The quantum Rabi model (QRM) describes a two-level system interacting with a bosonic mode and it is one of the simplest models of light-matter interactions. If the coupling strength is small, the QRM can be approximated by the Jaynes-Cummings (JC) model, where counter-rotating terms are neglected. Although these models have only few degrees of freedom, recent work has shown that a suitable limit of both the QRM [1] and JC model [2] displays a quantum phase transition similar to Dicke superradiance. In this talk we extend these results to the anisotropic QRM, where rotating- and counter-rotating terms have different weights. This question is important since typical realizations of strong light-matter interactions (e.g., in circuit QED) naturally have finite anisotropy. Furthermore, the quantum phase transition has different universal properties in the known JC and isotropic QRM limits. Through a combination of analytic and numerical approaches we compute phase diagram, scaling functions, and critical exponents, which allows us to establish that the universality class with finite anisotropy is the same of the QRM. We also find other interesting features, like a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the JC limit.

[1] M.-J. Hwang, R. Puebla, and M. B. Plenio, Phys. Rev. Lett. 115, 180404 (2015).
[2] M.-J. Hwang and M. B. Plenio, Phys. Rev. Lett. 117, 123602 (2016).