Dynamical Quantum Phase Transitions in the Dissipative Lipkin-Meshkov-Glick Model with Proposed Realization in Optical Cavity QED

We present an optical cavity QED configuration that is described by a dissipative version of the Lipkin-Meshkov-Glick model of an infinitely coordinated spin system. This open quantum system exhibits both first- and second-order nonequilibrium quantum phase transitions as a single, effective field parameter is varied. Light emitted from the cavity offers measurable signatures of the critical behavior, including that of the spin-spin entanglement.

Figure 1

(a) Atomic level and excitation scheme. (b) Potential ring-cavity setup. The laser fields (dashed lines) are at frequencies that are not supported by the resonator, but can be injected through one of the resonator mirrors so as to be copropagating with the cavity fields through the ensemble.

Figure 2

Semiclassical (solid line) and finite-$N$ steady-state inversion and second-order moments for ${\Gamma }_a/\lambda =0.01$, ${\Gamma }_b/\lambda =0.2$, and $N=25$ (dotted line), 50 (short dashed line), 100 (long dashed line).

Figure 3

Transmission spectra in the linearized regime, for $h/\lambda =\{-0.6,-0.1,-0.01,h_{-}^c/\lambda ,0.05,0.3\}$ (top), and $\{0.5,0.95,0.995,h_{+}^c/\lambda ,1.1,1.3\}$ (bottom), with microscopic parameters ${\kappa }_a/{\delta }_a=0.02$, ${\lambda }_b/{\lambda }_a=0.32$, ${\kappa }_b/{\delta }_a=1$, ${\delta }_b=0$, giving ${\Gamma }_a/\lambda =0.01$, ${\Gamma }_b/\lambda =0.05$. We set ${\delta }_{a,b}^{-}=0$.

Figure 4

Maximum entanglement $C_R$ computed from the linearized HP ($N\to \infty$) model (solid) and from (5) for $N=100$ (dashed), with ${\Gamma }_a/\lambda =0.01$ and ${\Gamma }_b/\lambda =0.2$.