Jahn-Teller instability in dissipative quantum systems

We consider the steady states of a harmonic oscillator coupled so strongly to a two-level system (a qubit) that the rotating wave approximation cannot be made. The Hamiltonian version of this model is known as the E⊗β Jahn-Teller model. The semiclassical version of this system exhibits a fixed-point bifurcation, which in the quantum model leads to a ground state with substantial entanglement between the oscillator and the qubit. We show that the dynamical bifurcation survives in a dissipative quantum description of the system, amidst an even richer bifurcation structure. We propose an experimental implementation of this model based on a superconducting cavity: a superconducting junction in the central conductor of a coplanar waveguide.