The Jahn-Teller instability in dissipative quantum electromechanical systems

TL;DR

This paper investigates the Jahn-Teller instability in a strongly coupled quantum electromechanical system, revealing persistent bifurcations and entanglement in dissipative conditions, with proposed superconducting cavity experiments.

Contribution

It demonstrates the survival of dynamical bifurcations in a dissipative quantum Jahn-Teller model and suggests feasible experimental implementations.

Findings

Dissipative quantum Jahn-Teller systems exhibit rich bifurcation structures.

Ground states show significant entanglement between oscillator and qubit.

Proposed superconducting cavity setups enable experimental exploration.

Abstract

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 $E\otimes\beta$ 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 two experimental implementations of this model based on superconducting cavities: a parametrically driven nonlinear nanomechanical resonator coupled capacitively to a coplanar microwave cavity and a superconducting junction in the central conductor of a coplanar waveguide.