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Quantum Rabi model (QRM) is fascinating not only because of its broadrelevance and but also due to its few-body quantum phase transition. Inpractice both the bias and the nonlinear coupling in QRM are importantcontrolling parameters in experimental setups. We study the interplay of thebias and the nonlinear interaction with the linear coupling in the ground statewhich exhibits various patterns of symmetry breaking and different orders oftransitions. Several situations of tricriticality are unveiled in the lowfrequency limit and at finite frequencies. We find that the fullquantum-mechanical effect leads to novel transitions, tricriticalities andquadruple points, which are much beyond the semiclassical picture. We clarifythe underlying mechanisms by analyzing the energy competitions and theessential changeovers of the quantum states, which enables us to extract mostanalytic phase boundaries.

Symmetry breaking patterns, tricriticalities and quadruple points in quantum Rabi model with bias and nonlinear interaction