Self-organization and non-reciprocity in cavity QED with an atomic tweezer array

Driven-dissipative systems serve as a testbed for studies of non-equilibrium phenomena. We realize driven-dissipative versions of the Dicke model in an experiment that combines cavity QED with an atomic tweezer array. In one realization of the Dicke model, by driving the atoms transverse to the cavity with light polarized along the cavity axis, Raman scattering into the cavity leads to a superradiant phase transition where the atomic spins precess in synchrony and break U(1) symmetry. The system also exhibits a Z₂ symmetry in certain parameter regimes due to linear birefringence of the cavity. We additionally observe that the light scattered into the cavity cools the atoms. Another realization of the Dicke model occurs via optomechanical self-organization, where the atomic motion is coupled to the cavity field. We also theoretically investigate a version of the Dicke model that exhibits discrete higher symmetry breaking where the atoms are allowed to couple to the cavity field with different, complex coefficients. This system also exhibits non-reciprocal forces arising from the interference of the light scattered by different atoms.