Regulation of photon–photon interaction on quantum phase transitions of the two-mode three-level quantum Rabi model

We study the quantum phase transitions and critical scaling behavior of a two-mode three-level quantum Rabi model with photon–photon interaction. When the frequency ratio η of the energy level spacing of atoms to the boson mode tends to infinity, the phase transition of the model is discovered. The model is analytically solved to obtain the critical point of phase transition, when the two lowest-energy levels are degenerate. We also extract the critical exponents by numerical scaling of order parameter at a sufficiently large but finite η value, thus obtaining that the phase transition of the model belongs to the mean-field universality class. Our work reveals that quantum phase transitions of the two-mode three-level quantum Rabi model can be effectively regulated through photon–photon interaction.