Superradiant phase transition in quantum Rabi dimer with staggered couplings

We study the quantum phase transitions and the critical behavior of the quantum Rabi dimer model, where the two cavities are not equivalent. In our model the coupling strength in each cavity is individually tuned as what usually happens in experimental systems. In the frequency-ratio limit with an infinite ratio of the atomic transition frequency to the cavity frequency, the model is analytically solved so that we find a superradiant phase transition and the order parameter of the system is found to be the normal mode of the linear combination of the two cavity modes. Thus we can determine precisely the critical points and depict the associated phase diagram. We also extract the critical exponents through calculating the universal scaling function and thus conclude that the phase transition of the model belongs to the mean-field universality class. The von Neumann entropy and l₁ norm coherence are adopted to analyze the quantum phase transition and the associate critical phenomena. The critical points and critical exponents extracted from these information measures agree with ones distilled by the order parameter. We expect this work could stimulate the further study on the multi-cavity models with disorder, where a series of nonequivalent cavities are cascaded.