Quasienergy description of the driven Jaynes-Cummings model

TL;DR

This paper introduces a quasienergy framework for analyzing the driven Jaynes-Cummings model, revealing how multiphoton transitions and tunneling phenomena influence the system's nonlinear response, with applications in superconducting circuit QED.

Contribution

It develops a nonperturbative quasienergy approach to the driven Jaynes-Cummings model, connecting multiphoton transitions with resonant tunneling and metastable quasienergy wells.

Findings

Quasienergy surface exhibits level spacing governed by an effective Planck constant.

Multiphoton transitions interpreted as resonant tunneling events.

Stationary states form as mixtures of localized quasienergy states, affecting nonlinear response.

Abstract

We analyze the driven resonantly coupled Jaynes-Cummings model in terms of a quasienergy approach by switching to a frame rotating with the external modulation frequency and by using the dressed atom picture. A quasienergy surface in phase space emerges whose level spacing is governed by a rescaled effective Planck constant. Moreover, the well-known multiphoton transitions can be reinterpreted as resonant tunneling transitions from the local maximum of the quasienergy surface. Most importantly, the driving defines a quasienergy well which is nonperturbative in nature. The quantum mechanical quasienergy state localized at its bottom is squeezed. In the Purcell limited regime, the potential well is metastable and the effective local temperature close to its minimum is uniquely determined by the squeezing factor. The activation occurs in this case via dressed spin flip transitions rather than via quantum activation as in other driven nonlinear quantum systems such as the quantum Duffing oscillator. The local maximum is in general stable. However, in presence of resonant coherent or dissipative tunneling transitions the system can escape from it and a stationary state arises as a statistical mixture of quasienergy states being localized in the two basins of attraction. This gives rise to a resonant or an antiresonant nonlinear response of the cavity at multiphoton transitions. The model finds direct application in recent experiments with a driven superconducting circuit QED setup.