Driven-dissipative dynamics with trapped ions and qubit-arrays

Coming out of a hot oven, a trapped ion can be cooled by light down to a thousandth degree above Kelvin just by applying radiation pressure. Despite this reality, existing theories of the cooling dynamics are mostly limited to the final stage of the cooling where the time-dependence and anharmonicity of the trap can be neglected. I will present a semiclassical framework based on action-angle phase-space coordinates, that advances the understanding of laser cooling dynamics far from thermal equilibrium. Using this approach we analyze different regimes of motion resulting from the combination of a time-dependent trap drive and laser damping, which can lead to the capture of a particle in large-amplitude, stochastic limit cycles. At the same time, trapped-ion experiments are well suited also for studying many-body driven-dissipative dynamics. Within one- and two-dimensional crystals of trapped ions, the electronic states forming a two-level system (equivalent to a spin-1/2) of different ions, can be coupled using light. When strongly driven and at the presence of dissipative processes, interacting spins form a fundamental model of nonequilibrium dynamics, which describes also solid-state systems such as superconducting circuits coupled to an array of light cavities. I will present an ongoing study focusing on the role of quantum correlations in determining the system's phase beyond the meanfield limit, and how the phases and dynamics depend on the dimension, the interaction, and other system parameters.