Abstract
We assess the suitability of quantum and semiclassical initial-value representations (IVRs), exemplified by the coupled coherent states (CCS) method and the Herman–Kluk (HK) propagator, respectively, for modeling the dynamics of an electronic wave packet in a strong laser field, if this wave packet is initially bound. Using Wigner quasiprobability distributions and ensembles of classical trajectories, we identify signatures of over-the-barrier and tunnel ionization in phase space for static and time-dependent fields and the relevant sets of phase-space trajectories to model such features. Overall, we find good agreement with the full solution of the time-dependent Schrödinger equation (TDSE) for Wigner distributions constructed with both IVRs. Our results indicate that the HK propagator does not fully account for tunneling and over-the-barrier reflections. This leads to a dephasing in the time-dependent wave function, which becomes more pronounced for longer times. However, it is able to partly reproduce features associated with the wave packet crossing classically forbidden regions, although the trajectories employed in its construction always obey classical phase-space constraints. We also show that the CCS method represents a fully quantum initial value representation and accurately reproduces the results of a standard TDSE solver. Finally, we show that the HK propagator may be successfully employed to compute the time-dependent dipole acceleration and high-harmonic spectra. Nevertheless, the outcome of the semiclassical computation exhibits disagreements with the TDSE, as a consequence of the previously mentioned dephasing.
Highlights
Initial-value representations (IVRs) such as the coupled coherent states method [1] and the Herman Kluk propagator [2] are widely used in many areas of science
This efficiency may be increased by employing several strategies, such as dominant Hamiltonians in specific phase-space regions [3, 4], or quantum-state reprojection [5, 6]. All these features make initial-value representations very attractive to strong-field and attosecond science. It is well known since two decades that strong-field phenomena such as high-order harmonic generation (HHG), abovethreshold ionization (ATI) or nonsequential double ionization (NSDI), may be described as the result of the laser-induced scattering or recombination of an electron with its parent ion [7]
The results presented in this paper strongly suggest that semiclassical initial-value representations, a concrete example of which is the Herman Kluk propagator, may be employed for describing strong-field wave-packet dynamics, even if this wave packet is initially bound and located within the core region
Summary
Initial-value representations (IVRs) such as the coupled coherent states method [1] and the Herman Kluk propagator [2] are widely used in many areas of science These approaches allow an intuitive interpretation of a time-dependent wave packet in terms of trajectories in phase space, and account for binding potentials, external fields and quantum-interference effects. Ensembles of electrons that behave according to the above-mentioned recollision picture are constructed in order to mimic the behavior of the quantum mechanical wave packet and both the external laser field and the binding potentials are fully incorporated This is the key idea behind classical-trajectory methods, which have reproduced key features such as the low-energy structure in ATI [12] and the Vshaped structure observed in NSDI [13, 14]. In the Appendix we discuss the fact that the HK and the CCS methods share a common origin
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