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Observation of Population Inversion by Optical Adiabatic Rapid Passage
Abstract
I report the observation of population inversion by optical adiabatic rapid passage. These observations, on an ${\mathrm{NH}}_{3}$ infrared transition with all the relevant parameters known, agree with theoretical expectations. The pressure dependence of ${T}_{1}$, obtained by this technique, makes possible the first estimate of the collision-induced rotational lifetime of ${\mathrm{NH}}_{3}$ in an excited band, which is significantly longer than the rotational lifetime in the ground vibrational band.
... The optical excitation scheme presented here is a modified version of adiabatic rapid passage (ARP), which utilizes a frequencyswept pulse to realize quantum state inversion. [63][64][65] In ARP, the laser pulse is linearly chirped, with an electric field given by ...
... For ARP, the adiabatic condition may be satisfied in the presence of such variations such that high-fidelity inversion is maintained. [63][64][65][66] Furthermore, the choice of the positive chirp in the laser pulses used to drive the emitter leads to inversion via the lower-energy dressed state, which suppresses phonon-induced dephasing processes at low temperatures in contrast to other driving schemes. 56 Robust inversion has been demonstrated using ARP in solid-state emitters based on excitons in semiconductor QDs in recent years, 56,[66][67][68][69][70][71][72] including the driving of a triggered single photon source. ...
We present a driving scheme for solid-state quantum emitters, referred to as Notch-filtered Adiabatic Rapid Passage (NARP), that utilizes frequency-swept pulses containing a spectral hole resonant with the optical transition in the emitter. NARP enables high-fidelity state inversion and exhibits robustness to variations in the laser pulse parameters, benefits that derive from the insensitivity of the condition for adiabatic evolution. NARP also offers the advantage of immunity to phonon-mediated excitation-induced dephasing when positively-chirped control pulses are used. Our resonant driving approach could be combined with spectral filtering of the scattered pump light and photonic devices for enhanced collection efficiency to realize simultaneous high indistinguishability and brightness in single photon source applications.
... The optical excitation scheme presented here is a modified version of adiabatic rapid passage (ARP) which utilizes a frequency-swept pulse to realize quantum state inversion [63][64][65]. In ARP, the laser pulse is linearly-chirped, with an electric field given by ...
... In addition, the laser system used to drive the emitter can fluctuate in both intensity (leading to changes in the pulse area θ = dt) and the laser central frequency ω l causing changes in ∆ 0 . For ARP, the adiabatic condition may be satisfied in the presence of such variations such that high-fidelity inversion is maintained [63][64][65][66]. Furthermore, the choice of positive chirp in the laser pulses used to drive the emitter leads to inversion via the lower-energy dressed state, which may be used to suppress phonon-induced dephasing processes at low temperature, in contrast to other driving schemes [67]. ...
We present a driving scheme for solid-state quantum emitters using frequency-swept pulses containing a spectral hole resonant with the optical transition in the emitter. Our scheme enables high-fidelity state inversion, exhibits robustness to variations in the laser pulse parameters and is immune to phonon-mediated excitation-induced dephasing, benefits that derive from the the insensitivity of the adiabaticity condition to variations in the experimental parameters. Our resonant driving approach could be combined with spectral filtering of the scattered pump light and photonic devices for enhanced collection efficiency to realize simultaneous high indistinguishability and brightness in single photon source applications.
... An ideal quantum state preparation scheme for triggering photon emission would be insensitive to variations in the QD optical transition energy while simultaneously enabling resonant driving of the excitonic system. ARP uses frequency-swept laser pulses to invert the state of the exciton by adiabatically transferring the system through an anti-crossing between the dressed states of the QD in the presence of the light field [31][32][33]. ARP provides a more robust approach to quantum state inversion than a Rabi rotation because, provided the system is initially in the ground state, the dressed state is uniquely identified with the exciton at the end of the laser pulse. ARP has been demonstrated in single QDs for inverting excitons [34][35][36][37] and biexcitons [38], for realizing a triggered QD single-photon source [39] and for demonstrating dynamic decoupling in the strong driving regime [40,41]. ...
... , where E p (t) is the pulse envelope, ω l is the center frequency of the laser pulse, and α is the temporal chirp [31][32][33]. The eigenstates of the QD in the presence of the laser field are the dressed states (|Ψ ± ⟩), each of which corresponds to a dynamic admixture of the bare QD states |0⟩ and |1⟩, where |0⟩ (|1⟩) represents the absence (presence) of a single exciton in the QD. ...
Adiabatic rapid passage (ARP) is demonstrated in a single In(Ga)As quantum dot (QD) over a wide range of laser tuning relative to the exciton transition energy to assess the level of robustness of this quantum state inversion gate for practical QD systems. Our experiments indicate a drop in exciton inversion by only 5% for a detuning of 9.3 meV, indicating accessible detunings that span the typical inhomogeneous broadening of self-assembled QD ensembles. Our findings indicate that ARP is an ideal control protocol for synchronous triggering of quantum light sources for applications in photonic quantum technology.
... By applying an intense narrowband emission in the THz domain, the precise coherent control of a two-(or few-) level system with Rabi oscillation has been experimentally realized [2-6], which is capable of converting a known initial pure state into an arbitrary final state in principle. In order to transfer the population with high efficiency, the power of THz waves should be high enough, and the adiabatic rapid passage (ARP) [7] can be a complementary technique, which has already been demonstrated as a versatile tool in the optical regime [8][9][10][11][12]. Unlike Rabi oscillation, the ARP is a more robust technique, and adiabatic population transfer is largely unaffected by the variation in the optical field, interaction time, and atomic dipole moment. ...
... By applying an intense narrowband emission in the THz domain, the precise coherent control of a two-(or few-) level system with Rabi oscillation has been experimentally realized [2][3][4][5][6], which is capable of converting a known initial pure state into an arbitrary final state in principle. In order to transfer the population with high efficiency, the power of THz waves should be high enough, and the adiabatic rapid passage (ARP) [7] can be a complementary technique, which has already been demonstrated as a versatile tool in the optical regime [8][9][10][11][12]. Unlike Rabi oscillation, the ARP is a more robust technique, and adiabatic population transfer is largely unaffected by the variation in the optical field, interaction time, and atomic dipole moment. ...
It is of scientific significance to explore the terahertz radiation source with the performances of high power, tunable frequency, and controllable chirp for the realization of coherent control of quantum systems. How to realize frequency chirp control of terahertz synchrotron radiation is the last puzzle to be completed. In this Letter, we propose a method to control the radiation frequency chirp with precision. A novel photomixing scheme is presented to generate a longitudinally modulated laser pulse with non-uniform time intervals between the adjacent micro-peaks, which means that there is a chirp in the modulation frequency, and this chirp can be continuously tuned. The interaction is made to occur between an electron beam and the modulated laser pulse in a modulator (an undulator tuned at the laser wavelength), then terahertz synchrotron radiation with the same spectrum characteristics as the modulated laser will be generated when the electron beam passes through the following bending magnet. We expect that this method will open a new way for the coherent control of quantum systems in the terahertz regime.
... To shelve atomic population into the metastable 3 P 0 state, we utilize an adiabatic rapid passage (ARP) pulse [29] to robustly transfer more than 90% of the lattice trapped ground state population to the metastable state. Due to Doppler effects from atomic motion, atoms not yet trapped into the optical lattice are only weakly excited. ...
We demonstrate programmable control over the spatial distribution of ultra-cold atoms confined in an optical lattice. The control is facilitated through a combination of spatial manipulation of the magneto-optical trap and atomic population shelving to a metastable state. We first employ the technique to load an extended (5 mm) atomic sample with uniform density in an optical lattice clock, reducing atomic interactions and realizing remarkable frequency homogeneity across the atomic cloud. We also prepare multiple spatially separated atomic ensembles and realize multi-ensemble clock operation within the standard one-dimensional (1D) optical lattice clock architecture. Leveraging this technique, we prepare two oppositely spin-polarized ensembles that are independently addressable, offering a platform for implementing spectroscopic protocols for enhanced tracking of local oscillator phase. Finally, we demonstrate a relative fractional frequency instability at one second of $2.4(1) \times10^{-17}$ between two ensembles, useful for characterization of intra-lattice differential systematics.
... Adiabatic passage technique allows such robustness but at the cost of slow and inexact dynamics [5][6][7]. Composite pulses, made of a π−pulse sequence with welldefined phases, are a powerful and simple tool for robust control [8][9][10][11][12][13] even if they are not optimal in terms of control time or energy used. Composite pulses have been recently implemented on IBM's computers [14]. ...
The ability of pulse-shaping devices to generate accurately quantum optimal control is a strong limitation to the development of quantum technologies. We propose and demonstrate a systematic procedure to design robust digital control processes adapted to such experimental constraints. We show to what extent this digital pulse can be obtained from its continuous-time counterpart. A remarkable efficiency can be achieved even for a limited number of pulse parameters. We experimentally implement the protocols on IBM quantum computers for a single qubit, obtaining an optimal robust transfer in a time T = 382 ns.
... The temporal waveform of the chirped CP THz field can be controlled by adjusting the density distribution of the gas. The chirped THz field is expected to realize adiabatic rapid passage [30] and Rabi flopping [6] in the THz regime, as the chirped laser field can be used to control the population of two-level systems such as atoms [31] and quantum dots [32]. In addition, the chirped THz source may also find applications in time-domain spectroscopy, molecular orientation control, and high-order harmonic generation [33]. ...
... However, in this case, there are two types of ion sites for both light fields with different Rabi frequencies that reduce the effectiveness of the rephasing pulses if ordinary π pulses are used. To overcome this issue in all ROSE protocol implementations, we used complex hyperbolic secant (CHS) pulses [52,53] implemented under adiabatic rapid passage conditions [54,55]. The electric field of these pulses (m = 1, 2) is defined by ...
We report an observation of the linear Stark effect in a Tm3+:Y3Al5O12 crystal with the distribution of the Stark coefficient over the ion ensemble. We associate this effect with local lattice distortions near the positions of Tm3+ ions. Using this effect, the addressable storage of a series of weak light pulses in a cavity-assisted scheme of the revival of silenced echo quantum memory protocol is implemented. In this memory scheme, we also demonstrate storage of a light pulse on the few photon level. The application of an optical resonator makes it possible to increase the memory efficiency in this crystal and to reduce the minimal number of photons in the input signal pulse to 5.6 for the signal-to-noise ratio of 1 in the retrieved echo pulse. The results are in good agreement with the theoretical analysis. The possible ways of the further improvement of the implemented memory scheme are also discussed.
... To fully exploit the intensity-error resilience [44] offered by the SU(2) geometry of the twolevel control, the optical pulses need to be shaped on a time scale fast enough to suppress the spontaneous emission, and also slow enough to avoid uncontrolled multiphoton couplings in real atoms. We note that optical methods for two-level rapid adiabatic passage [45] itself are well-developed for population transfers in atoms and molecules using ultrafast lasers [46,47]. However, these ultrafast techniques typically demand control field Rabi frequencies Ω c beyond the THz level with intense pulses at low repetition rates, not easily adaptable to our desired goals. ...
The absorption of traveling photons resonant with electric dipole transitions of an atomic gas naturally leads to electric dipole spin-wave excitations. For a number of applications, it would be highly desirable to shape and coherently control the spatial waveform of the spin waves before spontaneous emission can occur. This paper details a recently developed optical control technique to achieve this goal, where counterpropagating, shaped subnanosecond pulses impart subwavelength geometric phases to the spin waves by cyclically driving an auxiliary transition. In particular, we apply this technique to reversibly shift the wave vector of a spin wave on the D2 line of laser-cooled Rb87 atoms by driving an auxiliary D1 transition with shape-optimized pulses, so as to shut off and recall superradiance on demand. We investigate a spin-dependent momentum transfer during the spin-wave control process, which leads to a transient optical force as large as ∼1ℏk/ns, and study the limitations to the achieved 70∼75% spin-wave control efficiency by jointly characterizing the spin-wave control and matter-wave acceleration. Aided by numerical modeling, we project potential future improvements of the control fidelity to the 99% level when the atomic states are better prepared and by equipping a faster and more powerful pulse shaper. Our technique also enables a background-free measurement of the superradiant emission to unveil the precise scaling of the emission intensity and decay rate with optical depth.
... 绝热跃迁方法(rapid adiabatic passage, RAP) 是指在满足量子绝热近似的条件下连续改变哈密 顿量, 使原子通过绝热跃迁改变布居数, 实现与功 率无关的均匀跃迁几率 [15] , 从而制备密度比例空 间均匀的原子团的方法 [16] . 实验证明这是一种对 环境因素不敏感的方法, 可以实现10 -3 量级均匀的 原子团, 大大减小了碰撞频移的不确定度 [12,16−19] . ...
Cold collision frequency shift is one of the major systematic effects which limit the frequency uncertainty of the cesium fountain atomic clock. It is proportional to the effective atomic density, which is defined as the average density over the initial spacial and velocity distribution. The measurement of the frequency shift is based on a differential method, in which the fountain clock is operated with two different atomic densities, i.e. high density and low density, in turn. The clock frequency without collision shift can be achieved by linear extrapolation with the frequencies and density ratios of two states. For the density ratio is estimated with the atom number, it plays a crucial role in generating atoms with same density distribution for reducing systematic uncertainty in cold collision frequency shift estimation. The rapid adiabatic passage method is used in Cesium fountain clock to realize homogeneous transition probability, which modulates the amplitude and frequency of microwave continuously to prepare atom sample. To investigate the precision of this method, theoretical analysis and experimental measurement are both used here. An equation of deviation is derived from the time evolution of Bloch vector. The vector rotates at angular speed Ω with the rotation axis processing at lower angular speed. The deviations in the two directions on the surface of Bloch sphere are determined by the equations which are similar to wave equations, and can be simplified into wave equations when the deviations are sufficiently small. It is shown in the equations that the deviations are stimulated by angular velocity and angular acceleration of the precession, and is inversely proportional to the square of Ω. Further calculation shows that the deviation becomes smaller when the amplitude of microwave frequency and Rabi frequency are close to each other. It is then confirmed experimentally. The effects of some other parameters, such as the pulse length and time delay, on transition probability are also measured, showing that the RAP method is insensitive to these parameters up to a large scope. The precision of RAP method is dominated by three factors. The first factor is the product of rotating angular speed Ω and pulse length T, i.e. ΩT: The increase of ΩT can reduce the uncertainty to a satisfactory degree. The second factor is the uncertainty of resonant frequency, so the measurement is required to be precise. The third factor is the unexpected atoms which are not selected by the microwave, and may be attributed to pulling light. After optimizing the parameters, the ratio of low density to high density can approach to 0.5 with 3 × 10–3 uncertainty, which leads to a systematic relative uncertainty of cold collision shift up to 1.6 × 10–16.
... With a bit of thought, one would conclude that this sweep should be slow relative to the Rabi frequency Ω R but also fast with respect to the decay rate of the upper state so that spontaneous emission is negligible and the form of the OBEs in Equations (2.34) is valid. This process therefore just about warrants the oxymoronic term adiabatic rapid passage (ARP) that it has acquired in the literature [83][84][85], and is particularly useful when full population inversion is desired in an ensemble of atoms that may exhibit a broad range of detunings and Rabi frequencies due to, for example, Doppler shifts or variations in laser intensity. We shall revisit this in another context in Chapter 9. ...
Ultracold samples of laser-cooled atoms are quantum systems over which modern atomic physicists can exert exquisite control. Largely decoupled from their environment, they can act as near-ideal test masses for inertial sensors based on atom interferometry and are well suited to experiments in coherent control of quantum systems that probe the fundamental nature of quantum mechanics and pave the way for practical quantum simulation and computation.
This thesis details a series of experimental results that arise from the coherent control of rubidium atoms with laser light, focusing on the interplay between these interactions and atomic velocities; the laser frequency an atom ‘sees’ is Doppler shifted according to its velocity, while conservation of momentum dictates that, in exchanging photons with a laser, an atom’s velocity is altered.
Coherent light–atom interactions can thus be tailored either to measure or to narrow the spread of velocities in an ultracold atomic gas. Alternatively, it can be desirable to design interactions that are homogeneous across a large spread of atomic velocities. All of these aspects are explored in this thesis.
The velocity-sensitive interactions that lie at the heart of atom-interferometric inertial sensors are reexamined in a manner that yields considerable insight into the underlying processes and culminates in a novel, precise and elegant technique for measuring the velocity of ultracold atoms that is used to reveal the Gaussian nature of the velocity spread in a cloud with an effective temperature of 18.7(6) µK, undistorted by artefacts that plague other methods.
Furthermore, optimal control techniques are applied to the problem of coherently and uniformly manipulating the quantum states of atoms in an ensemble with a large spread of velocities, even subject to variations in laser intensity. A broadband inversion pulse is demonstrated to change the internal state of 99.8(3) % of atoms in a ∼35 µK ensemble and — for the first time — this technique is used to optimise an entire atom interferometry sequence, yielding a threefold enhancement in the measurement contrast.
Finally, a version of grey molasses cooling — in which atoms accumulate in velocity-dependent ‘dark’ states, narrowing their momentum spread and increasing their phase space density — is demonstrated with phase-coherent cooling beams; dark states that exist in this system prove to be particularly resilient to the spatially varying light shifts that are present in an optical dipole trap, and this is used both to enhance the number of atoms loaded into such a trap — by a factor of 7 compared to loading from a conventional optical molasses — and to further cool them once they are loaded in a technique that has promising prospects for the rapid production of ultracold, trapped, atoms.<br/
... We demonstrate decoherence suppression using ARP, for which frequency-swept optical control pulses are used to invert the exciton transition in the QD [29]. The control pulse is given by ...
We demonstrate suppression of dephasing tied to deformation potential coupling of confined electrons to longitudinal acoustic (LA) phonons in optical control experiments on large semiconductor quantum dots (QDs) with emission compatible with the low-dispersion telecommunications band at 1.3 µm. By exploiting the sensitivity of the electron–phonon spectral density to the size and shape of the QD, we demonstrate a fourfold reduction in the threshold pulse area required to enter the decoupled regime for exciton inversion using adiabatic rapid passage (ARP). Our calculations of the quantum state dynamics indicate that the symmetry of the QD wave function provides an additional means to engineer the electron–phonon interaction. Our findings will support the development of solid-state quantum emitters in future distributed quantum networks using semiconductor QDs.
... To fully exploit the intensity-error resilience [44] offered by the SU(2) geometry of the twolevel control, the optical pulses need to be shaped on a time scale fast enough to suppress the spontaneous emission, and also slow enough to avoid uncontrolled multiphoton couplings in real atoms. We note that optical methods for two-level rapid adiabatic passage [45] itself are well-developed for population transfers in atoms and molecules using ultrafast lasers [46,47]. However, these ultrafast techniques typically demand control field Rabi frequencies Ω c beyond the THz level with intense pulses at low repetition rates, not easily adaptable to our desired goals. ...
The absorption of traveling photons resonant with electric dipole transitions of an atomic gas naturally leads to electric dipole spin wave excitations. For a number of applications, it would be highly desirable to shape and coherently control the spatial waveform of the spin waves before spontaneous emission can occur. This work details a recently developed optical control technique to achieve this goal, where counter-propagating, shaped sub-nanosecond pulses impart sub-wavelength geometric phases to the spin waves by cyclically driving an auxiliary transition. In particular, we apply this technique to reversibly shift the wave vector of a spin wave on the $D2$ line of laser-cooled $^{87}$Rb atoms, by driving an auxiliary $D1$ transition with shape-optimized pulses, so as to shut off and recall superradiance on demand. We investigate a spin-dependent momentum transfer during the spin-wave control process, which leads to a transient optical force as large as $\sim 1\hbar k$/ns, and study the limitations to the achieved $70\sim 75\%$ spin wave control efficiency by jointly characterizing the spin-wave control and matterwave acceleration. Aided by numerical modeling, we project potential future improvements of the control fidelity to $99\%$ level when the atomic states are better prepared and by equipping a faster and more powerful pulse shaper. Our technique also enables a background-free measurement of the superradiant emission to unveil the precise scaling of the emission intensity and decay rate with optical depth for the first time to our knowledge.
... The demonstration of low-threshold, high-fidelity inversion in our experiments points to the potential for practical QD-based quantum light sources that could be initialized in parallel and operated at elevated temperatures. We demonstrate decoherence suppression using ARP, for which frequency-swept optical control pulses are used to invert the exciton transition in the QD 54,55 . ...
We demonstrate full suppression of dephasing tied to deformation potential coupling of confined electrons to longitunidal acoustic (LA) phonons in optical control experiments on large semiconductor quantum dots (QDs) with emission compatible with the low-dispersion telecommunications band at 1.3~$\mu$m. By exploiting the sensitivity of the electron-phonon spectral density to the size and shape of the QD, we demonstrate a four-fold reduction in the threshold pulse area required to enter the decoupled regime for exciton inversion using adiabatic rapid passage (ARP). Our calculations of the quantum state dynamics provide good agreement with our experimental results and indicate that the symmetry of the QD wave function provides an additional means to engineer the electron-phonon interaction. Our findings will support the development of solid-state quantum emitters in future distributed quantum networks using semiconductor QDs.
... To achieve ∆ and η(r i ) independent population inversion, the simplest choice is a quasi-adiabatic pulse. With Ω c = Ω 0 sin(πt/τ c ) and δ c = −δ 0 cos(πt/τ c ), stability of near unity inversion efficiency against ∆ and η has been studied in detail in the context of nuclear magnetic resonance [78], molecular spectroscopy [79], and matter-wave accelerations [34,71]. Efficient and error-resilient inversion is achievable with (Ω 0 , δ 0 ) close in magnitude and for Ω c dt beyond 3π, as in this work. ...
We demonstrate quantum control of collective spontaneous emission by fast state-dependent geometric phase patterning. In particular, by driving transition cycles in $^{87}$Rb D1 line with counter-propagating, shaped sub-nanosecond pulse pairs, we temporally control a few-photon D2-excited $^{87}$Rb gas in its directional superradiant states, which allows one to redirect the superradiance with high efficiency on timescales much faster than the emission time itself, and even turn off the collective emission for its recall later. Accompanying the phase writing is efficient optical acceleration of the laser-cooled gas, which is measured to corroborate with our estimation of $\sim70\%$ control efficiency limited by hyperfine interaction and spontaneous decay. Substantial improvement of the control efficiency is expected with better atomic state preparation and with shorter and more advanced pulse control techniques. Our work represents a first step toward accurate, active control of collective optical dipoles for studying many-body dissipative dynamics of excited gases, as well as for numerous quantum optical applications.
... The atomic variables C g and C e depend on z and t for a given detuning ∆. The detunings can be made time-dependent [14,15], position-dependent or both [16] but this is not the case here. ...
... In this paper we describe how we approached this task and the numerical optimization that goes into creating an ideal case. The major shift in framework we made is viewing the process of magneto-association, otherwise known as a Feshbach Resonance (FR), through the lens of the well understood coherent process of Rapid Adiabatic Passage (RAP) [4,5,[14][15][16]. With that shift, we attempt to find a suitable dark state for this process and optimize accordingly. ...
We present a method for the creation and control of cold molecules that involves coherently combining Feshbach Resonances and STIRAP. We present analytical and numerical results showing how to optimize this process that can be implemented using techniques readily available in standard experimental setups. This will provide a link in the chain from atoms to ground state molecules and can serve as a building block towards more complex processes in coherent ultracold chemistry.
... Initially investigated for nuclear magnetic resonance [1], it was experimentally implemented with lasers for the first time in the 70s (a list of experiments can be found in a review [3]). The necessary time-varying resonance condition was achieved by very different means: Stark shifts in molecules [7], chirping the laser frequency [8] positiondependent Doppler shift of the laser beam [9], or manipulating coupled waveguides [10]. The selected population of adiabatic states with chirped pulses has been measured "in situ" by weak-field ionization of the Starkshifted states [11,12]. ...
We demonstrate that by changing the direction of the chirp in VUV pulses one can switch between excitation and ionization with very high contrast, if the carrier frequency of the light is resonant with two bound states. This is a surprising consequence if rapid adiabatic passage is extended to include transitions to the continuum. The chirp phase locks the linear combination of two resonantly coupled bound states whose ionization amplitudes interfere constructively or destructively depending on the chirp direction under suitable conditions. We derive the phenomenon in a minimal model and verify the effect with calculations for helium as a realistic example.
... Various fields of contemporary physics require atoms and molecules prepared in specified quantum states which are crucial in many areas of modern atomic and molecular physics, such as quantum information, atom optics, laser-controlled chemical reactions and state-to- state collision. In the last two or three decades, many efficient schemes were proposed and employed for the population transfer, such as adiabatic passage (1)(2)(3), tem- poral coherent control (4-6) and stimulated Raman adi- abatic passage (7,8), opening new routes for coherent laser control of atomic and molecular processes (9)(10)(11)(12)(13). ...
https://www.tandfonline.com/eprint/5U6KhTZPaIaxk46Gbzsk/full
... Various fields of contemporary physics require atoms and molecules prepared in specified quantum states which are crucial in many areas of modern atomic and molecular physics, such as quantum information, atom optics, laser-controlled chemical reactions and state-to- state collision. In the last two or three decades, many efficient schemes were proposed and employed for the population transfer, such as adiabatic passage (1)(2)(3), tem- poral coherent control (4-6) and stimulated Raman adi- abatic passage (7,8), opening new routes for coherent laser control of atomic and molecular processes (9)(10)(11)(12)(13). ...
We report a scheme to achieve coherent population transfer in a four-level double-Lambda closed-loop atomic system by utilizing the coherent beams with Laguerre–Gaussian profiles. It is demonstrated that a maximal population transfer is achieved for a special value of the relative phase of the applied fields. We then compare the results with a similar configuration, but for the laser pulses with the usual Gaussian profiles and conclude that using the Laguerre–Gaussian modes can result in almost complete population transfer. Besides, the creation of a superposition between two lower states can be achieved through properly changing the relative phase. The suggested scheme may hold great practicality for the realization of the population transfer as well as creation of the superposition between states in the quantum systems with multiple states.
... The atomic variables C g and C e depend on z and t for a given detuning ∆. The detunings can be made time-dependent [14,15], position-dependent or both [16] but this is not the case here. ...
We review a series of quantum memory protocols designed to store the quantum information carried by light into atomic ensembles. In particular, we show how a simple semiclassical formalism allows to gain insight into various memory protocols and to highlight strong analogies between them. These analogies naturally lead to a classification of light storage protocols into two categories, namely photon echo and slow-light memories. We focus on the storage and retrieval dynamics as a key step to map the optical information into the atomic excitation. We finally review various criteria adapted for both continuous variables and photon-counting measurement techniques to certify the quantum nature of these memory protocols.
... 30,31 The RAP method is better known in atomic physics community for various applications. 32,33 More recently, it has also been beautifully implemented for mid-IR excitation by the Beck's group in surface scattering experiments. 8,26,31,34 In contrast to the direct absorption-an incoherent excitation, RAP is a coherent process. ...
In order to achieve a more efficient preparation of a specific ro-vibrationally excited reactant state
for reactive scattering experiments, we implemented the rapid adiabatic passage (RAP) scheme to
our pulsed crossed-beam machine, using a single-mode, continuous-wave mid-infrared laser. The
challenge for this source-rotatable apparatus lies in the non-orthogonal geometry between the molecular
beam and the laser propagation directions. As such, the velocity spread of the supersonic beam
results in a significantly broader Doppler distribution that needs to be activated for RAP to occur
than the conventional orthogonal configuration. In this report, we detail our approach to shifting,
locking, and stabilizing the absolute mid-infrared frequency. We exploited the imaging detection
technique to characterize the RAP process and to quantify the excitation efficiency. We showed that
with appropriate focusing of the IR laser, a nearly complete population transfer can still be achieved in
favorable cases. Compared to our previous setup—a pulsed optical parametric oscillator/amplifier in
combination with a multipass ring reflector for saturated absorption, the present RAP scheme with a
single-pass, continuous-wave laser yields noticeably higher population-transfer efficiency.
... Such a population transfer by adiabatic passage via a level crossing was initially implemented in nuclear magnetic resonance [25]. Laser-driven adiabatic passage in atoms and molecules was proposed by Treacy [26] and demonstrated first in the infrared by Stark-shifting the transition frequency [27] or by sweeping the laser frequency through resonance [28]. In the 80s, adiabatic passage was observed also in the near-infrared [29] and with visible light [30]. ...
We study adiabatic light transfer in systems of two coupled waveguides with spatially varying detuning of the propagation constants, providing an analogy to the quantum phenomena of rapid adiabatic passage (RAP) and two-state stimulated Raman adiabatic passage (two-state STIRAP). Experimental demonstration using a photoinduction technique confirms the robust and broadband character of the structures that act as broadband directional couplers and broadband beam splitters, respectively.
... The net result is complete population transfer from state 1/r 1 to state lCr 2. It should be appreciated that the adiabatic and diabatic intervals can occur in either ordering: the pump pulse may either precede or follow the Stark pulse. The SCRAP technique resembles the early experiment by Loy (1974), who used adiabatic quasistatic pulses of about 5 ms duration to induce Stark shifts. However, he induced two sequential population transfers per pulse--excitation for the leading edge and deexcitation for the trailing edge of each pulse as in the left column of Fig. 42--resulting in no net population transfer. ...
... It played an important role in atomic clocks by forming a Ramsey atomic interferometer [13]. Two-photon Rabi oscillation was also realized in an atomic Raman system where two strong driving fields are present [14]. Recently, Rabi oscillation between photons of Raman write field and the frequency-offset Stokes field was demonstrated [16] in Raman process where the driving field is a strong atomic spin wave. ...
Coherent wave splitting is crucial in interferometers. Normally, the waves after this splitting are of the same type. But recent progress in interactions between atom and light has led to the coherent conversion of photon to atomic excitation. This makes it possible to split an incoming light wave into a coherent superposition state of atom and light and paves the way for an interferometer made of different types of waves. Here we report on a Rabi-like coherent-superposition oscillation observed between an atom and light in a Raman process. We construct a new kind of hybrid interferometer based on the atom–light coherent superposition state. Interference fringes are observed in both the optical output intensity and atomic output in terms of the atomic spin wave strength when we scan either or both of the optical and atomic phases. Such a hybrid interferometer can be used to interrogate atomic states by optical detection and will find its applications in precision measurement and quantum control of atoms and light.
The lack of ability to determine and implement accurately quantum optimal control is a strong limitation to the development of quantum technologies. We propose a digital procedure based on a series of pulses where their amplitudes and (static) phases are designed from an optimal continuous-time protocol for given type and degree of robustness, determined from a geometric analysis. This digitalization combines the ease of implementation of composite pulses with the potential to achieve global optimality, i.e., to operate at the ultimate speed limit, even for a moderate number of control parameters. We demonstrate the protocol on IBM’s quantum computers for a single qubit, obtaining a robust transfer with a series of Gaussian or square pulses in a time T=382 ns for a moderate amplitude. We find that the digital solution is practically as fast as the continuous one for square subpulses with the same peak amplitudes.
Terahertz pulses with controlled spectral-temporal waveform have great potential in expanding the scope of state-of-the-art terahertz researches, such as terahertz-driven resonant and nonresonant control over matter and light, ultrafast terahertz spectroscopy, and terahertz-driven acceleration. Here, we propose and demonstrate a method to generate a prescribed terahertz chirped waveform with a well-designed tapered corrugated wakefield structure. We develop a deterministic procedure to derive the parameters of the corrugated structure that generates the desired spectral-temporal waveform with certain shape of chirp, central frequency, bandwidth, and pulse duration. The experimental results from ultrashort electron bunches passing through a well-designed tapered corrugated structure are demonstrated. Time-frequency analysis of the terahertz electric field measured by electro-optical sampling shows clear chirp from 0.38 to 0.6 THz. Calibrated measurements of the radiated energy indicate 10 µJ per pulse for an incident beam charge of 300 pC.
Adiabatic Rapid Passage (ARP) allows the inversion of atomic states much faster than absorption–spontaneous-emission cycles with a concomitant large increase in momentum exchange rate and, hence, the applied optical forces. We have implemented ARP with appropriate modulators and polarizers on metastable He atoms on the 23S→23P transition at λ≈ 1083.3 nm. We have measured the velocity dependence of this force and have been surprised by the appearance of large peaks in the magnitude of this force at regularly spaced velocity intervals. Such unexpected behavior suggests that unexpected coherence effects come into play in optical forces, including those used for laser cooling.
Much of the recent development of single-photon sources is driven by the desire to apply them to protocols and technologies that use the interference of two or more photons, such as quantum repeaters or boson sampling. In all of these cases, the indistinguishability of the produced photons is a key requirement. For those applications that want to scale to larger photon numbers, source efficiency is equally important. In this chapter, we will discuss two competing solutions, sources based on nonlinear optics and quantum dots, as the most-used single-quantum emitters.
A model of the process of adiabatic tracking on a system of size-quantized levels of isolated spherical quantum dots (QDs) in an electric field is proposed, which, due to the Stark effect, creates intervals between levels varied by the field. The method of perturbation theory for degenerate states is used to analyze the splitting and partial lifting of the degeneracy of levels in the lower part of the spectrum of a spherical QD. Using the pseudospin electric dipole vector model, we study the process of adiabatic inversion on a system of selected pairs of QD levels, the energy intervals between which are subject to a monotonous change by an external electric field. The course of the process of adiabatic tracking is analyzed in the case of a linear dependence of the electric field on time, at different values of the amplitude of the radiation pulse field. An asymmetry in the course of change in the amplitude profile of the inversion oscillations is revealed, which can affect the process of detecting non-stationary stimulated amplification. It is pointed out that it is possible to trace the inversion process, when the variation of the resonance detuning can be determined by the selection of the radii of the spherical QDs.
In contrast to light, matter-wave optics of quantum gases deals with interactions even in free space and for ensembles comprising millions of atoms. We exploit these interactions in a quantum degenerate gas as an adjustable lens for coherent atom optics. By combining an interaction-driven quadrupole-mode excitation of a Bose-Einstein condensate (BEC) with a magnetic lens, we form a time-domain matter-wave lens system. The focus is tuned by the strength of the lensing potential and the oscillatory phase of the quadrupole mode. By placing the focus at infinity, we lower the total internal kinetic energy of a BEC comprising 101(37) thousand atoms in three dimensions to 3/2 kB·38−7+6 pK. Our method paves the way for free-fall experiments lasting ten or more seconds as envisioned for tests of fundamental physics and high-precision BEC interferometry, as well as opens up a new kinetic energy regime.
The effect of the laser frequency tuning rate on a weak optical absorption line profile ~(10⁻⁵–10⁻⁷) cm⁻¹ under conditions when the molecules were in a high-quality optical resonator was studied. The authors used a diode laser and an analytical cavity with two pairs of mirrors with reflectivity of 99% and 99.98% in the ~1.4 μm region. Water vapor at reduced pressure (0.03–1) Torr served as an absorbing medium. A high spectral resolution was obtained by directing laser radiation into the cavity with a small offset relative to its axis (off-axis ICOS). The frequency tuning rate was varied within (10²–10³) cm⁻¹ s⁻¹. With the increase of the rate, a shift and asymmetry of the Doppler absorption profile were observed. When the tuning direction was changed and the rate was kept the same, the effect preserved in time and mirrored symmetrically on the frequency scale. The measurements were consistent with calculations that took into account the finite lifetime of photons in the cavity and the real ratio of the effective optical path to the coherence length of the laser radiation. Limitations on the frequency tuning rate were discussed using quantitative absorption spectroscopy methods for measuring molecule concentrations.
Dipole spin-wave states of atomic ensembles with wave vector k(ω) mismatched from the dispersion relation of light are difficult to access by far-field excitation but may support rich phenomena beyond the traditional phase-matched scenario in quantum optics. We propose and demonstrate an optical technique to efficiently access these states. In particular, subnanosecond laser pulses shaped by a home-developed wideband modulation method are applied to shift the spin wave in k space with state-dependent geometric phase patterning, in an error-resilient fashion and on timescales much faster than spontaneous emission. We verify this control through the redirection, switch off, and recall of collectively enhanced emission from a Rb87 gas with ∼75% single-step efficiency. Our work represents a first step toward efficient control of electric dipole spin waves for studying many-body dissipative dynamics of excited gases, as well as for numerous quantum optical applications.
The efficient transfer of excitations between different levels of a quantum system is a task with many applications. Among the various protocols to carry out such a state transfer in driven systems, rapid adiabatic passage (RAP) is one of the most widely used. Here we show both theoretically and experimentally that adding a suitable amount of loss to the driven Hamiltonian turns a RAP protocol into a scheme for encircling an exceptional point including the chiral state transfer associated with it. Our work thus discloses an intimate connection between a whole body of literature on RAP and recent studies on the dynamics in the vicinity of an exceptional point, which we expect to serve as a bridge between the disjoint communities working on these two scenarios.
We observe clear evidence of adiabatic passage between photon populations via a four-wave mixing process, implemented through a dispersion sweep arranged by a core diameter taper of an optical fiber. Photonic rapid adiabatic passage through the cubic electric susceptibility thus opens precise control of frequency translation between broadband light fields to all common optical media. Areas of potential impact include optical fiber and on-chip waveguide platforms for quantum information, ultrafast spectroscopy and metrology, and extreme light-matter interaction science.
We propose a method of laser isotope separation based on the phenomenon of adiabatic inversion and illustrate the method in a multilevel system consisting of a single ground state and multiplet excited states. In this model, population may be transferred from the ground state to one of the excited manifolds with nearly 100% efficiency by using laser pulses, the envelope of which rises slowly and then decays rapidly on an internal time scale that can be precisely calculated. Adiabatic inversion in this model is strongly dependent on the laser frequency, thus permitting separation of isotopes by faking advantage of small shifts in molecular or atomic energy level spacings. The criterion that determines whether a laser pulse is adiabatic also depends strongly on the laser frequency and thereby enhances the separation. We demonstrate the effectiveness of the method with a solution of the time-dependent Schroedinger equation for a specific model of two isotopes.
We present a method for the creation and control of cold molecules that involves coherently combining Feshbach resonances and stimulated Raman adiabatic passage. We present analytical and numerical results showing how to optimize this process that can be implemented using techniques readily available in standard experimental setups. This will provide a link in the chain from atoms to ground-state molecules and can serve as a building block towards more complex processes in coherent ultracold chemistry.
We study the conditions that must be met for successful preparation of a large ensemble in a specific target quantum state using Stark-induced adiabatic Raman passage (SARP). In particular, we show that the threshold condition depends on the relative magnitudes of the Raman polarizability (r0v) and the difference of the optical polarizabilities (Δα00→vj) of the initial (v = 0, j = 0) and the target (v, j) rovibrational levels. Here, v and j are the vibrational and rotational quantum numbers, respectively. To illustrate how the operation of SARP is controlled by these two parameters, we experimentally prepared D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0) in a beam of D2 (v = 0, j = 0) molecules using a sequence of partially overlapping pump and Stokes laser pulses. By comparing theory and experiment, we were able to determine the Raman polarizability r02 ≈ 0.3 × 10⁻⁴¹ Cm/(V/m) and the difference polarizabilities Δα00→20 ≈ 1.4 × 10⁻⁴¹ Cm/(V/m) and Δα00→22 ≈ 3.4 × 10⁻⁴¹ Cm/(V/m) for the two Raman transitions. Our experimental data and theoretical calculations show that because the ratio r/Δα is larger for the (0,0) → (2,0) transition than the (0,0) → (2,2) transition, much less optical power is required to transfer a large population to the (v = 2, j = 0) level. Nonetheless, our experiment demonstrates that substantial population transfer to both the D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0) is achieved using appropriate laser fluences. Our derived threshold condition demonstrates that with increasing vibrational quantum number, it becomes more difficult to achieve large amounts of population transfer.
The preparation of excitonic states in semiconductor quantum dots is a prerequisite for the application of quantum dots in quantum information technology, e.g., as source of single or entangled photons. For quantum dots embedded in the semiconductor matrix, the interaction with phonons significantly modifies the ideal preparation schemes. Due to the electron-phonon interaction Rabi rotations and the population inversion induced by excitation with chirped pulses can be damped, while an active use of phonons allows for a phonon-assisted state preparation. Under certain conditions the reappearance regime can be entered, in which the phonon influence is negligible. For a quantum dot in a cavity, the properties of the emitted light can also be modified by the phonons. In this review, the effects of electron-phonon interaction on the different optical state preparation protocols are explained and the latest experimental and theoretical results implementing these protocols are presented.
We demonstrate that, by changing the direction of the chirp in vacuum-ultraviolet pulses, one can switch between excitation and ionization with very high contrast, if the carrier frequency of the light is resonant with two bound states. This is a surprising consequence of rapid adiabatic passage if extended to include transitions to the continuum. The chirp phase locks the linear combination of the two resonantly coupled bound states whose ionization amplitudes interfere constructively or destructively depending on the chirp direction under suitable conditions. We derive the phenomenon in a minimal model and verify the effect with calculations for helium as a realistic example.
Optical forces on atoms irradiated with a single frequency of light have been extensively studied for many years, both theoretically and experimentally. The two-level atom model has been used to describe a wide range of optical force phenomena and to successfully exploit a large range of applications. New areas of study were opened up when the multiple levels of real atoms were considered. In contrast, using multifrequency light on a single atomic transition has not been studied as much, but using such light also results in very significant differences in the optical forces. This Colloquium outlines the basic concepts of forces resulting from the use of two-frequency light (bichromatic force) and swept frequency light (adiabatic rapid passage force). Both of these forces derive from stimulated processes only and as a result can produce coherent exchange of momentum between atoms and light. The consequences are impressively larger forces with comparably larger velocity capture ranges and even atom cooling without spontaneous emission.
The procedure of stimulated-Raman adiabatic passage (STIRAP), one of many well-established techniques for quantum-state manipulation, finds widespread application in chemistry, physics, and information processing. Numerous reviews discuss these applications, the history of its development, and some of the underlying physics. This tutorial supplies material useful as background for the STIRAP reviews as well as related techniques for adiabatic manipulation of quantum structures, with emphasis on the theory and simulation rather than on experimental results. It particularly emphasizes the picturing of behavior in various abstract vector spaces, wherein torque equations offer intuition about adiabatic changes. Appendices provide brief explanations of related coherent-excitation topics and useful evaluations of relative strengths of coherent transitions—the Rabi frequencies—involving Zeeman sublevels.
This document is part of Subvolume A 'Laser Fundamentals', Part 1 of Volume 1 'Laser Physics and Applications' of Landolt-Börnstein - Group VIII 'Advanced Materials and Technologies'. It contains: 1.1.1 The laser oscillator 1.1.2 The electromagnetic field 1.1.2.1 Maxwell's equations 1.1.2.2 Homogeneous, isotropic, linear dielectrics 1.1.2.2.1 The plane wave 1.1.2.2.2 The spherical wave 1.1.2.2.3 The slowly varying envelope (SVE) approximation 1.1.2.2.4 The SVE-approximation for diffraction 1.1.2.3 Propagation in doped media 1.1.3 Interaction with two-level systems 1.1.3.1 The two-level system 1.1.3.2 The dipole approximation 1.1.3.2.1 Inversion density and polarization 1.1.3.2.2 The interaction with a monochromatic field 1.1.3.3 The Maxwell-Bloch equations 1.1.3.3.1 Decay time T 1 of the upper level (energy relaxation) 1.1.3.3.1.1 Spontaneous emission 1.1.3.3.1.2 Interaction with the host material 1.1.3.3.1.3 Pumping process 1.1.3.3.2 Decay time T 2 of the polarization (entropy relaxation) 1.1.4 Steady-state solutions 1.1.4.1 Inversion density and polarization 1.1.4.2 Small-signal solutions 1.1.4.3 Strong-signal solutions 1.1.5 Adiabatic equations 1.1.5.1 Rate equations 1.1.5.2 Thermodynamic considerations 1.1.5.3 Pumping schemes and complete rate equations 1.1.5.3.1 The three-level system 1.1.5.3.2 The four-level system 1.1.5.4 Adiabatic pulse amplification 1.1.5.5 Rate equations for steady-state laser oscillators 1.1.6 Line shape and line broadening 1.1.6.1 Normalized shape functions 1.1.6.1.1 Lorentzian line shape 1.1.6.1.2 Gaussian line shape 1.1.6.1.3 Normalization of line shapes 1.1.6.2 Mechanisms of line broadening 1.1.6.2.1 Spontaneous emission 1.1.6.2.2 Doppler broadening 1.1.6.2.3 Collision or pressure broadening 1.1.6.2.4 Saturation broadening 1.1.6.3 Types of broadening 1.1.6.3.1 Homogeneous broadening 1.1.6.3.2 Inhomogeneous broadening 1.1.6.4 Time constants 1.1.7 Coherent interaction 1.1.7.1 The Feynman representation of interaction 1.1.7.2 Constant local electric field 1.1.7.3 Propagation of resonant coherent pulses 1.1.7.3.1.1 2π-pulse in a loss-free medium 1.1.7.3.1.2 π-pulse in an amplifying medium 1.1.7.3.2 Superradiance 1.1.8 Notations References for 1.1
We have developed a means to control rapidly frequency-chirped laser light at large detuning, by controlling the input modulation frequency of a \(\sim\)7 GHz signal into an electro-optical phase modulator in an injection-locked laser system. We show that we can extend the capabilities of the system to effectively pulse the laser on timescales less than 3 ns by turning the injection lock on/off and create arbitrary frequency-chirp shapes on the laser on the tens of nanosecond time scales. We have been able to use this pulsed frequency-chirped laser to control the excitation of a thermal Rb gas via rapid adiabatic passage.
Strong-field coherent control deals with the efficient excitation of a quantum system into a preselected final state. In order to understand the underlying control mechanisms, the transient dynamics of the laser-dressed states need to be considered in addition. In this paper, we present a route towards a complete picture of non-perturbative coherent control. To this end, we study near-resonant chirped excitation of potassium atoms as a model system for resonant strong-field control. Combining a two-colour pump–probe scheme with photoelectron spectroscopy, we simultaneously observe final state and transient excitation dynamics in the strongly driven atom. As demonstrated on the prototype scenario, the scheme enables a detailed understanding of the physical mechanisms governing the interaction. Our results highlight the power of two-colour time-resolved photoelectron spectroscopy to shed light onto the different aspects of non-perturbative coherent control.
Various effective-spin systems in atomic physics are investigated. The first example is the photon with its two states of circular polarization. The photon’s coherent superposition states can be mapped onto the surface of the Bloch sphere. The next example presents two atomic states involved in a resonance transition, driven by laser or microwave radiation. This leads to Rabi oscillations, photon free induction decay, quantum beats, photon echoes, and Ramsey signals. In molecular physics, a well known example of a two-state system is a nitrogen atom in the double-well potential of an ammonia molecule. A modern version of this experiment is a Bose–Einstein condensate in a double-well optical trap.
Quantum state-specific preparation and alignment of a molecular beam of methane are two central concepts in this thesis work. In this chapter, I explain the processes by which the molecules in the molecular beam are rovibrationally excited and aligned. Experimental evidence of the extent of state-specific preparation is shown.
As described in the introduction of Chap. 4, including Sects. 4.1 and 4.2. nonlinear interactions of light with matter are of fundamental importance for photonic applications. It may be worth with reading these sections before continuing.
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The phenomenological Bloch equations are solved for transient nutation in optical two-level systems, using the Feynman—Vernon—Hellwarth representation. The resulting solutions display an exponentially damped oscillatory behavior, from which the relaxation times T1 and T2 may be derived. Transient nutation signals were observed using time-resolved microwave spectroscopy with rapid switching of applied Stark fields. Observed collision relaxation rates are (5.25 ± 0.50) MHz/torr for OCS—OCS, (1.96 ± 0.30) MHz/torr for OCS—He and (1.67 ± 0.20) MHz/torr for OCS—Ar. For NH3NH3 relaxation the rate is (23.2 ± 3.5) MHz/torr for the (8,7) inversion line.
The effect of velocity-changing collisions on the optical phase memory of coherently prepared molecular gas samples is examined by the method of Stark-pulse switching. Experiments are interpreted through the solution of a transport equation, which extends the earlier Fokker-P1anck description known both in NMR and in Dicke line narrowing. The magnitude of a characteristic velocity jump for binary molecular collisions and its cross section are thereby obtained.
It is well known that collisions between molecules can influence their optical lineshape through changes in molecular velocity. Theoretical discussions 1 – 5 of this problem usually invoke a Brownian motion diffusion model in velocity space that is based on a solution of the Fokker-Planck equation.6,7 A Doppler or Gaussian lineshape is predicted for low pressure and a Lorentzian profile for high pressure, the width becoming narrower with increasing presure as first recognized by Dicke.1 To be valid, these treatments imply characteristically small Doppler phase changes ktΔurms ≪ 1 over the period of observation t where \(
\mathop {\rm{k}}\limits^ \to
\) is the propagation vector of light and Δurms is a characteristic velocity jump, essentially the root mean square change in velocity per collision.
The infrared vibration-rotation transitions ν2[qQ-(8,7)] of 14NH3 and ν2[qQ-(4,4)] of 15NH3 have been pumped by the P(13) and P(15) lines, respectively, of an N2O laser, and the resulting changes in the molecular populations of the rotational levels have been monitored by observing the microwave inversion lines. Large variations of the intensities of the monitored lines have been observed. In addition, small variations of neighboring inversion lines due to collision-induced transitions have also been found. The dependence of the efficiency of pumping on the frequency difference between the laser line and the NH3 absorption line (which was varied by using a Stark field) and on the pressure of the sample was studied. The results can be explained by using Karplus and Schwinger's theory of saturation and by taking into account a "hole burning" on the Doppler profile of the absorption line.
A transient two-photon process is observed in the infrared which exhibits all the co-operative properties associated with superradiant two-level systems. It arises when a cw laser beam excites a molecular sample whose level degeneracy is suddenly removed by a Stark field. The resulting emission, which heterodynes with the laser, gives precise ground- and excited-state Stark splittings, and decays with a homogeneous relaxation time since Doppler dephasing effects are absent in forward scattering.
The Stark spectrum of the ν2 band of 14NH3 is studied using CO2 and N2O lasers equipped with a grating for the laser line selection. About 100 coincidences between NH3 lines of J≤7 and the laser lines are obtained. The NH3 line positions relative to the laser lines are calculated using the data for the dipole moment obtained by the same experiment.
Adiabatic inversion at 10.6 and 10.3 microns wavelength has been observed by studying the transmission of chirped pulses generated by a carbon dioxide laser through samples of sulphur hexafluoride and ammonia at pressures in the range of 10−3 Torr to 10−2 Torr.
Adiabatic inversion of the populations between a pair of levels connected by electric dipole transitions is predicted when the system is subjected to a strong light pulse in which the carrier frequency is swept through the transition resonance.
The infrared vibration-rotation transitions ν2[qQ-(8,7)] of 14NH3 and ν2[qQ-(4,4)] of 15NH3 have been pumped by the P(13) and P(15) lines, respectively, of an N2O laser, and the resulting changes in the molecular populations of the rotational levels have been monitored by observing the microwave inversion lines. Large variations of the intensities of the monitored lines have been observed. In addition, small variations of neighboring inversion lines due to collision-induced transitions have also been found. The dependence of the efficiency of pumping on the frequency difference between the laser line and the NH3 absorption line (which was varied by using a Stark field) and on the pressure of the sample was studied. The results can be explained by using Karplus and Schwinger's theory of saturation and by taking into account a "hole burning" on the Doppler profile of the absorption line.
The absolute absorption intensities of the fundamental vibration bands in ammonia and phosphine have been measured. Normal coordinates are calculated for each of the vibrations and the intensities interpreted in terms of bond moments μ and their derivatives ∂μ/∂r.
Values of ∂μ/∂r for the NH and PH bonds in the A1 mode are 0.6 and 1.2 D/A, respectively; in the E mode the corresponding values are 0.2 and 0.8 D/A.
Values of the vibrational bond moments found are 1.0 D (A1) and 0.5 D (E) for the NH bond; 0.7 or 0.5 D (A1) and 1.2 or 0.6 D (E) for the PH bond.
The relation of these vibrational bond moments to the molecular dipole moment and the moment (μu.p.) of the unshared pair of electrons is discussed in detail. After corrections have been applied for changes in magnitude and direction of μu.p. during the vibrations, the results for NH3 are compatible with the following static moments: μNH∼0.7D(H+),μu.p.∼0.7D.The data for PH3 are less internally consistent. ``Likely'' moments, taken from the A1 bending vibration, are μPH∼0.2(H+), μu.p.∼0.2D.
The near coincidence of the P(16) line of the CO2 laser in 10.6 μm and the ν 2 [qR − (0,0)] line of 15NH3 was used to measure the pressure broadening and the absolute absorption coefficient of the latter transition. The pressure broadening parameter was determined to be Δνp=13.3±1.2 MHz∕torr, and the transition dipole moment of the ν2 vibrational transition was determined to be 0.239 D.
The velocity‐selective characteristic of the interaction between a monochromatic radiation field and a Doppler‐broadened molecular transition is utilized to obtain a narrow saturation resonance for molecules with a given velocity component along the propagation direction of the radiation field. The width of the observed resonance gives the dependence of collision broadening on molecular velocity. The effect is observed in an infrared transition in NH 3 for self‐broadening and foreign gas broadening by Xe.
A simple application of the Stark-pulse technique, developed by Brewer and Shoemaker, demonstrates optical free induction decay-the optical analog of free induction decay in NMR. A molecular sample which is coherently prepared by a cw laser beam exhibits such a decay when it is suddenly switched out of resonance by a Stark field. Observations are presented for a nondegenerate Doppler-broadened infrared transition of N${\mathrm{H}}_{2}$D, where the sample is optically thin, and the decay behavior can be compared quantitatively with a solution of the Bloch equations. When the molecular sample is prepared under steady-state conditions, the solutions are analytic; for pulse excitation, a numerical solution is required. The treatment invokes a hard-collision relaxation model. Such characteristics as the abrupt termination of the decay and the related edge echo, which result from Doppler dephasing, can be examined for Stark pulses of finite extent.
Photon echo and optical nutation have been easily observed in ${\mathrm{C}}^{13}$${\mathrm{H}}_{3}$F and N${\mathrm{H}}_{2}$D by applying Stark pulses which shift the molecular levels into resonance with cw laser radiation. Numerical computations of the nutation effect agree with observation, and echo characteristics closely follow predictions of existing theories. The $T_{2}^{}{}_{}{}^{$'${}}$ pressure dependence, from infrared-echo measurements, indicates that ${\mathrm{C}}^{13}$${\mathrm{H}}_{3}$F relaxes primarily by rotational energy transfer.
Four separate shots at increasing Stark pulse durations are displayed
- Msec
Msec/div. Four separate shots at increasing Stark pulse durations are displayed.