We focus on the interaction of light and matter in atomic and optomechanical systems. These highly controllable and engineerable systems present access to new regimes and research opportunities that often do not exist outside the laboratory. As such, they frequently depart from more commonplace systems which are well understood. We extend our understanding of thermodynamic phase transitions, spontaneous symmetry breaking, and quantum-enhanced sensing to new regimes.

Traditionally, phase transitions are defined in thermodynamic equilibrium. However, inspired by the success of the phase transition paradigm in non-equilibrium fields, we derive an effective thermodynamics for the mechanical excitations of an optomechanical system. Noting the common frequency separation between optical and mechanical components, we study the dynamics of the mechanical modes under the influence of the steady state of the optical modes. We identify a sufficient set of constraints which allow us to define an effective equilibrium for the mechanical

system. We demonstrate these constraints by studying the buckling transition in an optomechanical membrane-in-the-middle system, which spontaneously breaks a parity symmetry. Having established a thermodynamic limit, we characterize the nature of the phase transition, which can change order based on system parameters. We extend our framework, proposing an photonic systems which realizes an SO(N) symmetry breaking transition of the same nature as the membrane-in-the-middle system. While we have treated these systems in the classical limit, their open nature has pronounced effects when other noise sources are suppressed. We study the canonical optomechanical system to unravel the origin of the semiclassical force and potential on the mechanics. We find that this force, while conservative with respect to the mechanics, deeply depends on the quantum back-action due to photon loss from the cavity.

Additionally, we study the ability of cold atoms to sense rotation. We consider bosonic atoms confined to a one-dimensional ring. Employing Luttinger liquid theory to study the excitations, we find that in the strongly-repulsive regime, atomic currents can be manipulated and superposed by controlling a laser barrier. These superpositions provide a Heisenberg-limited rotation sensing method. When we include noise, the precision is reduced, but the performance still surpasses the standard quantum limit. We comment on the applicability of such a sensor for inertial sensing.