Phase separation in driven-dissipative quantum systems

The driven Dicke model is an exemplary problem in quantum optics. This simple model illustrates how a collection of atoms, under the combination of external driving by light and nonlinear dissipation, can give rise to a driven-dissipative phase transition, where observable properties can exhibit non-smooth changes even as the system's parameters are smoothly tuned. The model is conceptually very simple, assuming that atoms interact in a permutation-invariant manner with a single electromagnetic field mode. While this allows its solution to be easily understood, it also makes the model hard to apply to most realistic systems. Recently, a prominent experiment claimed to observe the driven-dissipative phase transition in an ensemble of atoms in free space driven by light. This result generated significant excitement and discussion within the scientific community, as the complex system in question lacks the permutation invariance and single-mode nature of the original theoretical problem. We developed a minimal theoretical model that elucidated the observations. Interestingly, we showed that what was observed is not a phase transition, but a novel phase separation in a driven-dissipative system, where different parts of the system acquire macroscopically different properties, and which can mimic the non-smooth behavior expected in a phase transition. Our work clarifies key conceptual differences between realistic extended atom-light interfaces and minimal single-mode quantum optics models, and how a richer set of many-body phenomena should emerge in realistic systems.