Exploring non-equilibrium dynamics in spin-boson models for quantum simulation and metrology

We investigate non-equilibrium quantum dynamics and the generation of entanglement in a trapped-ion simulator of the paradigmatic Dicke model, which describes the coupling of a collective spin to a single harmonic oscillator. The spin and boson degrees of freedom of the model are encoded in the electronic and collective vibrational states, respectively, of a trapped-ion array. As a first investigation, we study a series of dynamical phase transitions in the Dicke model. We systematically investigate the role of quantum fluctuations in the dynamics by contrasting results obtained from initial conditions that are distinguished by the presence or absence of a well-defined classical limit. For the latter, we further investigate distinctions that arise between integrable and chaotic regimes of the model, using observables including spin and boson squeezing, which are relevant for metrological applications, as well as simpler to access observables such as the mean collective magnetization. As a second investigation, we explore the utility of non-equilibrium spin-boson dynamics for developing quantum-enhanced approaches to quantum logic spectroscopy of ensembles of ions. Specifically, we investigate the utility of spin-boson entanglement as a resource and compare protocols based on different types of spin-boson couplings. We evaluate their respective benefits and drawbacks in the context of realistic experimental imperfections and constraints. Collectively, our findings are relevant for next generation quantum enhanced sensors build on a trapped ion architecture.