Abstract
In this paper, we analytically and numerically study the sideband interaction dynamics of the driven quantum Rabi model (QRM). We focus in particular on the conditions when the external transverse drive fields induce first-order sideband interactions. Inducing sideband interactions between two different systems is an essential technique for various physical models, including the QRM. However, despite its importance, a precise analytical study has not been reported yet that successfully explains the sideband interaction rates in a driven QRM applicable for all system parameter configurations. In our paper, we analytically derive the sideband interaction rates based on second-order perturbation theory, not relying on the rotating wave approximation (RWA). Our formula are valid for all ranges of drive frequencies and system's parameters. Our analytical derived formula agrees well with the numerical results in a regime of moderate drive amplitudes. Interestingly, we have found a nontrivial longitudinal drive effect derived from the transverse drive Hamiltonian. This accounts for significant corrections to the sideband interaction rates that are expected without considering the derived longitudinal effect. Using this approach, one can precisely estimate the sideband interaction rates in the QRM not confining themselves within specific parameter regimes for moderate drive amplitudes. This provides important contributions for quantitatively understanding experiments described by the driven QRM.
Highlights
The quantum Rabi model (QRM) [1] constitutes the essence of the light-matter interactions at the quantum level
We investigate the parameter regimes that are familiar in circuit quantum electrodynamics (QED) experiments
We investigate if the transverse drive field accounts for a derived longitudinal drive effect, which significantly contributes to the total sideband interaction rates
Summary
The quantum Rabi model (QRM) [1] constitutes the essence of the light-matter interactions at the quantum level. The systems can be modeled by the QRM These cases successfully demonstrate the state transfer from the qubit to the cavity, introducing tuneability into the qubit’s transition frequency leads to another side-effect: Pure dephasing induced by external noise. Whereas a number of studies have examined how the external transverse drive fields affect the qubits or similar systems beyond the RWA [12,13,14,15,16], and there are a few studies quantitatively discussing the sideband interaction rates between the qubits and cavities [9,11,17,18,19,20], a satisfactory quantitative study of the driven QRM beyond the RWA regime and considering the derived longitudinal drive effect has not yet been reported.
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