Non-Local Quantum Phase Transitions

In the thermodynamic limit, thermal or quantum fluctuations can drive many-body systems into symmetry-broken states that do not directly follow microscopic conservation laws. Here, we show that nonlocal quantum fluctuations of bath modes can induce a correlated symmetry breaking in remote critical systems, regardless of their distance. Using the framework of driven-dissipative phase transitions, we theoretically analyze a system composed of distant critical resonators, each coupled to an independent Markovian bath, when the environmental modes are prepared in a broadband two-mode squeezed state. We present a gedankenexperiment where two identical copies of such critical resonator-bath systems are placed at large, possibly space-like separations, assuming that the environment modes are in pre-shared entangled states. We derive microscopically the Lindblad master equation for the global system, considering a Caldeira-Leggett model for the bosonic baths, whose modes are taken to be in a broad-band two-mode squeezed state. We characterize the global system phase diagram and critical region through a combination of analytical and numerical methods.