Anisotropic quantum Rabi-Stark model

Abstract

We study the anisotropic Rabi-Stark model by the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived, which zeros produce the energy spectra. The first-order quantum phase transitions are detected by level crossing of the first excited state and the ground-state with the use of the pole structure of the derived transcendental functions. As the nonlinear Stark coupling is the same as the cavity frequency, all energy levels close at the critical coupling. The critical gap exponents are independent of the anisotropy as long as the counter-rotating wave coupling is present, but essentially change if the counter-rotating wave coupling disappears completely. It is suggested that the gapless Goldstone mode excitations could appear above a critical coupling in the present one qubit and single mode cavity coupling model in the rotating-wave approximation.