Quantum and semiclassical phase-space dynamics of a wave packet in strong fields using initial-value representations

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 phasespace 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.

Near-threshold photoelectron holography beyond the strong-field approximation

“…The initial spread of the electronic wave packet has been shown to be necessary for a good quantitative agreement with the TDSE in the context of high-order harmonic generation (HHG) [53][54][55][56]. This initial spread seems to be very important for strong-field ionization as well, as recent phase-space studies revealed that orbit-based methods that incorporate this spread exhibit a nearly quantitative agreement with the TDSE, even if tunnel ionization is not properly accounted for [57]. In addition, in the very low-energy region of the spectra, the CQSFA simulation exhibits a marked discrepancy with respect to the TDSE result.…”

“…This may be due to the initial momentum and position spread that exists for the TDSE, but is absent for the CQSFA. In fact, recent studies on HHG [53][54][55][56] and strong-field ionization [57] indicate that this spread is necessary for a quantitative agreement with the TDSE.…”

Quantum bridges in phase space: interference and nonclassicality in strong-field enhanced ionisation

“…Wigner functions have been widely employed in quantum optics and quantum information, but are underused in strong-field and attosecond physics. There are however studies of ionisation [18,40,43,44], rescattering [45,46] and entanglement [47] in this context. In strong-field ionisation, seminal studies [43] for a zero-range potential in a static field identified a tail that could be associated with a classical tunnelling trajectory far from the core region, and with tunnel ionisation close to the core.…”

Coupled-coherent-states approach for high-order harmonic generation

“…As mentioned earlier, this reordering results in changes to the effective potential, giving a shallower potential than the form in coordinate representation such as that used in [42]. The kinetic energy term of the Hamiltonian is obtained through operator reordering and the potential terms through integration with equation (1).…”

“…A similar version of the CCS method to that reported here has been used previously in Ref. [42] for the study of quantum dynamics in phase space. In Section II we provide the necessary theory in order to understand our results including an overview of the CCS method and its governing equations (sections II A and II B), a description of the theoretical model used to show the efficacy of the CCS method for generating HHG spectra (section II C) and a description of the necessary modifications made to the CCS method in order to model this system (section II D).…”