Synchronization in a quantum gas with cavity-mediated long-range interactions

The excitation spectrum of a many-body system reveals fundamental properties of its interactions, symmetries, and proximity to phase transitions. When an excitation mode softens to zero energy, the system becomes increasingly susceptible to fluctuations, signaling the onset of a phase transition. Beyond this well-known paradigm, the crossing of excitation branches can also lead to profound dynamical effects. Here, we show that in a Bose-Einstein condensate of ⁸⁷Rb atoms coupled to an optical cavity, roton-like modes undergo a dissipation-induced synchronization near a phase transition. The interplay between cavity-mediated long-range interactions and photon dissipation via cavity leakage enables a regime where two distinct roton modes coalesce. Using a novel Bragg spectroscopy technique, we demonstrate that this synchronization modifies the system’s critical properties and leads to the emergence of a dynamical instability. Our findings establish a connection between synchronization and mode softening in open quantum systems and provide new perspectives on nonequilibrium critical phenomena.