Higher symmetry breaking and nonreciprocity in a driven-dissipative Dicke model

Higher symmetries in interacting many-body systems often give rise to new phases and unexpected dynamical behavior. Here, we theoretically investigate a variant of the Dicke model with higher-order discrete symmetry, resulting from complex-valued coupling coefficients between quantum emitters and a bosonic mode. We propose a driven-dissipative realization of this model focusing on optomechanical response of a driven atom tweezer array comprised of n subensembles and placed within an optical cavity, with the phase of the driving field advancing stepwise between subensembles. Examining stationary points and their dynamical stability, we identify a phase diagram for n ≥ 3 with three distinctive features: a Z n ( Z 2 n ) symmetry-breaking superradiant phase for even (odd) n , a normal unbroken-symmetry phase that is dynamically unstable due to nonreciprocal forces between emitters, and a first-order phase transition separating these phases. This n -phase Dicke model may be equivalently realized in a variety of optomechanical or optomagnonic settings, where it can serve as a test bed for studying high-order symmetry breaking and nonreciprocal interactions in open systems.