Circuit QED scheme for realization of the Lipkin-Meshkov-Glick model

TL;DR

This paper proposes a circuit QED implementation of the Lipkin-Meshkov-Glick model using superconducting qubits and a driven cavity, revealing phase transition signatures and entanglement properties.

Contribution

It introduces a novel scheme to realize the LMG model in circuit QED, including analysis of phase transitions and entanglement in a driven, dissipative environment.

Findings

Long-range order mediated by cavity field

Second order phase transition reflected in cavity output

Emergence of bistable regimes under relaxation

Abstract

We propose a scheme in which the Lipkin-Meshkov-Glick model is realized within a circuit QED system. An array of N superconducting qubits interacts with a driven cavity mode. In the dispersive regime, the cavity mode is adiabatically eliminated generating an effective model for the qubits alone. The characteristic long-range order of the Lipkin-Meshkov-Glick model is here mediated by the cavity field. For a closed qubit system, the inherent second order phase transition of the qubits is reflected in the intensity of the output cavity field. In the broken symmetry phase, the many-body ground state is highly entangled. Relaxation of the qubits is analyzed within a mean-field treatment. The second order phase transition is lost, while new bistable regimes occur.