laser technology over the last decades have been also a great add for laser cooling of molecules because many lasers are necessary to successfully cool the molecules. A detailed principle and development of laser cooling of molecules as well as the current status of the field are reviewed to give an introductory of the growing field of ultracold molecular physics.
... A radically different approach for creating intense beams of molecules and molecular radicals is the so-called cryogenic buffer gas beam source, first introduced by Maxwell et al [11] and further developed by Patterson and Doyle [12], van Buuren et al [13], Barry et al [14], Hutzler et al [15,16] and others. In this method, molecules are introduced into a cold cell by a capillary [11-13, 17, 18], by laser ablation of a target containing a precursor [11,12,14,15,[19][20][21][22][23][24][25][26][27][28][29][30] or by letting laser ablated atoms react with a donor gas [31][32][33][34]. The hot molecules are cooled by collisions with cold helium or neon buffer gas. ...
Recently, we have demonstrated a method to record the longitudinal phase-space distribution of a pulsed cryogenic buffer gas cooled beam of barium fluoride molecules with high resolution. In this paper, we use this method to determine the influence of various source parameters. Besides the expected dependence on temperature and pressure, the forward velocity of the molecules is strongly correlated with the time they exit the cell, revealing the dynamics of the gas inside the cell. Three observations are particularly noteworthy: (1) The velocity of the barium fluoride molecules increases rapidly as a function of time, reaches a maximum 50–200 µs after the ablation pulse and then decreases exponentially. We attribute this to the buffer gas being heated up by the plume of hot atoms released from the target by the ablation pulse and subsequently being cooled down via conduction to the cell walls. (2) The time constant associated with the exponentially decreasing temperature increases when the source is used for a longer period of time, which we attribute to the formation of a layer of isolating dust on the walls of the cell. By thoroughly cleaning the cell, the time constant is reset to its initial value. (3) The velocity of the molecules at the trailing end of the molecular pulse depends on the length of the cell. For short cells, the velocity is significantly higher than expected from the sudden freeze model. We attribute this to the target remaining warm over the duration of the molecular pulse giving rise to a temperature gradient within the cell. Our observations will help to optimize the source parameters for producing the most intense molecular beam at the target velocity.
... In 2004, Di Rosa [10] proposed three conditions that diatomic candidates for laser cooling need to satisfy: (1) short radiative lifetimes for the upper states, (2) highly diagonal Frank-Condon factors (FCFs), and (3) no interference from intermediate states. Since the SrF molecule was experimentally cooled to the μK level using three lasers by Shuman et al [11] in 2010, YO [12], CaF [13], YbF [14], CaH [15], and BaH [16] molecules have also been successively cooled. Especially, the direct laser cooling of the BaH [16] molecule indicates the feasibility of laser cooling and trapping heavy molecules with relatively long-lived excited electronic states, despite previously unexplored this technical challenge. ...
The highly diagonal Frank-Condon factors (FCFs) are necessary for the laser cooling scheme, which means that only the molecules with the appropriate ground and excited electronic states can become candidates. Here, the laser cooling feasibility of the PbX (X = F, Cl, Br, and I) molecules is explored through four-component relativistic calculations. The potential energy curves and transition dipole moments of five Ω states are calculated and used to solve the Schrödinger equation of nuclear motion to obtain the rovibrational energy levels, spectroscopic parameters, the Einstein coefficients, and FCFs. Using the X12Π1/2 ↔ X22Π3/2 transition with highly diagonal FCFs, we construct optical schemes that can provide 104 ~ 105 scattering phonons with four pumping lasers for PbX. The Doppler/recoil temperatures of PbX are 419.05 / 57.55, 9.63 / 61.20, 4.95 / 49.98, and 0.71 / 40.17 nK, respectively. Since the 10-4 s of the long spontaneous emission lifetime, the temperatures below microkelvin orders of magnitude can be achieved only if the adequate pre-cooling temperature is satisfied.
... 近十几年来, 利用激光冷 却分子的实验研究进展迅速. 2010年, Shuman等 [12] 首次使用三束激光冷却了双原子分子SrF, 证实了 激光冷却分子的可行性; 2013年, Hummon等 [13] 实现了YO分子束的激光冷却; 同年, Zhelyazkova 先前对可冷却候选体系的理论研究主要集中 在线性双原子分子, 如碱土金属氢、卤化物AlBr [15] , BaF [16] , AlH, AlF [17] 等, 以及IVA, VA族氢化物 等 [18,19] . 2019年, Ivanov等 [20] 首先利用运动方程耦 2020年, Augenbraun等 [ 本文通过EA-EOM-CCSD方法 [29] , 结合cc- ...
The CaSH molecule is an important target in the field of laser cooling non-linear polyatomic molecules. Successful cooling of such molecules marks a breakthrough of the technical limitations of laser cooling diatomic and linear triatomic molecules. To identify the possible optical cycle in cooling CaSH, precise geometries of the CaSH ground state and the three lowest excited states, along with their excitation energy, are determined by utilizing the EA-EOM-CCSD (electron attachment equation-of-motion coupled cluster singles and doubles) method, in combination with energy extrapolation using cc-pVXZ /cc-pCVXZ( X = T, Q ) serial basis sets. Geometric parameters of the ground state \begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}{'} $\end{document} are found to be RCaS= 2.564 Å, RSH= 1.357 Å, and∠CaSH= 91.0°. Additionally, the equilibrium geometries of three excited states are also obtained. The \begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{'}}{{'}}} $\end{document} state has a similar equilibrium structure to the ground state, while the \begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}{'} $\end{document}and \begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}{'} $\end{document}states exhibit significant conformer distortions. Specifically, the CaS bond of the \begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}{'} $\end{document} state and \begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}{'} $\end{document} state tend to contract, and the CaSH angel bends by 5° relative to the ground state. The vertical excitation energy from the ground state to \begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}{'} $\end{document}, \begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{'}}{{'}}} $\end{document} and \begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}{'} $\end{document} are of 1.898, 1.945 and 1.966 eV, respectively, which are in good agreement with the previous experimental results. Moreover, the potential energy surfaces of the four lowest electronic states of CaSH are calculated by EA-EOM-CCSD with 3ζ level of basis sets. The nuclear equations of motion are solved to obtain the vibrational frequencies of the CaS bond stretching and CaSH bending. The vibrational frequencies of the (0,1,0) mode and the CaS stretching frequency of four states are 316 cm–1, 315 cm–1, 331 cm–1 and 325 cm–1, which are in close agreement with the available experimental results. The frequencies of the CaSH bending mode are presented for the first time, with the values of 357 cm–1, 396 cm–1, 384 cm–1, 411 cm–1 for the \begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}{'} $\end{document}, \begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}{'} $\end{document}, \begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{'}}{{'}}} $\end{document} and \begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}{'} $\end{document}states, respectively. Theoretical calculations give the Frank-Condon factors of 0.9268, 0.9958 and 0.9248 for the \begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}{'}({\mathrm{0,0}},0) $\end{document} to \begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}{'}({\mathrm{0,0}},0) $\end{document}, \begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{'}}{{'}}}({\mathrm{0,0}},0) $\end{document} and \begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}{'}({\mathrm{0,0}},0) $\end{document} transitions. All three excited states are the bright states with considerable oscillator strength relative to the ground state. Based on the Frank-Condon factor and lifetime of excited states, the \begin{document}$ {{\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}{'}({\mathrm{0,0}},0)\to \tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{'}}{{'}}}({\mathrm{0,0}},0) $\end{document} transition is regarded as the main cooling cycle for the CaSH molecule. The corresponding pump light wavelength is 678 nm. By exciting the vibrational excited states (0,1,0) and (0,0,1) of the \begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}{'} $\end{document} state to \begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}{'}({\mathrm{0,0}},0) $\end{document} using lasers at 664 nm and 668 nm, respectively, the optical cooling branch ratio of CaSH is expected to exceed 0.9998.
... In recent years, cold and ultracold molecules [1] have received considerable attention owing to successful demonstrations of cooling and trapping of molecules [2] and their importance in high-resolution spectroscopy [3]. Due to the characteristics of long-range ion-atom potential, ion-neutral collisions [4][5][6] are different from neutral-neutral and ion-ion collisions. ...
In this paper, we extensively study the electronic structure, interactions, and dynamics of the (MgCs)+ molecular ion. The exchanges between the alkaline atom and the low-energy cationic alkaline earths, which are important in the field of cold and ultracold quantum chemistry, are studied. We use an ab initio approach based on the formalism of non-empirical pseudo-potential for Mg2+ and Cs+ cores, large Gaussian basis sets, and full-valence configuration interaction. In this context, the (MgCs)+ cation is treated as an effective two-electron system. Adiabatic potential energy curves and their spectroscopic constants for the ground and the first 20 excited states of 1,3Σ+ symmetries are determined. Furthermore, we identify the avoided crossings between the electronic states of 1,3Σ+ symmetries. These crossings are related to the charge transfer process between the two ionic limits, Mg/Cs+ and Mg+/Cs. Therefore, vibrational-level spacings and the transition and permanent dipole moments are presented and analyzed. Using the produced potential energy data, the ground-state scattering wave functions and elastic cross-sections are calculated for a wide range of energies. In addition, we predict the formation of a translationally and rotationally cold molecular ion (MgCs)+ in the ground-state electronic potential energy through a stimulated Raman-type process aided by ion–atom cold collision. In the low-energy limit (<1 mK), elastic scattering cross-sections exhibit Wigner law threshold behavior, while in the high-energy limit, the cross-sections act as a function of energy E go as E−1/3. A qualitative discussion about the possibilities of forming cold (MgCs)+ molecular ions by photoassociative spectroscopy is presented.
... The rotational constants, combined with ab initio corrections for zero-point and electronic effects, allow precise semiexperimental equilibrium structures to be derived. The well-resolved 1,2 H, 13 C, 25 Mg, and 87 Sr magnetic hyperfine structure has also been analyzed, providing detailed information on the ground-state electronic structure for these three systems, in particular the distribution of the unpaired electron used for optical cycling. By examining trends in structure, bonding, and hybridization down Group IIA of the Periodic Table, we show that the CCH ligand in the three examined cases is largely insensitive to the identity of the metal, as shown by both the equilibrium geometries and by the unpaired electron distribution, which is highly localized around the metal. ...
The unique optical cycling efficiency of alkaline earth metal-ligand molecules has enabled significant advances in polyatomic laser cooling and trapping. Rotational spectroscopy is an ideal tool for probing the molecular properties that underpin optical cycling, thereby elucidating the design principles for expanding the chemical diversity and scope of these platforms for quantum science. We present a comprehensive study of the structure and electronic properties in alkaline earth metal acetylides with high-resolution microwave spectra of 17 isotopologues of MgCCH, CaCCH, and SrCCH in their 2Σ+ ground electronic states. The precise semiexperimental equilibrium geometry of each species has been derived by correcting the measured rotational constants for electronic and zero-point vibrational contributions calculated with high-level quantum chemistry methods. The well-resolved hyperfine structure associated with the 1,2H, 13C, and metal nuclear spins provides further information on the distribution and hybridization of the metal-centered, optically active unpaired electron. Together, these measurements allow us to correlate trends in chemical bonding and structure with the electronic properties that promote efficient optical cycling essential to next-generation experiments in precision measurement and quantum control of complex polyatomic molecules.
... For example, stable degenerate molecular gases can be used to simulate strongly interacting lattice spin models, providing a promising platform for the study of anyonic excitations [10]. Even though degenerate atomic Bose and Fermi gases are now being produced routinely, the experimental realization of degenerate molecular gases had been, despite impressive progress by many groups [11][12][13][14][15][16][17][18][19][20][21][22][23], up until 2019 [24] hampered detrimentally by losses. The experimentally measured loss-rate coefficients were found to increase linearly with the temperature, in nice agreement with predictions derived from two-body physics, i.e., the Bethe-Wigner threshold law [25][26][27][28] and multi-channel quantum defect theory [29,30]. ...
Motivated by the experimental realization of single-component degenerate Fermi gases of polar ground state KRb molecules with intrinsic two-body losses [L. De Marco, G. Valtolina, K. Matsuda, W. G. Tobias, J. P. Covey, and J. Ye, A degenerate Fermi gas of polar molecules, Science 363, 853 (2019)], this work studies the finite-temperature loss rate of single-component Fermi gases with weak interactions. First, we establish a relationship between the two-body loss rate and the $p$-wave contact. Second, we evaluate the contact of the homogeneous system in the low-temperature regime using $p$-wave Fermi liquid theory and in the high-temperature regime using the second-order virial expansion. Third, conjecturing that there are no phase transitions between the two temperature regimes, we smoothly interpolate the results to intermediate temperatures. It is found that the contact is constant at temperatures close to zero and increases first quadratically with increasing temperature and finally -- in agreement with the Bethe-Wigner threshold law -- linearly at high temperatures. Fourth, applying the local-density approximation, we obtain the loss-rate coefficient for the harmonically trapped system, reproducing the experimental KRb loss measurements within a unified theoretical framework over a wide temperature regime without fitting parameters. Our results for the contact are not only applicable to molecular $p$-wave gases but also to atomic single-component Fermi gases, such as 40K and 6Li.
... Compared with atoms, diatomic molecules have a sophisticated energy level structure that on one side can directly bring more challenges to the manipulation and control of them, such as laser cooling and magneto-optical trapping, and on the other side exhibit enhanced sensitivity in precision measurement such as the searches for fundamental symmetry violations, as well as broadening the horizon of molecular reaction dynamics of cold molecules and their astrophysical relevance. 1−9 As early as 2004, Di Rosa presented a brief survey of candidate molecules for laser cooling and magneto-optical trapping, 10 after which polar heavy-atom molecules SrF, 11,12 CaF, 13,14 and YO 15,16 have already been successfully demonstrated in direct laser cooling techniques and magneto-optical traps (MOTs). DeMille and his co-workers first demonstrated the optical cooling cycle for SrF in the A 2 Π 1/2 ← X 2 Σ + transition 17 and further realized its transverse cooling in a substantial flux at velocities <50 m/s, 11,18 prior to its capture in the threedimensional (3D) MOT at temperatures of 2.5 mK, 250 μK, and 14 μK, respectively. ...
Alkaline-earth-metal monohydrides MH (M = Be, Mg, Ca, Sr, Ba) have long been regarded as promising candidates toward laser cooling and trapping; however, their rich internal level structures that are amenable to magneto-optical trapping have not been completely explored. Here, we first systematically evaluated Franck-Condon factors of these alkaline-earth-metal monohydrides in the A2Π1/2 ← X2Σ+ transition, exploiting three respective methods (the Morse potential, the closed-form approximation, and the Rydberg-Klein-Rees method). The effective Hamiltonian matrix was introduced for MgH, CaH, SrH, and BaH individually in order to figure out their molecular hyperfine structures of X2Σ+, the transition wavelengths in the vacuum, and hyperfine branching ratios of A2Π1/2(J' = 1/2,+) ← X2Σ+(N = 1,-), followed by possible sideband modulation proposals to address all hyperfine manifolds. Lastly, the Zeeman energy level structures and associated magnetic g factors of the ground state X2Σ+(N = 1,-) were also presented. Our theoretical results here not only shed more light on the molecular spectroscopy of alkaline-earth-metal monohydrides toward laser cooling and magneto-optical trapping but also can contribute to research in molecular collisions involving few-atom molecular systems, spectral analysis in astrophysics and astrochemistry, and even precision measurement of fundamental constants such as the quest for nonzero detection of electron's electric dipole moment.
... The best understood examples exhibiting favorable vibrational properties are alkaline earth monofluorides (SrF [75], CaF [76,77]) and oxides like YO [78,79]. The calculated valence electron distribution of the CaF ground state is shown in Fig. 2a. ...
An increasingly large variety of molecular species are being cooled down to low energies in recent years, and innovative ideas and powerful techniques continue to emerge to gain ever more precise control of molecular motion. In this brief review we focus our discussions on two widely employed cooling techniques that have brought molecular gases into the quantum regime: association of ultracold atomic gases into quantum gases of molecules and direct laser cooling of molecules. These advances have brought into reality our capability to prepare and manipulate both internal and external states of molecules quantum mechanically, opening the field of cold molecules to a wide range of scientific explorations.
... According to the atom trapping principle, MOTs can be classified into dark magnetic traps [33], spin-polarized magnetic traps [34], pyramidal MOTs [35,36], conical and axialconical MOTs [37,38] and so on. According to the structure of MOTs, they are mainly divided into two-dimensional MOTs [39][40][41][42][43] and three-dimensional MOTs [44]. ...
The cold atomic gravimeter (CAG) has the advantage of high measurement accuracy and does not need to be calibrated on a regular basis. To achieve cold atom interference, it is first necessary to cool and trap the atoms by magneto-optical trap (MOT). However, there are many types of MOTs, and their trapping and cooling results directly affect the atomic interference, and thus, the measurement accuracy of a CAG. MOTs should be designed or selected correctly for different application needs. This paper reviews the research history of MOTs and analyzes their structure and principles. The current status of applications of different types of MOTs is highlighted. Their advantages and disadvantages are summarized, and perspectives for the development of MOTs for cold atomic gravimetry are presented.
... This effect is illustrated in figure 1(c) for F = 1 → F ′ = 1, for a case where g F > 0 and g F ′ = 0. Here, molecules absorb preferentially from the restoring laser in either m = ±1, while they are equally likely to absorb from either direction for m = 0; thus, on average, a restoring force is felt by the molecule. The second technique is called the radio-frequency MOT (rfMOT) [2,51,52]. Here, the polarization and magnetic field orientation are switched synchronously at a rate comparable to the photon scattering rate (typically ω rf ∼ Γ/5), such that, after molecules have fallen into an optically dark Zeeman state for a given field and polarization, the field and polarization orientations both reverse, allowing for continuous scatter primarily from the restoring laser ( figure 1(d)). ...
Recent experiments have demonstrated direct cooling and trapping of diatomic and triatomic molecules in magneto-optical traps (MOTs). However, even the best molecular MOTs to date still have density 10 ⁻⁵ times smaller than in typical atomic MOTs. The main limiting factors are: (i) inefficiencies in slowing molecules to velocities low enough to be captured by the MOT, (ii) low MOT capture velocities, and (iii) limits on density within the MOT resulting from sub-Doppler heating [J. A. Devlin and M. R. Tarbutt, Phys. Rev. A 90 , 063415 (2018)]. All of these are consequences of the need to drive `Type-II' optical cycling transitions, where dark states appear in Zeeman sublevels, in order to avoid rotational branching. We present simulations demonstrating ways to mitigate each of these limitations. This should pave the way towards loading molecules into conservative traps with sufficiently high density and number to evaporatively cool them to quantum degeneracy.
... The most immediate application is to reveal the properties of the molecules [60,61,62]. Other examples includes laser cooling experiments [63,64], astronomical observations [65], and, of course, nuclear magnetic resonance which has many applications including ones in medicine. ...
The thesis presents methods for the variational calculation of fine and hyperfine resolved rovibronic spectra of diatomic molecules, as part of the ExoMol and ExoMolHD projects. The theory of these methods has been fully discussed. The corresponding algorithms have been implemented based on previous works of the ExoMol Group. The line lists of two molecules, NO and VO has been calculated, which validates the proposed methods. Nitric oxide is one of the principal oxides of nitrogen, which plays a significant role the investigations of our atmosphere and astrophysics. Due to its importance, the radical has been investigated in numerous theoretical and experimental works. However, there is no NO ultraviolet line list in well-known databases. A major issue in generating a UV line list for NO results from the difficulty of modelling the valence-Rydberg interaction between its B2Π and C2Π states. To address the problem, a spectroscopic model has been proposed to resolve the energy structures of B2Π and C2Π coupled states. Based on the model, an accurate line list, called XABC, has been computed, which covers the pure rotational, vibrational and rovibronic spectra of 14N16O. Vanadium monoxide is also an open shell diatomic system. Its dominating isotopologue 51V16O has non-zero nuclear spin, I = 7/2. The interaction between the spin of unpaired electrons and the nuclear spin yields a very pronounced hyperfine structure. The widely used effective Hamiltonian method for hyperfine structure is not applicable to give accurate line list of VO, as the interactions between the electronic states of VO reshape its line positions and intensities. This thesis presents a variational algorithm for the calculation of hyperfine structure and spectra of diatomic molecules. The hyperfine-resolved IR spectra of VO has been computed from first principles, considering necessary nuclear hyperfine coupling curves.
... In recent years, coherently associated bialkali molecules, KRb and NaK, have been cooled to quantum degeneracy [7][8][9], leading to the observation of dipolar-mediated spin many-body dynamics [10]. Direct laser cooling of diatomic molecules [11][12][13][14][15], in the past decade, has given an impetus to the goal of making a quantum gas of laser cooled molecules that allows for a much broader range of molecules to be used for scientific applications. Important advances include demonstrating magneto-optical trapping (MOT) [16][17][18][19][20] and cooling to sub-Doppler temperatures [20][21][22][23] for several directly cooled molecular species. ...
Direct laser cooling of molecules has reached a phase space density exceeding 10$^{-6}$ in optical traps, but with rather small molecular numbers. To progress towards quantum degeneracy, a mechanism is needed that combines sub-Doppler cooling and magneto-optical trapping (MOT) to facilitate near unity transfer of ultracold molecules from the MOT to a conservative optical trap. Using the unique energy level structure of YO molecules, we demonstrate the first blue-detuned MOT for molecules that is optimized for both gray-molasses sub-Doppler cooling and relatively strong trapping forces. This first sub-Doppler molecular MOT provides an increase of phase-space density by two orders of magnitude over any previously reported molecular MOT.
... O ptical cycling transitions in atoms allow laser cooling of the center-of-mass motion, laser state preparation, and laser-induced fluorescence (LIF) state detection�openchannel operations at the heart of many promising applications of quantum technology, including quantum computation, 1,2 atomic clocks, 3,4 and quantum simulation. 5,6 Optical cycling and cooling schemes have also been demonstrated in diatomic 7,8 and even some small polyatomic molecules, 9,10 including SrF, 11 YO,12 CaF, 13,14 YbF, 15 BaF, 16,17 MgF, 18 AlF, 19 SrOH, 20 CaOH, 21,22 YbOH, 23 and CaOCH 3 . 24 Because they possess rich internal structures and complex interactions, molecules provide new opportunities in studies of dark matter detection, 25,26 measurement of electron's electric-dipole moment, 27−29 parity violation tests, 30,31 and changes to fundamental constants. ...
We report the production and spectroscopic characterization of strontium(I) phenoxide (SrOC6H5 or SrOPh) and variants featuring electron-withdrawing groups designed to suppress vibrational excitation during spontaneous emission from the electronically excited state. Optical cycling closure of these species, which is the decoupling of the vibrational state changes from spontaneous optical decay, is found by dispersed laser-induced fluorescence spectroscopy to be high, in accordance with theoretical predictions. A high-resolution, rotationally resolved laser excitation spectrum is recorded for SrOPh, allowing the estimation of spectroscopic constants and identification of candidate optical cycling transitions for future work. The results confirm the promise of strontium phenoxides for laser cooling and quantum state detection at the single-molecule level.
... Even worse, however, molecular MOTs thus far all Towards improved loading, cooling, and trapping of molecules in magneto-optical traps5 are equally likely to absorb from either direction for m = 0; thus, on balance, a restoring force is felt by the molecule. The second technique is called the radio-frequency MOT (rfMOT) [47,48,2]. Here, the polarization and magnetic field orientation are switched synchronously at a rate comparable to the photon scattering rate (typically ω rf ∼ Γ/5), such that, after molecules have fallen into an optically dark Zeeman state for a given field and polarization, the field and polarization reverse, allowing for continuous scatter primarily from the restoring laser ( Fig. 1(d)). ...
Recent experiments have demonstrated direct cooling and trapping of diatomic and triatomic molecules in magneto-optical traps (MOTs). However, even the best molecular MOTs to date still have density $10^{-5}$ times smaller than in typical atomic MOTs. The main limiting factors are: (i) inefficiencies in slowing molecules to velocities low enough to be captured by the MOT, (ii) low MOT capture velocities, and (iii) limits on density within the MOT resulting from sub-Doppler heating~[J. A. Devlin and M. R. Tarbutt, Phys. Rev. A \textbf{90}, 063415 (2018)]. All of these are consequences of the need to drive `Type-II' optical cycling transitions, where dark states appear in Zeeman sublevels, in order to avoid rotational branching. We present simulations demonstrating ways to mitigate each of these limitations. This should pave the way towards loading molecules into conservative traps with sufficiently high density and number to evaporatively cool them to quantum degeneracy.
... Optical cycling transitions in atoms allow laser cooling of the center-of-mass motion, laser state preparation, and laser-induced fluorescence (LIF) state detection -openchannel operations at the heart of many promising applications of quantum technology, including quantum computation [1,2], atomic clocks [3,4], and quantum simulation [5,6]. Optical cycling and cooling schemes have also been demonstrated in diatomic [7,8] and even some small polyatomic molecules [9,10], including SrF [11], YO [12], CaF [13,14], YbF [15], BaF [16,17], MgF [18], AlF [19], SrOH [20], CaOH [21], YbOH [22] and CaOCH 3 [23]. Because they possess rich internal structures and complex interactions, molecules provide new opportunities in studies of dark matter detection [24,25], measurement of electron's electric-dipole moment [26][27][28], parity violation tests [29,30], and changes to fundamental constants [31,32]. ...
We report the production and spectroscopic characterization of strontium (I) phenoxide ($\mathrm{SrOC}_6\mathrm{H}_5$, or SrOPh) and variants featuring electron-withdrawing groups designed to suppress vibrational excitation during spontaneous emission from the electronically excited state. Optical cycling closure of these species, which is the decoupling of vibrational state changes from spontaneous optical decay, is found by dispersed laser-induced fluorescence spectroscopy to be high, in accordance with theoretical predictions. A high-resolution, rotationally-resolved laser excitation spectrum is recorded for SrOPh, allowing the estimation of spectroscopic constants and identification of candidate optical cycling transitions for future work. The results confirm the promise of strontium phenoxides for laser cooling and quantum state detection at the single-molecule level.
... [1][2][3][4][5][6][7][8][9] Using trapped-ion hardware and theory from atomic physics, small molecules have been laser cooled and shown to exhibit these properties. [10][11][12][13][14] The success of these molecules relies on high Franck-Condon factors (FCFs), which in many cases is quite close to the vibrational branching ratios in these species. [15] In the past, trapping and laser cooling molecules larger than a few atoms seemed formidable due to an increase in the number of vibrational modes, therefore a likely increase in vibrational branching. ...
Designing closed, laser-induced optical cycling transitions in trapped atoms or molecules is useful for quantum information processing, precision measurement, and quantum sensing. Larger molecules that feature such closed transitions are particularly desirable, as they extend the scope of applicability of such systems. The search for molecules with robust optically cycling centers has been a challenge, and requires design principles beyond trial-and-error. Here, two design principles are proposed for the particular architecture of M-O-R, where M is an alkaline earth metal radical, and R is a ligand: 1) Fairly large saturated hydrocarbons can serve as ligands, R, due to a substantial HOMO-LUMO gap that encloses the cycling transition, so long as the R group is rigid. 2) Electron-withdrawing groups, via induction, can enhance Franck-Condon factors (FCFs) of the optical cycling transition, as long as they do not disturb the locally linear structure in the M-O-R motif. With these tools in mind, larger molecules can be trapped and used as optical cycling centers, sometimes with higher FCFs than smaller molecules.
... In order to reach the ground state, however, it is often necessary to use a sideband cooling technique after initial Doppler cooling [2,3]. Laser cooling techniques have now been applied to a wide variety of systems, including atoms and ions [4][5][6], complex molecules [7][8][9][10] and mechanical oscillators [11,12]. While laser cooling can be very successful for some systems, there exist many systems of interest for which direct application of laser cooling is either impractical or impossible, particularly if the intention is to cool the motion to the ground state. ...
Measurement-based cooling is a method by which a quantum system, initially in a thermal state, can be prepared in its ground state through some sort of measurement. This is done by making a measurement that heralds the system being in the desired state. Here we demonstrate the application of a measurement-based cooling technique to a trapped atomic ion. The ion is pre-cooled by Doppler laser cooling to a thermal state with a mean excitation of $\bar n \approx 18$ and the measurement-based cooling technique selects those occasions when the ion happens to be in the motional ground state. The fidelity of the heralding process is greater than 95%. This technique can be applied to other systems that are not as amenable to laser cooling as trapped ions.
... By using high-level ab initio calculations, we investigated series of diatomic radical cations designed to create a localized electronic transition suitable for optical cycling. The results demonstrate that the localized electronic excitation picture exploited in OCCs in neutral molecules 38,40,41,[60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75] to some extent holds for isoelectronic cations formed by transitionmetal atoms. This result applies to molecular cations that either contain a transition metal atom or have multiple bonds, which is different from the behavior of other cations 1 . ...
Molecules with optical cycling centers (OCCs) are highly desirable in the context of fundamental studies as well as applications (e.g., quantum computing) because they can be effectively cooled to very low temperatures by repeated absorption and emission (hence, cycling). Charged species offer additional advantages for experimental control and manipulation. We present a systematic computational study of a series of diatomic radical-cations made of a d-block metal and a p-block ligand, that are isoelectronic (in their valence shell) to the successfully laser-cooled neutral molecules. Using high-level electronic structure methods, we characterize state and transition properties of low-lying electronic states and compute Franck-Condon factors. The computed branching ratios and radiative lifetimes reveal that the electronic transitions analogous to those successfully used in the laser cooling of neutral molecules are less than optimal in the cations. We propose alternative transitions suitable for optical cycling and highlight trends that could assist future designs of OCCs in charged or neutral molecules.
... Magnetic dark states that occur in these 'type II' transitions are remixed by rapidly switching laser polarizations between σ + and σ − with a Pockels cell at 1.0 MHz. Trapping is maintained by modulating the current through the anti-Helmholtz MOT coils in phase with the polarization switching 11,12,32,52,53 . Each of the six MOT beams has a 1/e 2 Gaussian diameter of 10 mm (truncated at a diameter of 19 mm by in-vacuum baffles), and the laser power in each beam is equally balanced between the N J p X( ″= 1, ″ = 3/2, ″= −) ∼ and ∼ N J p X( ″= 1, ″ = 1/2, ″= −) components. ...
Laser cooling and trapping1,2, and magneto-optical trapping methods in particular2, have enabled groundbreaking advances in science, including Bose–Einstein condensation3–5, quantum computation with neutral atoms6,7 and high-precision optical clocks8. Recently, magneto-optical traps (MOTs) of diatomic molecules have been demonstrated9–12, providing access to research in quantum simulation13 and searches for physics beyond the standard model14. Compared with diatomic molecules, polyatomic molecules have distinct rotational and vibrational degrees of freedom that promise a variety of transformational possibilities. For example, ultracold polyatomic molecules would be uniquely suited to applications in quantum computation and simulation15–17, ultracold collisions18, quantum chemistry19 and beyond-the-standard-model searches20,21. However, the complexity of these molecules has so far precluded the realization of MOTs for polyatomic species. Here we demonstrate magneto-optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). After trapping, the molecules are laser cooled in a blue-detuned optical molasses to a temperature of 110 μK, which is below the Doppler cooling limit. The temperatures and densities achieved here make CaOH a viable candidate for a wide variety of quantum science applications, including quantum simulation and computation using optical tweezer arrays15,17,22,23. This work also suggests that laser cooling and magneto-optical trapping of many other polyatomic species24–27 will be both feasible and practical. The polyatomic molecule calcium monohydroxide is magneto-optically trapped and cooled below the Doppler cooling limit, making it a candidate for applications in quantum simulation and computation.
... Although keenly anticipated almost three decades ago [1,2], the heyday of optical trapping of molecules arrived only recently along with the techniques to laser-cool molecular translation down to the ultracold regime (less than or equal to 1 mK) (see Refs. [3][4][5][6][7][8][9][10][11][12][13][14][15] as well as recent reviews in [16][17][18]). However, optical traps had been loaded as early as 1998 with ultracold molecules produced by dimer formation from ultracold atoms in a magneto-optical trap [19] and in the 2000s by magnetoassociation [20][21][22] or by photoassociation [23,24] of ultracold atoms. ...
A detailed treatment of an electro-optical trap for polar molecules, realized by embedding an optical trap within a uniform electrostatic field, is presented and the trap's properties analyzed and discussed. The electro-optical trap offers significant advantages over an optical trap that include an increased trap depth and conversion of alignment of the trapped molecules to marked orientation. Tilting the polarization plane of the optical field with respect to the electrostatic field diminishes both the trap depth and orientation and lifts the degeneracy of the ±M states of the trapped molecules. These and other features of the electro-optical trap are examined in terms of the eigenproperties of the polar and polarizable molecules subject to the combined permanent and induced electric dipole interactions at play.
... By using high-level ab initio calculations, we investigated series of diatomic radical cations designed to create a localized electronic transition suitable for optical cycling. The results demonstrate that the localized electronic excitation picture exploited in OCCs in neutral molecules 38,40,41,[60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75] to some extent holds for isoelectronic cations formed by transitionmetal atoms. This result applies to molecular cations that either contain a transition metal atom or have multiple bonds, which is different from the behavior of other cations 1 . ...
Molecules with optical cycling centers (OCCs) are highly desirable in the context of fundamental studies as well as applications (e.g., quantum computing) because they can be effectively cooled to very low temperatures by repeated absorption and emission (hence, cycling). Charged species offer additional advantages for experimental control and manipulation. We present a systematic computational study of a series of diatomic radical-cations made of a d-block metal and a p-block ligand, that are isoelectronic (in their valence shell) to the successfully laser-cooled neutral molecules. Using high-level electronic structure methods, we characterize state and transition properties of low-lying electronic states and compute Franck-Condon factors. The computed branching ratios and radiative lifetimes reveal that the electronic transitions analogous to those successfully used in the laser cooling of neutral molecules are less than optimal in the cations. We propose alternative transitions suitable for optical cycling and highlight trends that could assist future designs of OCCs in charged or neutral molecules.
Transition dipole moments of Stark/Zeeman-hyperfine-rotational spectra of [Formula: see text] within the vibronic ground state of BrF molecule are deduced, and thus, the transition selection rules are summarized. Unlike the nearly equal linewidth in the other spectral region, the hyperfine-rotational spectral linewidth strongly depends on its transition probability due to the only natural broadening acts. Thereafter, the Stark/Zeeman-hyperfine-rotational spectra are simulated, which could help to assign the experimental spectra. In addition, the quadratic dependence of the Stark spectral shift on the applied electric field is fitted with the fitting correlation of 0.9999, which may be applied in the mapping of a complex electrostatic field. Our results are helpful for the investigations of the field-controlled cold molecular collision, the cold molecular manipulation, the cold molecular further cooling, and other related aspects as well.
Ab initio CASSCF/MRCI + Q calculations have been used to investigate the electronic structure and transition properties of the alkaline earth astatine molecules SrAt and BaAt. The adiabatic potential energy curves have been computed and plotted for the low-lying electronic states in the representations 2S+1Λ+/− and Ω(±) (with and without spin–orbit coupling effect). The spectroscopic and vibrational constants have been deduced for the corresponding bound states. An analysis of the Franck–Condon factors, the Einstein Coefficients, and the branching ratios among different vibrational levels has shown that both SrAt and BaAt molecules are suitable candidates for Doppler and Sysphus laser cooling. Experimental laser cooling schemes and conditions for these two molecules have been proposed. These results may pave the way for new spectroscopic and laser cooling experiments of alkaline earth astatine molecules.
High-level configuration interaction method including the spin-orbit coupling is performed to investigate the low-lying electronic states of AuB that is not reported by the experiment. The electronic structure in our work is preformed through the three steps stated below. First of all, Hartree-Fock method is performed to compute the singlet-configuration wavefunction as the initial guess. Next, we generate a multi-reference wavefunction by means of state-averaged complete active space self-consistent field (SACASSCF). The last, the wavefunctions from CASSCF are utilized as reference, the exact energy point values are calculated by the explicitly dynamic correlated multi-reference configuration interaction method (MRCI). The Davidson correction (+Q) is put forward to surmount the size-consistence problem caused by the MRCI method. The spin-orbit effect and correlation for inner shell and valence shell electrons are considered into our calculation to make a guarantee of accuracy. The potential energy curves of 12 Λ-S electronic states are obtained. Depended the explicit potential energy curves, we calculate the spectroscopic constants through solving radial Schrödinger equation numerically. We analysis the influence of electronic state configuration on the dipole moment with the help of the variation of dipole moment as the function of nuclear distance. The spin-orbit matrix elements for parts of low-lying states are computed, and the relation of spin-orbit coupling and predissociation are discussed. The predissociation is analyzed with the help of the obtained spin-orbit matrix elements of the 4 Λ-S states which spilt into 12 Ω states. It indicates that due to absence of the intersections between the curves of spin-orbit matrix elements related with the 4 low-lying Λ-S states, the predissociation for these low-lying states will not occur. Finally, the properties of optical transition between the ground Ω state A¹∏1 and first excited Ω state X¹∑0⁺ are discussed in laser-cooling filed by analyzing the Franck-Condon factors and radiative lifetime. And the transition dipole moment is also calculated. But our results reveal that the AuB is not an ideal candidate for laser-cooling. In conclusion, this work is helpful to deepen the understanding of AuB, especially in structures of electronic states, interaction between excited states and optical transition properties.
The majority of molecules proposed for laser cooling and trapping experiments have Σ-type ground states. Specifically, 2Σ states have cycling transitions analogous to D1 lines in alkali-metal atoms while 1Σ states offer both strong and weak cycling transitions analogous to those in alkaline-earth atoms. Despite this proposed variety, to date, only molecules with 2Σ-type ground states have successfully been confined and cooled in magneto-optical traps. While none of the proposed 1Σ-type molecules have been successfully laser cooled and trapped, they are expected to have various advantages in terms of exhibiting a lower chemical reactivity and an internal structure that benefits the cooling schemes. Here, we present the prospects and strategies for optical cycling in AlCl—a 1Σ molecule—and report on the characterization of the A1Π state hyperfine structure. Based on these results, we carry out detailed simulations on the expected capture velocity of a magneto-optical trap for AlCl. Finally, using ab initio calculations, we identify the photodissociation via a 31Π state and photoionization process via the 31Σ+ state as possible loss mechanisms for a magneto-optical trap of AlCl.
The possible laser cooling of AuAl molecules was investigated using high‐level ab initio calculations and considering the spin‐orbit coupling effect. Multi‐reference configuration interaction and the Davidson correction were also employed. Six Λ‐S electronic states were obtained, which were divided into 14 Ω states via spin‐orbit coupling. The optical transition showed potential for laser‐cooling applications owing to its highly diagonal Franck‐Condon factors and larger vibrational branching ratios. A possible optical cycling scheme using four lasers at near‐resonance wavelengths to eliminate vibrational branching loss is proposed. This scheme can be experimentally tested in future laser‐cooling experiments.
Motivated by the experimental realization of single-component degenerate Fermi gases of polar ground state KRb molecules with intrinsic two-body losses [L. De Marco et al., A degenerate Fermi gas of polar molecules, Science 363, 853 (2019).], this work studies the finite-temperature loss rate of single-component Fermi gases with weak interactions. First, we establish a relationship between the two-body loss rate and the p-wave contact. Second, we evaluate the contact of the homogeneous system in the low-temperature regime using p-wave Fermi liquid theory and in the high-temperature regime using the second-order virial expansion. Third, conjecturing that there are no phase transitions between the two temperature regimes, we smoothly interpolate the results to intermediate temperatures. It is found that the contact is constant at temperatures close to zero and increases first quadratically with increasing temperature and finally—in agreement with the Bethe-Wigner threshold law—linearly at high temperatures. Fourth, applying the local-density approximation, we obtain the loss-rate coefficient for the harmonically trapped system, reproducing the experimental KRb loss measurements within a unified theoretical framework over a wide temperature regime without fitting parameters. Our results for the contact are not only applicable to molecular p-wave gases but also to atomic single-component Fermi gases, such as K40 and Li6.
A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.
On the basis of correcting various errors (spin-orbit coupling effects, scalar relativity effects, core-valence correlation effects and basis set truncation), the potential energy curves of 10 Λ-S states and 26 Ω states of AlH molecule are calculated using icMRCI+Q method. The transition dipole moments of 6 pairs of transitions between the X¹∑⁺0⁺,a³Π0⁺,a³Π1a³Π2, and A¹Π1 states are calculated using the icMRCI/AV6Z* theory with the contain of spin-orbit coupling effects. The spectral and transition data obtained here for AlH molecule are in very good agreement with the available experimental measurements. We find that:(1) the transition intensities are relatively strong of the Q(J") branches for the (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4) and (1, 5) bands of the A¹Π1-X¹∑⁺0⁺ transition, with the increase of J", the Einstein A coefficients and vibrational branching ratios gradually decrease, and the weighted absorption oscillator strengths gradually increases of Δυ=0 bands, the Einstein A coefficients, vibrational branching ratios, and weighted absorption oscillator strengths gradually increase for the Δυ≠0 bands; (2) the radiation lifetimes of A¹Π1(υ'=0, 1) increases slowly as the J' increases. (3) The A¹Π1(υ'=0 and 1, J'=1, +)→X¹∑⁺0⁺(υ"=0-3, J"=1, -) transition of AlH molecule satisfies the criteria for laser cooling of diatomic molecules, that is, the vibrational branching ratios of the highly diagonal distribution, the extremely short radiation lifetimes of the A¹Π1(υ'=0 and 1, J'=1, +) states, and the intermediate electronic states a³Π0⁺, a³Π1, and a³Π2do not interfere with laser cooling. Therefore, based on the cyclic transition A¹Π1(υ'=0and 1, J'=1, +)↔X¹∑⁺0⁺(υ"=0-3, J''=1, -), we propose a feasible scheme for laser cooling of AlH molecule. When cooling, 2.541×10⁴ photons can be scattered using four pump lasers in the visible range, which are enough to cool AlH to the ultra-cold temperatures, and the Doppler and recoil temperatures of the main transition are in the order of μK.
Direct laser cooling of molecules has reached a phase-space density exceeding 10−6 in optical traps but with rather small molecular numbers. To progress toward quantum degeneracy, a mechanism that combines sub-Doppler cooling and magneto-optical trapping would facilitate near unity transfer of ultracold molecules from the magneto-optical trap (MOT) to a conservative optical trap. Using the unique energy level structure of YO molecules, we demonstrate the first blue-detuned MOT for molecules that is optimized for both gray-molasses sub-Doppler cooling and relatively strong trapping forces. This first sub-Doppler molecular MOT provides an increase of phase-space density by 2 orders of magnitude over any previously reported molecular MOT.
Measurement-based cooling is a method by which a quantum system, initially in a thermal state, can be prepared probabilistically in its ground state through some sort of measurement. This is done by making a measurement that heralds the system being in the desired state. Here we demonstrate the application of a measurement-based cooling technique to a trapped atomic ion. The ion is precooled by Doppler laser cooling to a thermal state with a mean excitation of n¯≈18 and the measurement-based cooling technique selects those occasions when the ion happens to be in the motional ground state. The fidelity of the heralding process is greater than 95%. This technique could be applied to other systems that are not as amenable to laser cooling as trapped ions.
Over the past decade, tremendous progress has been made to extend the tools of laser cooling and trapping to molecules. Those same tools have recently been applied to polyatomic molecules (molecules containing three or more atoms). In this review, we discuss the scientific drive to bring larger molecules to ultralow temperatures, the features of molecular structure that provide the most promising molecules for this pursuit, and some technical aspects of how lasers can be used to control the motion and quantum states of polyatomic molecules. We also present opportunities for and challenges to the use of polyatomic molecules for science and technology.
The transition dipole of the hyperfine-rotation spectra of J = 1←0 within the vibronic ground (X¹Σ, v = 0) state of BrF are derived, and thus, the transition selection rules are summarized as: ΔJ = ±1; ΔF1 = 0, ±1 and ΔF= 0, ±1, and those of ΔF1 = ΔF are intense while those of ΔF1 ≠ ΔF are weak. Some spectral lines are resulted from both the electric and nuclear magnetic dipole transitions due to perturbations, however, the magnetic only contributes about one-billionth in the spectral intensity. The spectral linewidth is determined to be about 18 kHz by calculating the spectral transition probability. The obtained spectral linewidth and relative intensities are consistent with the experimental results. Additionally, the hyperfine-rotation spectral positions are determined by diagonalizing the Hamiltonian matrix in the basis of |JI1F1I2F>, which is also in good agreement with the experiments within 10⁻⁸ (one-fiftieth of the spectral line width). Hence, the microwave hyperfine-rotation spectrum is simulated. In addition, we find that, the nuclear spin-spin interaction not only slightly shifts the hyperfine-rotation spectral positions but also changes the sequence of the spectra. As to those constants unavailable molecules, the fairly precise molecular constants can be achieved by quantum chemical calculation, say for example employing MOLPRO program, and then the simulated spectra can guide the spectral assignment. Besides the guidance of spectral assignment, our results are helpful for other applications related as well, for example, absolute single quantum state preparation.
Designing closed, laser-induced optical cycling transitions in trapped atoms or molecules is useful for quantum information processing, precision measurement, and quantum sensing. Larger molecules that feature such closed transitions are particularly desirable, as the increased degrees of freedom present new structures for optical control and enhanced measurements. The search for molecules with robust optical cycling centers is a challenge which requires design principles beyond trial-and-error. Two such principles are proposed for the particular M-O-R framework, where M is an alkaline earth metal radical, and R is a ligand: (1) Large, saturated hydrocarbons can serve as ligands, R, due to a substantial HOMO-LUMO gap that encloses the cycling transition, so long as the R group is rigid. (2) Electron-withdrawing groups, via induction, can enhance Franck-Condon factors (FCFs) of the optical cycling transition, as long as they do not disturb the locally linear structure in the M-O-R motif. With these tools in mind, larger molecules can be trapped and used as optical cycling centers, sometimes with higher FCFs than smaller molecules.
Cryogenic buffer gas beams are central to many cold molecule experiments. Here, we use absorption and fluorescence spectroscopy to directly compare molecular beams of AlF, CaF, MgF and YbF molecules, produced by chemical reaction of laser ablated atoms with fluorine rich reagents. The beam brightness for AlF is measured as 2×1012 molecules per steradian per pulse in a single rotational state, comparable to an Al atomic beam produced in the same setup. The CaF, MgF and YbF beams show an order of magnitude lower brightness than AlF and far below the brightness of Ca and Yb beams. The addition of either NF3 or SF6 to the cell extinguishes the Al atomic beam, but has a minimal effect on the Ca and Yb beams. NF3 reacts more efficiently than SF6, as a significantly lower flow rate is required to maximise the molecule production, which is particularly beneficial for long-term stability of the AlF beam. We use NO as a proxy for the reactant gas as it can be optically detected. We demonstrate that a cold, rotationally pure NO beam can be generated by laser desorption, thereby gaining insight into the dynamics of the reactant gas inside the buffer gas cell.
A promising laser cooling candidate molecule is essential for laser cooling experiments. In this study, the possibility of laser cooling an ⁸⁸Sr³⁵Cl molecule is investigated using an ab initio method. Seven low-lying Λ-S and six Ω electronic states of the ⁸⁸Sr³⁵Cl molecule are calculated at a multi-reference configuration interaction level of theory. Spectral constants of bound states of fitted values are in good agreement with experimental values, which are better than the previously obtained theoretical data for higher excitation states. The resulting permanent and transition dipole moments near the equilibrium bond length are close to the theoretical values. Potential energy curves and transition dipole moments are used for obtaining highly diagonally distributed Franck-Condon factors for the A²Π → X²Σ⁺ transition using the LEVEL program. A short radiative lifetime of the A²Π state is determined; a laser cooling scheme is designed in the vibration level that requires a cooling main laser beam and two repumping laser beams. Transition spectral data of hyperfine energy levels with errors relative to the experimental data do not exceed −0.25∼0.19 MHz when using a quantum effective Hamiltonian approach. This study provides a helpful reference for experimental observation and operation of laser cooling the ⁸⁸Sr³⁵Cl molecule.
Molecules with optical cycling centres (OCCs) are highly desirable in the context of fundamental studies as well as applications (e.g. quantum computing) because they can be effectively cooled to very low temperatures by repeated absorption and emission (hence, cycling). Charged species offer additional advantages for experimental control and manipulation. We present a systematic computational study of a series of diatomic radical-cations made of a d-block metal and a p-block ligand, that are isoelectronic (in their valence shell) to the successfully laser-cooled neutral molecules. Using high-level electronic structure methods, we characterise state and transition properties of low-lying electronic states and compute Franck–Condon factors. The computed branching ratios and radiative lifetimes reveal that the electronic transitions analogous to those successfully used in the laser cooling of neutral molecules are less than optimal in the cations. We propose alternative transitions suitable for optical cycling and highlight trends that could assist future designs of OCCs in charged or neutral molecules.
The TlCl molecule has previously been investigated theoretically and proposed as promising candidates for laser cooling searches [X. Yuan et. al. J. Chem. Phys., 149, 094306, 2018]. From these results, the cooling process, which would proceed by transitions between a ³ Π ⁺ 0 and X ¹ Σ ⁺ 0 states, had as potential bottleneck the long lifetime (6.04 μs) of the excited state a ³ Π ⁺ 0 , that would prohibit experimentally control the slowing region. Here, we revisit this system by employing four-component Multireference Configuration Interaction (MRCI) calculations and investigate the effect of such approaches on the calculated transition momentsbetween a ³ Π ⁺ 0 and a ³ Π 1 excited states of TlCl as well as TlF, the latter serving as a benchmark between theory and experiment. Wherever possible, MRCI results have been cross-validated by, and turned out to be consistent with, four-component equation of motion coupled-cluster (EOM-CC) and polarization propagator (PP) calculations. We find that the results of TlF are very closed to experiment values, while for TlCl thelifetime of the a3Π+0 state is now estimated to be 175 ns, which is much shorter than previous calculations indicated, thus yielding a different, more favorable cooling dynamics. By solving the rate-equation numerically, we provide evidence that TlCl could have cooling properties similar to those of TlF. Our investigations also point to the potential benefits of enhancing the stimulated radiation in optical cycle to improve cooling efficiency.
For the first time, the spectroscopy and transition properties of SeCl+ are systematically reported. The potential energy curves of 22 Λ - S states and the corresponding 51 Ω states in the first and second dissociation channels of SeCl+ are calculated using the internally contracted multiconfiguration interaction and Davidson correction method. The phenomenon of avoided crossing in Ω states below 30,000 cm-1 is discussed in detail. The spectroscopy constants are obtained by fitting the potential energy curves, and also the Franck-Condon factors and radiation lifetimes of the X3Σ0+- ↔ 21Σ0++ transition are calculated. Between X3Σ0+- and 21Σ0++, the Franck-Condon factors are large, close to 1, but the radiation lifetime is large too. According to the calculation results, it is determined that direct laser cooling of SeCl+ is considered infeasible.
We measure the upper-state lifetime and two ratios of vibrational branching fractions fv′v on the B 3Π1(v′)-X 1Σ+(v) transition of TlF. We find the B-state lifetime to be 99(9) ns. We also determine that the off-diagonal vibrational decays are highly suppressed: f01/f00<2×10−4 and f02/f00=1.10(6)%, in excellent agreement with their predicted values of f01/f00<8×10−4 and f02/f00=1.0(2)% based on Franck-Condon factors calculated using Morse and Rydberg-Klein-Rees (RKR) potentials. The implications of these results for the possible laser cooling of TlF and fundamental symmetries experiments are discussed.
Recent advances in the magnetic trapping and evaporative cooling of atoms to nanokelvin temperatures have opened important areas of research, such as Bose-Einstein condensation and ultracold atomic collisions. Similarly, the ability to trap and cool molecules should facilitate the study of ultracold molecular physics and collisions; improvements in molecular spectroscopy could be anticipated. Also, ultracold molecules could aid the search for electric dipole moments of elementary particles. But although laser cooling (in the case of alkali metals,,) and cryogenic surface thermalization (in the case of hydrogen,) are currently used to cool some atoms sufficiently to permit their loading into magnetic traps, such techniques are not applicable to molecules, because of the latter's complex internal energy-level structure. (Indeed, most atoms have resisted trapping by these techniques.) We have reported a more general loading technique based on elastic collisions with a cold buffer gas, and have used it to trap atomic chromium and europium,. Here we apply this technique to magnetically trap a molecular species-calcium monohydride (CaH). We use Zeeman spectroscopy to determine the number of trapped molecules and their temperature, and set upper bounds on the cross-sectional areas of collisional relaxation processes. The technique should be applicable to many paramagnetic molecules and atoms.
The parameter Wa, which characterizes nuclear-spin-dependent parity violation (PV) in the molecular spin-rotational Hamiltonian, was computed with a quasirelativistic Hartree-Fock approach for radium fluoride (RaF) and found to be one of the largest absolute values predicted so far. The peculiar electronic structure of RaF leads to highly diagonal Franck-Condon matrices between the energetically lowest two electronic states, which qualifies RaF for direct laser cooling. A subset of diatomic molecules with a wide range of internal structures suitable for this cooling technique is also indicated. As trapped cold molecules offer superior coherence times, RaF can be considered promising for high-precision experiments aimed at molecular PV.
Polar molecules have a rich internal structure and long-range dipole-dipole interactions, making them useful for quantum-controlled applications and fundamental investigations. Their potential fully unfolds at ultracold temperatures, where various effects are predicted in many-body physics, quantum information science, ultracold chemistry and physics beyond the standard model. Whereas a wide range of methods to produce cold molecular ensembles have been developed, the cooling of polyatomic molecules (that is, with three or more atoms) to ultracold temperatures has seemed intractable. Here we report the experimental realization of optoelectrical cooling, a recently proposed cooling and accumulation method for polar molecules. Its key attribute is the removal of a large fraction of a molecule's kinetic energy in each cycle of the cooling sequence via a Sisyphus effect, allowing cooling with only a few repetitions of the dissipative decay process. We demonstrate the potential of optoelectrical cooling by reducing the temperature of about one million CH(3)F molecules by a factor of 13.5, with the phase-space density increased by a factor of 29 (or a factor of 70 discounting trap losses). In contrast to other cooling mechanisms, our scheme proceeds in a trap, cools in all three dimensions and should work for a large variety of polar molecules. With no fundamental temperature limit anticipated down to the photon-recoil temperature in the nanokelvin range, we expect our method to be able to produce ultracold polyatomic molecules. The low temperatures, large molecule numbers and long trapping times of up to 27 seconds should allow an interaction-dominated regime to be attained, enabling collision studies and investigation of evaporative cooling towards a Bose-Einstein condensate of polyatomic molecules.
We present a two-dimensional 2D magneto-optical trap MOT setup for the production of a continuous collimated beam of cold 87 Rb atoms out of a vapor cell. The underlying physics is purely two-dimensional cooling and trapping, which allows for a high flux of up to 610 10 atoms/s and a small divergence of the resulting beam. We analyze the velocity distribution of the 2D MOT. The longitudinal velocity distribution of the atomic beam shows a broad feature full width at half maximum 75 m/s), centered around 50 m/s. The dependence of the flux on laser intensity, on geometry of the trapping volume, and on pressure in the vapor cell was investigated in detail. The influence of the geometry of the 2D MOT on the mean velocity of the cold beam has been studied. We present a simple model for the velocity distribution of the flux based on rate equations describing the general features of our source.
The feasibility of laser cooling AlH and AlF is investigated using ab initio quantum chemistry. All the electronic states corresponding to the ground and lowest two excited states of the Al atom are calculated using multi-reference configuration interaction (MRCI) and the large AV6Z basis set for AlH. The smaller AVQZ basis set is used to calculate the valence electronic states of AlF. Theoretical Franck-Condon factors are determined for the A(1)Π→ X(1)Σ(+) transitions in both radicals and found to agree with the highly diagonal factors found experimentally, suggesting computational chemistry is an effective method for screening suitable laser cooling candidates. AlH does not appear to have a transition quite as diagonal as that in SrF (which has been laser cooled) but the A(1)Π→ X(1)Σ(+) transition transition of AlF is a strong candidate for cooling with just a single laser, though the cooling frequency is deep in the UV. Furthermore, the a(3)Π→ X(1)Σ(+) transitions are also strongly diagonal and in AlF is a practical method for obtaining very low final temperatures around 3 μK.
The fluorescence spectrum resulting from laser excitation of the A(2)Π(1/2)←X(2)Σ(+) (0,0) band of ytterbium monofluoride, YbF, has been recorded and analyzed to determine the Franck-Condon factors. The measured values are compared with those predicted from Rydberg-Klein-Rees (RKR) potential energy curves. From the fluorescence decay curve the radiative lifetime of the A(2)Π(1/2) state is measured to be 28 ± 2 ns, and the corresponding transition dipole moment is 4.39 ± 0.16 D. The implications for laser cooling YbF are discussed.
Employing a two-stage cryogenic buffer gas cell, we produce a cold,
hydrodynamically extracted beam of calcium monohydride molecules with a near
effusive velocity distribution. Beam dynamics, thermalization and slowing are
studied using laser spectroscopy. The key to this hybrid, effusive-like beam
source is a "slowing cell" placed immediately after a hydrodynamic, cryogenic
source [Patterson et al., J. Chem. Phys., 2007, 126, 154307]. The resulting CaH
beams are created in two regimes. One modestly boosted beam has a forward
velocity of vf = 65 m/s, a narrow velocity spread, and a flux of 10^9 molecules
per pulse. The other has the slowest forward velocity of vf = 40 m/s, a
longitudinal temperature of 3.6 K, and a flux of 5x10^8 molecules per pulse.
Optical lattice clocks with extremely stable frequency are possible when many atoms are interrogated simultaneously, but this
precision may come at the cost of systematic inaccuracy resulting from atomic interactions. Density-dependent frequency shifts
can occur even in a clock that uses fermionic atoms if they are subject to inhomogeneous optical excitation. However, sufficiently
strong interactions can suppress collisional shifts in lattice sites containing more than one atom. We demonstrated the effectiveness
of this approach with a strontium lattice clock by reducing both the collisional frequency shift and its uncertainty to the
level of 10−17. This result eliminates the compromise between precision and accuracy in a many-particle system; both will continue to improve
as the number of particles increases.
A review is presented of some of the principal techniques of laser cooling and trapping that have been developed during the past 20 years. Its approach is primarily experimental, but its quantitative descriptions are consistent in notation with most of the theoretical literature. It begins with a simplified introduction to optical forces on atoms, including both cooling and trapping. Then its three main sections discuss its three selected features, (1) quantization of atomic motion, (2) effects of the multilevel structure of atoms, and (3) the effects of polychromatic light. Each of these features is an expansion in a different direction from the simplest model of a classical, two-level atom moving in a monochromatic laser field.
This article presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the Special Issue of the New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. Ultracold molecules offer promising applications such as new platforms for quantum computing, precise control of molecular dynamics, nanolithography, and Bose-enhanced chemistry. The discussion is based on recent experimental and theoretical work and concludes with a summary of anticipated future directions and open questions in this rapidly expanding research field. Comment: 82 pages, 9 figures, review article to appear in New Journal of Physics Special Issue on Cold and Ultracold Molecules
We propose a method for laser cooling and trapping a substantial class of polar molecules and, in particular, titanium (II) oxide (TiO). This method uses pulsed electric fields to nonadiabatically remix the ground-state magnetic sublevels of the molecule, allowing one to build a magneto-optical trap based on a quasicycling J' = J'' -1 transition. Monte Carlo simulations of this electrostatically remixed magneto-optical trap demonstrate the feasibility of cooling TiO to a temperature of 10 micrpK and trapping it with a radiation-pumping-limited lifetime on the order of 80 ms.
A novel atom trap is described using alternating current to generate the magnetic B field, together with high speed polarization switching of the damping laser field. This combination produces a trap as effective as a standard magneto-optical trap (MOT), with the advantage that the average B field is zero. No net current is hence induced in surrounding conductive elements, and the B field produced by the ac MOT is found to switch off >300 times faster than a conventional MOT. New experiments can hence be performed, including charged particle probing or detection of the cold target ensemble.
A quantum gas of ultracold polar molecules, with long-range and anisotropic interactions, not only would enable explorations of a large class of many-body physics phenomena but also could be used for quantum information processing. We report on the creation of an ultracold dense gas of potassium-rubidium (40K87Rb) polar molecules. Using a single step of STIRAP (stimulated Raman adiabatic passage) with two-frequency laser irradiation, we coherently transfer extremely weakly bound KRb molecules to the rovibrational ground state of either the triplet or the singlet electronic ground molecular potential. The polar molecular gas has a peak density of 10(12) per cubic centimeter and an expansion-determined translational temperature of 350 nanokelvin. The polar molecules have a permanent electric dipole moment, which we measure with Stark spectroscopy to be 0.052(2) Debye (1 Debye = 3.336 x 10(-30) coulomb-meters) for the triplet rovibrational ground state and 0.566(17) Debye for the singlet rovibrational ground state.
A new magnetooptical trap is demonstrated which confines atoms
predominantly in a 'dark' hyperfine level that does not interact with
the trapping light. This leads to much higher atomic densities as
repulsive forces between atoms due to rescattered radiation are reduced
and trap loss due to excited-state collisions is diminished. In such a
trap, more than 10 exp 10 sodium atoms have been confined to densities
approaching 10 exp 12 atoms/cu cm.
We demonstrate and characterize a high-flux beam source for cold, slow atoms or molecules. The desired species is vaporized using laser ablation, then cooled by thermalization in a cryogenic cell of buffer gas. The beam is formed by particles exiting a hole in the buffer gas cell. We characterize the properties of the beam (flux, forward velocity, temperature) for both an atom (Na) and a molecule (PbO) under varying buffer gas density, and discuss conditions for optimizing these beam parameters. Our source compares favorably to existing techniques of beam formation, for a variety of applications.
We have demonstrated Zeeman slowing and capture of neutral 225Ra and 226Ra atoms in a magneto-optical trap. The intercombination transition 1S0-->3P1 is the only quasicycling transition in radium and was used for laser-cooling and trapping. Repumping along the 3D1-->1P1 transition extended the lifetime of the trap from milliseconds to seconds. Room-temperature blackbody radiation was demonstrated to provide repumping from the metastable 3P0 level. We measured the isotope shift and hyperfine splittings on the 3D1-->1P1 transition with the laser-cooled atoms, and set a limit on the lifetime of the 3D1 level based on the measured blackbody repumping rate. Laser-cooled and trapped radium is an attractive system for studying fundamental symmetries.
We report the stopping of an atomic beam, using a series of pulsed electromagnetic coils. We use a supersonic beam of metastable neon created in a gas discharge as a monochromatic source of paramagnetic atoms. A series of coils is fired in a timed sequence to bring the atoms to near rest, where they are detected on a microchannel plate. Applications to fundamental problems in physics and chemistry are discussed.
This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.
Rotational analyses are extended to the emission spectra of several more bands in the delta upsilon = 0, -1 sequences of the A2Pi-X2Sigma+ system of yttrium monoxide excited in the discharge of a hollow cathode tube. Accurate positions for 69 band heads are presented, 12 of which, principally in the delta upsilon = -1 sequence (up to the 22-23 band), are observed for the first time. A consistent set of accurate rotational and vibrational constants is obtained for both states, up to upsilon double prime = 10 and upsilon prime = 9, from global band fittings; the upsilon-connected bands are treated simultaneously. It is noted that this corresponds to the reduction of approximately 3000 line wave numbers.
The reactions of Y and Sc with O2, NO, and SO2 have been investigated by the laser-induced fluorescence method. The excitation spectra are reported for metal oxide products formed under single-collision conditions in a beam–gas arrangement. Possible systematic errors which arise in deducing the internal state distributions from the spectra are discussed. The relative vibrational populations of metal oxides for all reactions are close to unbiased statistical distributions (in the sense of the information theoretic approach). Although the rotational distributions from the reactions with NO and SO2 also follow statistical behavior, those from the reactions with O2 peak significantly lower than the statistical ones. Radiative lifetimes are reported for the A and B states of YO and ScO, and the B and C states of LaO.
We demonstrate magnetic field enabled optical forces on a neutral indium atomic beam in a light field consisting of five frequencies. The role of dark magnetic ground state sublevels is studied and enables us to cool the atomic beam transversely to near the Doppler limit with laser frequencies tuned above the atomic resonance. The effect of laser cooling can be explained with transient effects in the light potential created by the standing wave light field where the atoms are optically pumped into the dark states and recycled by Larmor precession.
A molecular beam optical and rf–optical double resonance spectroscopic study of numerous vibrational components in the A2Π3/2–X2∑+ subband of gas phase YO has been performed. The fine and magnetic hyperfine parameters for v=0–4 of the X2∑+ state have been determined. The observed strong vibrational dependence of the spin–rotation parameter γ(X2∑+) is proposed to arise from a perturbation from two as yet unobserved low‐lying 2Π states coming from a three open‐shell configuration. The magnetic hyperfine parameters for the X2∑+ state can be interpreted in terms of a single unpaired electron model. An estimate for the A2Π excited state dipolar parameter has been established.
Atomic physics was revolutionized by the development of forced evaporative cooling, which led directly to the observation of Bose-Einstein condensation, quantum-degenerate Fermi gases and ultracold optical lattice simulations of condensed-matter phenomena. More recently, substantial progress has been made in the production of cold molecular gases. Their permanent electric dipole moment is expected to generate systems with varied and controllable phases, dynamics and chemistry. However, although advances have been made in both direct cooling and cold-association techniques, evaporative cooling has not been achieved so far. This is due to unfavourable ratios of elastic to inelastic scattering and impractically slow thermalization rates in the available trapped species. Here we report the observation of microwave-forced evaporative cooling of neutral hydroxyl (OH(•)) molecules loaded from a Stark-decelerated beam into an extremely high-gradient magnetic quadrupole trap. We demonstrate cooling by at least one order of magnitude in temperature, and a corresponding increase in phase-space density by three orders of magnitude, limited only by the low-temperature sensitivity of our spectroscopic thermometry technique. With evaporative cooling and a sufficiently large initial population, much colder temperatures are possible; even a quantum-degenerate gas of this dipolar radical (or anything else it can sympathetically cool) may be within reach.
Certain molecules, it seems, may be laser cooled by methods technically similar to those applied with abundant success in atomic physics. We discuss the spectroscopic criteria molecules should meet to make methods of Doppler cooling technically feasible and identify diatomic candidates. Some candidates, such as the alkaline-earth monohydrides (e.g. BeH and CaH), are paramagnetic and amenable to magneto-optical trapping. Our experimental study concentrates on CaH, and we present our recent high-resolution, molecular-beam-based measurements of low-J rotational lines within the A-X(0,0) band of CaH. From these measurements we report hyperfine separations in the A-state, as important to laser-cooling spectroscopy, and centroidal transition frequencies for comparison with existing values. We conclude with an outline of a possible magneto-optical trap for CaH.
Large parts of the periodic table cannot be cooled by current laser-based methods. We investigate whether zero energy fragmentation of laser cooled fluorides is a potential source of ultracold fluorine atoms. We report new ab initio calculations on the lowest electronic states of the BeF diatomic molecule including spin-orbit coupling, the calculated minima for the valence electronic states being within 1 pm of the spectroscopic values. A four colour cooling scheme based on the A(2)Π← X(2)Σ(+) transition is shown to be feasible for this molecule. Multi-Reference Configuration Interaction (MRCI) potentials of the lowest energy Rydberg states are reported for the first time and found to be in good agreement with experimental data. A series of multi-pulse excitation schemes from a single rovibrational level of the cooled molecule are proposed to produce cold fluorine atoms.
We demonstrate deceleration of a beam of neutral strontium monofluoride molecules using radiative forces. Under certain conditions, the deceleration results in a substantial flux of detected molecules with velocities ≲50 m/s. Simulations and other data indicate that the detection of molecules below this velocity is greatly diminished by transverse divergence from the beam. The observed slowing, from ∼140 m/s, corresponds to scattering ≳10(4) photons. We also observe longitudinal velocity compression under different conditions. Combined with molecular laser cooling techniques, this lays the groundwork to create slow and cold molecular beams suitable for trap loading.
Strategies to produce an ultracold sample of carbon atoms are explored and assessed with the help of quantum chemistry. After a brief discussion of the experimental difficulties using conventional methods, two strategies are investigated. The first attempts to exploit charge exchange reactions between ultracold metal atoms and sympathetically cooled C(+) ions. Ab initio calculations including electron correlation have been conducted on the molecular ions [LiC](+) and [BeC](+) to determine whether alkali or alkaline earth metals are a suitable buffer gas for the formation of C atoms but strong spontaneous radiative charge exchange ensure they are not ideal. The second technique involves the stimulated production of ultracold C atoms from a gas of laser cooled carbides. Calculations on LiC suggest that the alkali carbides are not suitable but the CH radical is a possible laser cooling candidate thanks to very favourable Frank-Condon factors. A scheme based on a four pulse STIRAP excitation pathway to a Feshbach resonance is outlined for the production of atomic fragments with near zero centre of mass velocity.
It has been roughly three decades since laser cooling techniques produced
ultracold atoms, leading to rapid advances in a vast array of fields.
Unfortunately laser cooling has not yet been extended to molecules because of
their complex internal structure. However, this complexity makes molecules
potentially useful for many applications. For example, heteronuclear molecules
possess permanent electric dipole moments which lead to long-range, tunable,
anisotropic dipole-dipole interactions. The combination of the dipole-dipole
interaction and the precise control over molecular degrees of freedom possible
at ultracold temperatures make ultracold molecules attractive candidates for
use in quantum simulation of condensed matter systems and quantum computation.
Also ultracold molecules may provide unique opportunities for studying chemical
dynamics and for tests of fundamental symmetries. Here we experimentally
demonstrate laser cooling of the molecule strontium monofluoride (SrF). Using
an optical cycling scheme requiring only three lasers, we have observed both
Sisyphus and Doppler cooling forces which have substantially reduced the
transverse temperature of a SrF molecular beam. Currently the only technique
for producing ultracold molecules is by binding together ultracold alkali atoms
through Feshbach resonance or photoassociation. By contrast, different proposed
applications for ultracold molecules require a variety of molecular
energy-level structures. Our method provides a new route to ultracold
temperatures for molecules. In particular it bridges the gap between ultracold
temperatures and the ~1 K temperatures attainable with directly cooled
molecules (e.g. cryogenic buffer gas cooling or decelerated supersonic beams).
Ultimately our technique should enable the production of large samples of
molecules at ultracold temperatures for species that are chemically distinct
from bialkalis.
Rydberg atoms with principal quantum number n >> 1 have exaggerated atomic
properties including dipole-dipole interactions that scale as n^4 and radiative
lifetimes that scale as n^3. It was proposed a decade ago to take advantage of
these properties to implement quantum gates between neutral atom qubits. The
availability of a strong, long-range interaction that can be coherently turned
on and off is an enabling resource for a wide range of quantum information
tasks stretching far beyond the original gate proposal. Rydberg enabled
capabilities include long-range two-qubit gates, collective encoding of
multi-qubit registers, implementation of robust light-atom quantum interfaces,
and the potential for simulating quantum many body physics. We review the
advances of the last decade, covering both theoretical and experimental aspects
of Rydberg mediated quantum information processing.
We demonstrate a scheme for optical cycling in the polar, diatomic molecule
strontium monofluoride (SrF) using the $X ^2\Sigma^+\toA^2\Pi_{1/2}$ electronic
transition. SrF's highly diagonal Franck-Condon factors suppress vibrational
branching. We eliminate rotational branching by employing a quasi-cycling
$N=1\to N^\prime=0$ type transition in conjunction with magnetic field remixing
of dark Zeeman sublevels. We observe cycling fluorescence and deflection
through radiative force of an SrF molecular beam using this scheme. With
straightforward improvements our scheme promises to allow more than $10^5$
photon scatters, possibly enabling the direct laser cooling of SrF.
We report the first experimental realization of magnetic trapping of a sample of cold radicals following multistage Zeeman deceleration of a pulsed supersonic beam. H atoms seeded in a supersonic expansion of Kr have been decelerated from an initial velocity of 520 m/s to 100 m/s in a 12-stage Zeeman decelerator and loaded into a magnetic quadrupole trap by rapidly switching the fields of the trap solenoids.
The confinement and cooling of an optically dense cloud of neutral sodium atoms by radiation pressure is reported. The trapping and damping forces were provided by three retroreflected laser beams propagating along orthogonal axes, with a weak magnetic field used to distinguish between the beams. As many as 10 million atoms have been trapped for 2 min, at densities exceeding 10 to the 11th atoms/cu cm. The trap was about 0.4 K deep, and the atoms, once trapped, were cooled to less than a millikelvin and compacted into a region less than 0.5 mm in diameter.
The motion of polar molecules can be controlled by time-varying inhomogeneous electric fields. In a Stark decelerator, this is exploited to accelerate, transport, or decelerate a fraction of a molecular beam. When combined with a trap, the decelerator provides a means to store the molecules for times up to seconds. Here, we review our efforts to produce cold molecules via this technique. In particular, we present a new generation Stark decelerator and electrostatic trap that selects a significant part of a molecular beam pulse that can be loaded into the trap. Deceleration and trapping experiments using a beam of OH radicals are discussed.
Modified-CPF and CASSCF/multireference-CI theoretical calculations are presented for the ground and low-lying states of YO and YS, ZrO and ZS, and NbO and NbS. The techniques employed are explained, and the calculated spectroscopic constants are presented in extensive tables. Good agreement is found with published experimental data on the oxides, and it is inferred that the sulfide results are accurate as well. Particular attention is given to the high-lying quartet manifold of states in YO and the (1) 3Pi-a3Delta transition of ZrS (possibly the source of the IR Keenan bands seen in S-star spectra).
We present a general discussion of the techniques of destabilizing dark states in laser-driven atoms with either a magnetic field or modulated laser polarization. We show that the photon scattering rate is maximized at a particular evolution rate of the dark state. We also find that the atomic resonance curve is significantly broadened when the evolution rate is far from this optimum value. These results are illustrated with detailed examples of destabilizing dark states in some commonly-trapped ions and supported by insights derived from numerical calculations and simple theoretical models. Comment: 14 pages, 10 figures
We acknowledge funding support for this work from AFOSR (MURI)
- Nsf Pfc
We acknowledge funding support for this work from
AFOSR (MURI), DOE, NIST, and NSF PFC at
JILA. M.T.H. acknowledges support from the NRC.
We thank K. Cossel and F. Adler for technical help.
- E L Raab
- M Prentiss
- A Cable
- S Chu
- D E Pritchard
E. L. Raab, M. Prentiss, A. Cable, S. Chu, D. E.
Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
- J R Guest
J. R. Guest, et al., Phys. Rev. Lett. 98, 093001
(2007).
- I Bloch
- J Dalibard
- W Zwerger
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys.
80, 885 (2008).
- M Saffman
- T G Walker
- K Mølmer
M. Saffman, T. G. Walker, K. Mølmer, Rev. Mod.
Phys. 82, 2313 (2010).
- M D Swallows
M. D. Swallows, et al., Science 331, 1043 (2011).
- L D Carr
- D Demille
- R V Krems
- J Ye
L. D. Carr, D. DeMille, R. V. Krems, J. Ye, New
Journal of Physics 11, 055049 (2009).
- K K Ni
K. K. Ni, et al., Science 322, 231 (2008).
- J D Weinstein
- R Decarvalho
- T Guillet
- B Friedrich
- J M Doyle
J. D. Weinstein, R. deCarvalho, T. Guillet,
B. Friedrich, J. M. Doyle, Nature 395, 148 (1998).
- S Van De Meerakker
- N Vanhaecke
- G Meijer
S. van de Meerakker, N. Vanhaecke, G. Meijer,
Annu. Rev. Phys. Chem. 57, 159 (2006).
- E Narevicius
E. Narevicius, et al., Phys. Rev. Lett. 100, 093003
(2008).
- Di Rosa
M. Di Rosa, European Physical Journal D 31, 395
(2004).
- B K Stuhl
- B C Sawyer
- D Wang
- J Ye
B. K. Stuhl, B. C. Sawyer, D. Wang, J. Ye, Phys.
Rev. Lett. 101, 243002 (2008).
- E S Shuman
- J F Barry
- D Demille
E. S. Shuman, J. F. Barry, D. DeMille, Nature 467,
820 (2010).