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

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.

Comments welcome. 20 pages, 9 figures

References in corpus (14)

• Circuit Quantum Electrodynamics
• The quantum Rabi model: solution and dynamics
• First-order sidebands in circuit QED using qubit frequency modulation
• Quantum amplification and simulation of strong and ultrastrong coupling of light and matter
• Superconducting cavity qubit with tens of milliseconds single-photon coherence time
• Selective Interactions in the Quantum Rabi Model
• Multiphoton resonance and chiral transport in the generalized Rabi model
• Photon creation from vacuum and interactions engineering in nonstationary circuit QED
• Defining the semiclassical limit of the quantum Rabi Hamiltonian
• Analytical comparison of the first- and second-order resonances for implementation of the dynamical Casimir effect in nonstationary circuit QED
• Bloch-Siegert oscillations in the Rabi model with an amplitude-modulated driving field
• Effective and efficient resonant transitions in periodically modulated quantum systems
• Averaging method and coherence applied to Rabi oscillations in a two-level system
• Spectrum analysis with parametrically modulated transmon qubits