Quantum phase transition of the Jaynes-Cummings model

Abstract: Herein, we propose an experimentally feasible scheme to show the quantum phase transition of the Jaynes-Cummings (JC) model by modulating the transition frequency of a two-level system in a quantum Rabi model with strong coupling. By tuning the modulation frequency and amplitude, the ratio of the effective coupling strength of the rotating terms to the effective cavity (atomic transition) frequency can enter the deep-strong coupling regime, while the counter-rotating terms can be neglected. Thus, a deep-strong JC model is obtained. The ratio of the coupling strength to resonance frequencies in the deep-strong JC model is two orders of magnitude larger than the corresponding ratio in the original quantum Rabi model. Our scheme can be employed in atom-cavity resonance and off-resonance cases, and it is valid over a broad range. The nonzero average cavity photons of the ground state indicate the emergence of a quantum phase transition. Further, we demonstrate the dependence of the phase diagram on the atom-cavity detuning and modulation parameters. All the parameters used in our scheme are within the reach of current experimental technology. Our scheme provides a new mechanism for investigating the critical phenomena of finite-sized systems without requiring classical field limits, thereby opening a door for studying fundamental quantum phenomena occurring in the ultrastrong and even deep-strong coupling regimes.