Symmetry Breaking and Phase Transition in a Driven-Dissipative Kerr Oscillator*

We show that quantum many-body effects can appear in a single non-linear oscillator that is driven by an external field in the presence of dissipation. This simple system is a paradigmatic example of open quantum many-body systems in which there has been great interest recently due to recent experimental advances such as quantum simulation. Here, weak non-linearity plays the role of the thermodynamic limit. Using both analytical and numerical methods, we demonstrate Z₂ symmetry breaking and the corresponding phase transition.