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.

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