Comparison of Quantum and Semiclassical Rabi models near multiphoton resonances in the presence of parametric modulation

TL;DR

This paper compares semiclassical and quantum models of a two-level atom interacting with a modulated electromagnetic field near multiphoton resonances, highlighting their agreement at short times and differences at longer durations.

Contribution

It provides approximate analytic solutions for the semiclassical Rabi model under parametric modulation and compares these with numerical quantum predictions in the multiphoton resonance regime.

Findings

Semiclassical and quantum dynamics agree at initial times for intense coherent states.

The models diverge at longer times due to collapse-revival phenomena.

Field state modifications are characterized through photon number statistics and entropies.

Abstract

We compare the semiclassical and quantum predictions for the unitary dynamics of a two-level atom interacting with a single-mode electromagnetic field in the presence of parametric modulation of the atomic parameters, in the regime of multiphoton atom-field resonances. We derive approximate analytic solutions for the semiclassical Rabi model when the atomic transition frequency and the atom-field coupling strength undergo harmonic external modulations. These solutions are compared to the predictions of the quantum Rabi model, which is solved numerically for the initial coherent state with a large average photon number, of the order of $10^4$, in the regime of three-photon resonance. We show that for initial times and sufficiently intense coherent state the semiclassical dynamics agrees quite well with the quantum one, although for large times it inevitably fails due to the lack of the collapse-revival behavior. Furthermore, we describe how the field state is modified throughout the evolution, presenting numeric results for the average photon number, entropies (related to the atom-field entanglement) and other quantities that characterize the photon number statistics of the electromagnetic field.