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Center for Nonlinear Studies |
Until recently, photonic systems have been restricted to a weakly interacting regime. With notable progress towards generating strong optical nonlinearities at the few-photon level, for example with atoms coupled to small-mode-volume optical devices, Rydberg polaritons, and circuit-QED devices, this situation is rapidly changing. The production of strongly interacting, driven and dissipative gases of photons appears to be feasible, and affords exciting opportunities to explore the properties of open quantum systems in unique contexts, while studying the applicability of theoretical treatments designed with more weakly interacting systems in mind. Along these lines, we study an array of coupled, coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-1/2 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify a variety of interesting steady states including spin density waves and limit cycles, which break the discrete translational symmetry of the system. Interestingly, the spin density waves possess canted antiferromagnetic order for a range of drive strengths, despite the ferromagnetic nature of the spin couplings. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.
Host: Malcolm Boshier