Nonreciprocal Phase Transitions in Driven-Dissipative Condensates

Driven-dissipative quantum many-body systems can exhibit novel nonequilibrium dynamical phases and phenomena. Here, we explore a new paradigm of nonequilibrium phase transitions, where nonreciprocal interactions and the non-Hermitian skin effect result in phase diagrams that are extremely sensitive to boundary conditions. We consider a one-dimensional lattice of nonlinear bosons described by a Lindblad master equation, where the interplay between coherent and incoherent dynamics generates nonreciprocal interactions between oscillators. We analyze the mean-field phase diagram for both periodic and open boundary conditions. Under periodic boundary conditions, the system hosts a single phase characterized by synchronized oscillatory steady states. In contrast, open boundary conditions give rise to a much richer phase diagram, featuring multiple static and dynamical phases, as well as exotic phase transitions between them. Our approach does not rely on post-selection or unphysical non-Hermitian Hamiltonians, and can be experimentally realized in platforms such as superconducting circuits.