Controlling the superradiant phase transition in the quantum Rabi model

In the ultrastrong-coupling regime, the quantum Rabi model can exhibit quantum phase transition (QPT) when the ratio of the qubit transition frequency to the frequency of the cavity field approaches infinity. However, it is challenging to control the QPT in few-body systems because of the limited coupling strength and the ${A}^{2}$ term. Here, we propose a practical scheme to manipulate the QPT of quantum Rabi model in the strong-coupling regime. By applying a periodic frequency modulation to the two-level system in a quantum Rabi model in the strong-coupling regime, an anisotropic quantum Rabi model with ultrastrong and tunable coupling strengths for rotating and counterrotating terms is obtained. The ground state and excitation energy of this model, in terms of the modulation parameters, are studied. We find that the QPT of the quantum Rabi model can be observed in the strong-coupling regime and externally controlled by the modulation.