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Determination of the peak intensity.The peak intensity in the laser focus is inferred from the momentum spectra of Ar+ ions (parallel to the polarization axis) by comparison with simulations. The measured Ar+ spectrum (open circles) is plotted together with simulated spectra calculated for three different intensities: 3.0×1014 W cm−2 (red line), 2.4×1014 W cm−2 and 3.6×1014 W cm−1 (narrow and wide black spectra respectively). The gray area in-between the two black curves represents the error bars of ±20% in the determination of the peak intensity.
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Despite their broad implications for phenomena such as molecular bonding or chemical reactions, our knowledge of multi-electron dynamics is limited and their theoretical modelling remains a most difficult task. From the experimental side, it is highly desirable to study the dynamical evolution and interaction of the electrons over the relevant time...
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Citations
... Classical approaches also comprise the overwhelming majority of NSDI studies in tailored fields [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], with good qualitative agreement with experiments. Furthermore, whenever quantum methods such as the strong-field approximation (SFA) [18,19,[37][38][39][40] the quantitative rescattering theory (QRS) [41][42][43][44], or the full numerical solution of the time-dependent Schrödinger equation (TDSE) [45][46][47][48][49][50] have been used, the emphasis was on the shapes of the electron momentum distributions due to the type of electron-electron interaction [45,46] or the field shape [47,48], and the physical mechanisms behind them. ...
... Fourth, there will be broken symmetries for fixed CEPs, which will influence the electron-momentum distributions and the quantum phase differences leading to interference patterns. Evidence that the fourfold symmetry is broken is provided in previous work [37,38], where we have studied the influence of the CEP on single-channel RESI distributions, and in experiments [23,63]. Therein, quantum interference was not included. ...
We perform a systematic analysis of single-channel quantum interference in laser-induced nonsequential double ionization with few-cycle pulses, using the strong-field approximation. We focus on a below-threshold intensity for which the recollision-excitation with subsequent ionization (RESI) mechanism is prevalent. We derive and classify several analytic interference conditions for single-channel RESI in arbitrary driving fields and address specific issues for few-cycle pulses. Since the cycles in a short pulse are no longer equivalent, there are several events whose dominance varies. We quantify this dominance for single excitation channels by proposing a dominance parameter. Moreover, there will be many types of superimposed interference fringes that must be taken into consideration. We find an intricate tapestry of patterns arising from phase differences related to symmetrization, temporal shifts and a combination of exchange and event interference.
Published by the American Physical Society 2024
... variety of physics topics. In the last three decades, strong electric field ionization of atoms and molecules has attracted a great deal of experimental and theoretical interest due to its abundance of nonlinear physical processes, such as high-harmonic generation (HHG) [1][2][3] and nonsequential double ionization (NSDI) [4][5][6][7][8][9]. In the presence of a weak electric field, the spectral levels of the atomic bound states are typically split and shifted, resulting in the well-known Stark effect [10][11][12]. ...
In this paper, we revisit the Stark effect of the hydrogen atom induced by a uniform static electric field. In particular, a general formula for the integral of associated Laguerre polynomials was derived by applying the method for Hermite polynomials of degree n proposed in the work [Anh-Tai T.D. et al., 2021 AIP Advances \textbf{11} 085310]. The quadratic Stark effect is obtained by applying this formula and the time-independent non-degenerate perturbation theory to hydrogen. Using the Siegert State method, numerical calculations are performed and serve as data for benchmarking. The comparisons are then illustrated for the ground and some highly excited states to provide an insightful look at the applicable limit and precision of the quadratic Stark effect formula for other atoms with comparable properties.
... The most detailed information about NSDI that experimental measurements can provide are the correlated twoelectron momentum distributions (CMDs). Since the first experiment conducted at the turn of this century, in which the CMDs for NSDI of Ar were measured by Weber et al [7], a number of kinematically complete measurements have been performed [2,[8][9][10][11][12][13][14][15][16]. All the above mentioned experimental measurements of CMDs are for NSDI of atoms in linearly polarized laser pulses and so far the mechanisms behind most of characteristic structures in the measured CMDs have been extensively investigated. ...
... All the above mentioned experimental measurements of CMDs are for NSDI of atoms in linearly polarized laser pulses and so far the mechanisms behind most of characteristic structures in the measured CMDs have been extensively investigated. Here are some particularly noteworthy examples: (i) The prominent fingerlike structure observed in the CMD for helium [10] has been intensively investigated by various theoretical models and all theoretical studies confirmed that the fingerlike structure is a consequence of the Coulomb interaction between the two emitted electrons [10,17,18]; (ii) The anticorrelated back-to-back emission of the two electrons along the polarization direction in the CMDs for Ar below the recollision threshold [12,13] has attracted a large number of theoretical studies [12,[19][20][21][22][23][24][25][26][27][28] despite that the assignment of the observed anticorrelation to specific mechanisms is still debateable [29]; (iii) Considerable theoretical efforts, by employing a simple onedimensional semiclassical model [14], a three-dimensional (3D) classical ensemble model [30], a 3D semiclassical model without using a free parameter [31], and the quantitative rescattering model (QRS) [32], have been devoted to unveiling the mechanism responsible for the cross-shaped structure observed in the carrier-envelope phase-averaged CMD in the near-single-cycle limit [14]. ...
... All the above mentioned experimental measurements of CMDs are for NSDI of atoms in linearly polarized laser pulses and so far the mechanisms behind most of characteristic structures in the measured CMDs have been extensively investigated. Here are some particularly noteworthy examples: (i) The prominent fingerlike structure observed in the CMD for helium [10] has been intensively investigated by various theoretical models and all theoretical studies confirmed that the fingerlike structure is a consequence of the Coulomb interaction between the two emitted electrons [10,17,18]; (ii) The anticorrelated back-to-back emission of the two electrons along the polarization direction in the CMDs for Ar below the recollision threshold [12,13] has attracted a large number of theoretical studies [12,[19][20][21][22][23][24][25][26][27][28] despite that the assignment of the observed anticorrelation to specific mechanisms is still debateable [29]; (iii) Considerable theoretical efforts, by employing a simple onedimensional semiclassical model [14], a three-dimensional (3D) classical ensemble model [30], a 3D semiclassical model without using a free parameter [31], and the quantitative rescattering model (QRS) [32], have been devoted to unveiling the mechanism responsible for the cross-shaped structure observed in the carrier-envelope phase-averaged CMD in the near-single-cycle limit [14]. ...
We use the improved quantitative rescattering (QRS) model to simulate the experimentally measured correlated two-electron momentum
distributions (CMDs) for nonsequential double ionization (NSDI) of Ne exposed to intense elliptically polarized laser pulses with
a central wavelength of 788 nm at a peak intensity of 5$\times10^{14}$ W/cm$^2$ for the ellipticities ranging from 0 to 0.25
[Kang \emph{et al} 2018 \emph{Phys. Rev. A} {\bf 97} 063403].
Only the CMDs for recollision direct ionization (RDI) are calculated and the contribution from recollision excitation with
subsequent ionization (RESI) is ignored. With the assumption that recollisions occur after the zero crossing of the electric
field along the major polarization, the QRS model successfully reproduces the experimentally observed asymmetry pattern of electron
pairs in the CMDs for NSDI of Ne under elliptical polarization. By reducing the peak intensity claimed in experiment by about 30\%,
good agreement is achieved between the present results and the experimental measurements.
... 近年来，随着激光技术的发展，强激光场中原子分子的动力学问题越来越 受到人们的关注 [1,2] 。当原子、分子与强激光场相互作用时，可以发现许多新的 物理现象，如阈上电离 [3][4][5] 、强场光电子全息 [6,7] 、高次谐波的产生 [8,9] 和非序列 双电离(nonsequential double ionization, NSDI) [10][11][12] 等。近几十年来，由于 NSDI 中存在强烈的电子关联现象 [13][14][15] ，如碰撞激发电离(recollision-induced direct 2 ionization, RII) [16,17] 、 碰 撞 激 发 场 致 电 离 (recollision-induced excitation with subsequent field ionization, RESI) [18] 和 NSDI 的多重碰撞 [19] 等, 而引起研究人员 的关注。 在强激光场与原子、分子相互作用时，NSDI 过程可以用三步模型来解释 [20,21] 。首先，当原子、分子处于强激光场中时，第一个电子(返回电子)通过隧 穿电离释放出来 [22] ，然后释放的电子在激光场的驱动下回到母离子附近，并与 第二个电子(束缚电子)发生重碰撞 [20,23] 。在这个过程中，由于两个电子发生了 重碰撞，返回电子会将部分能量传递给束缚电子，束缚电子可能会发生 RII 或 RESI。由于重碰撞过程的存在，NSDI 中两个电子的行为存在关联性，对此人 们进行了大量的理论和实验研究 [24,25] 。早期，NSDI 经常发生在线偏振激光场驱 动原子的情况下，而对于椭圆偏振激光场和圆偏振激光场，由于旋转的电场会 带来横向的漂移速度，使返回电子远离母离子，进而阻止了重碰撞过程 [26,27] 。 所以人们的研究主要集中于线偏振激光场和平行双色激光场来驱动 NSDI。近年 来，由两个不同频率的圆偏振激光场组成的双色圆偏振激光场(two-color circularly polarized, TCCP)得到了研究人员的关注 [28,29] ，由于它具有特殊的电场 结构和更多的可调参数，故对 TCCP 激光场的研究成为热点之一 [30][31][32][33] 。其中， ...
Electron correlation behaviors and recollision dynamics in nonsequential double ionization (NSDI) of Ar atoms in counter-rotating two-color elliptically polarized (TCEP) laser fields are investigated with the classical ensemble model. The combined electric field in counter-rotating TCEP laser pulses traces out a trefoil pattern, i.e., the waveform in a period shows three leaves in different directions, and each leaf is called a lobe. Different from counter-rotating two-color circularly polarized laser fields, the combined electric field has no spatial symmetry. The amplitudes of the three field lobes and the angles between them are different. Thus, the returning electron mainly returns to the parent ion from one direction, and the electron momentum distributions show strong asymmetry. Numerical results show that the NSDI yield gradually decreases as the ellipticity increases, and the correlated behavior of the correlated electron momentum along the long axis of the laser polarization plane gradually evolves from correlation behavior mainly located in the first and third quadrants to anti-correlation behavior mainly located in the second and fourth quadrants. In order to further understand the correlation behaviors of electron pairs, different characteristic times in the NSDI processes are discussed, respectively. It is found that single ionization events and recollision events gradually decrease, but single ionization time and recollision time change slightly. This may be the main reason for the decrease in NSDI yield. And as the ellipticity increases, the traveling time and the recollision energy gradually decrease, while the delay time increases. Therefore, we can conclude that ellipticity may be responsible for the NSDI processes. In addition, further analysis finds that the shape of the trajectories becomes more and more triangular as the ellipticity increases due to the counter-rotating TCEP laser fields of the specific dynamical symmetries of the total net electric field. And it is found that whether it is a “short trajectory” or a “long trajectory”, more of the population moves to the second and fourth quadrants as the ellipticity increases. The results show that increasing the ellipticity will gradually change the two electrons from emitting in the same direction to emitting in the opposite direction. This well demonstrates that both ellipticity and travelling time are responsible for the formation of the electron momentum distribution at the recollision time, meaning that both of them affect the emitted directions of both electrons.
... [20] This ionization process is called NSDI. [21][22][23] In this process, the two electrons generated by the recollision process are highly correlated, which has attracted extensive attention from experimental [24,25] and theoretical researchers. [26,27] With the deepening of research, the driving field used in the study of NSDI has gradually shifted from linearly polarized light to more complex light fields, such as counterrotating and co-rotating two-color circularly polarized (TCCP) laser fields. ...
The double ionization process of molecules driven by co-rotating two-color circularly polarized fields is investigated with a three-dimensional classical ensemble model. Numerical results indicate that a considerable part of the sequential double ionization (DI) events of molecules occur through internal collision double ionization (ICD), and the ICD recollision mechanism is significantly different from that in non-sequential double ionization (NSDI). By analyzing the results of internuclear distances R =5 a.u. and 2 a.u., these two recollision mechanisms are studied in depth. It is found that the dynamic behavior of the recollision mechanism of NSDI and ICD is similar. For NSDI, the motion range of electrons after the ionization is relatively large, and the electrons will return to the core after a period of time. While the ICD process electrons will rotate around the parent ion before ionization, and the distance of the electron motion is relatively small. After a period of time, the electrons will come back to the core and collides with another electron. Furthermore, the molecular internuclear distance has a significant effect on the electron dynamic behavior of the two ionization mechanisms. This study will help to understand the multi-electron ionization process of complex systems.
... A large number of theoretical and experimental studies have been performed to explore the correlated dynamics of the two electrons in NSDI. Two recollision mechanisms, recollision-impact ionization (RII) [20,21] and recollision-induced excitation with subsequent ionization (RESI) [22], in the NSDI process have been found. These two recollision mechanisms can be distinguished by the delay time. ...
... The shape of the ion momentum distribution is consistent with the shape of the negative vector potential of the electric field. Similar structures have been extensively studied both experimentally and theoretically [19,22]. In these studies, the results and analysis show that the RII is an important reason for the structure. ...
Using the classical ensemble model, we investigate the effect of laser wavelength on the electron dynamics process of nonsequential double ionization (NSDI) for linear triatomic molecules driven by a counter-rotating two-color circularly polarized laser field. Based on the delay time between recollision and final double ionization, two particular ionization channels are separated: recollision-impact ionization (RII) and recollision-induced excitation with subsequent ionization (RESI). Numerical results show that with the increase of the laser wavelength, the triangle structure of the ion momentum distribution becomes more obvious, which indicates that the electron–electron correlation of NSDI is enhanced. In addition, we find that the ratio of the RESI channel gradually decreases with the increase of the laser wavelength, while the ratio of the RII channel is opposite. However, the dominant channel is still RESI. It means that the two ionization channels can be controlled effectively by changing the laser wavelength.
... Thanks to the increase in intensity of ionizing pulses at x-ray Free-Electron-Laser facilities (XFELs) as well as with table-top setups, the use of XUV-pump XUV-probe schemes to study unperturbed correlated electronic motion in real time is on the horizon [4][5][6]. In these studies, double ionization plays a central role both because of its unique sensitivity to electronic correlation and because it enables the detection of correlated electron pairs in coincidence [7][8][9]. ...
As a step toward the full \emph{ab-initio} description of two-photon double ionization processes, we present a finite-pulse version of the virtual-sequential model for polyelectronic atoms. The model relies on the \emph{ab initio} description of the single ionization scattering states of both the neutral and ionized target system. As a proof of principle and a benchmark, the model is applied to the helium atom using the {\tt NewStock} atomic photoionization code. The results of angularly integrated observables, which are in good agreement with existing TDSE (time-dependent Schr\"odinger equation) simulations, show how the model is able to capture the role of electron correlation in the non-sequential regime at a comparatively modest computational cost. The model also reproduces the two-particle interference with ultrashort pulses, which is within reach of current experimental technologies. Furthermore, the model shows the modulation of the joint energy distribution in the vicinity of autoionizing states, which can be probed with XUV pulses of duration much longer than the characteristic lifetime of the resonance. The formalism discussed here applies also to polyelectronic atoms and molecules, thus opening a window on non-sequential and sequential double ionization in these more complex systems.
... Conclusions 10 variety of physics topics. In the last three decades, strong electric field ionization of atoms and molecules has attracted a great deal of experimental and theoretical interest due to its abundance of nonlinear physical processes, such as high-harmonic generation (HHG) [1][2][3] and nonsequential double ionization (NSDI) [4][5][6][7][8][9]. In the presence of a weak electric field, the spectral levels of the atomic bound states are typically split and shifted, resulting in the well-known Stark effect [10][11][12]. ...
In this article, we revisit the Stark effect of hydrogen atom induced by a uniform static electric field. In particular, a general formula for the integral of associated Laguerre polynomials was derived by applying the method for Hermite polynomials of degree n proposed in the work [Anh-Tai T.D. et al., 2021 AIP Advances 11 085310]. The quadratic Stark effect is obtained by applying this formula and the time-independent non-degenerate perturbation theory to hydrogen. Using the Siegert State method, numerical calculations are performed and serve as data for benchmarking. The comparisons are then illustrated for the ground state and some highly excited states of hydrogen to provide an insightful look at the applicable limit and precision of the quadratic Stark effect formula for other atoms with comparable properties.
... The ionization time can thus be mapped into the drift momentum under the strong laser, while the PMD can reveal the correlated drift momentum distribution. Previous studies of the finger-like patterns [14,15], the anti-correlated PMD [16][17][18][19] and other specific PMD structures [20,21], have greatly improved our understanding of NSDI. Thus, one may expect that PMD could still shed light about unexplored NSDI dynamics. ...
... Upon now, we have understood the main mechanisms of NSDI under mid-IR laser fields, however, how will the PMD evolve when the mid-IR laser field changes its parameters, such as the pulse duration, remains still unexplored. Studies based on the evolution of the PMD, just like NSDI in near 800 nm laser fields [20,32,33], can advance our knowledge about the strong-field NSDI dynamics. ...
We present a joint experimental and theoretical study of non-sequential double ionization (NSDI) in argon driven by a 3100-nm laser source. The correlated photoelectron momentum distribution (PMD) shows a strong dependence on the pulse duration, and the evolution of the PMD can be explained by an envelope-induced intensity effect. Determined by the time difference between tunneling and rescattering, the laser vector potential at the ionization time of the bound electron will be influenced by the pulse duration, leading to different drift momenta. Such a mechanism is extracted through a classical trajectory Monte Carlo-based model and it can be further confirmed by quantum mechanical simulations. This work sheds light on the importance of the pulse duration in NSDI and improves our understanding of the strong field tunnel-recollision dynamics under mid-IR laser fields.
... For linearly polarized light or for suitable two-color laser fields the electron can exchange energy with its parent ion by inelastic recollisions. Examples for processes which are enabled by electrons that return to their parent ions are the recombination of the tunneled electron with its parent ion [2,3], which can lead to the emission of high order harmonics [4][5][6], excitation of the parent ion [7], or nonsequential double ionization [8][9][10][11][12][13][14]. Previous studies in the strong field regime observed such energy exchange only if the electron recollided with its parent ion during the photoionization process. ...
We report on the strong field ionization of H2 by a corotating two-color laser field. We measure the electron momentum distribution in coincidence with the kinetic energy release (KER) of dissociating hydrogen molecules. In addition to a characteristic half-moon structure, we observe a low-energy structure in the electron momentum distribution at a KER of about 3.5 eV. We speculate that the outgoing electron interacts with the molecular ion, despite the absence of classical recollisions under these conditions. Time-dependent density functional theory simulations support our conclusions.
