Two-photon Rabi-Stark model

Abstract: The analytically exact solutions to the two-photon Rabi-Stark model are given by using the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived. The zeros of the transcendental functions reproduce completely the regular spectra. The first-order quantum phase transitions are also detected by the pole structure of the derived transcendental functions, similar to the one-photon Rabi-Stark model, different from the two-photon Rabi model where the energy levels for the ground-state and the first excited state do not cross. The spectra collapse characteristics resemble those in two-photon Rabi model. Some low lying levels can split off from the collapse energy, different from the one-photon Rabi-Stark model in which all levels collapse.