The goal of this WP is the experimental implementation of spin-boson models and the realization of dissipative time-crystals with trapped ions. Our experimental approach will be based on a linear string of trapped strontium ions. Spin states will be encoded in the ions’ electronic states, bosons are represented by the phonons of the ion motion. Spin manipulation will combine laser-driven interaction via the ions’ motional modes (bichromatic Mølmer-Sørensen and/or light-shift interaction), global spin rotations, and individual phase rotations (addressed AC-Stark shift operations). We will address current limitations in achieving long-term stability via sympathetic cooling with auxiliary ion(s) of another strontium isotope. We will further tailor dissipation by optical pumping on auxiliary ions. Initially, we will perform a simple benchmark of the experimental system using two interacting ions cooled by auxiliary ion(s), later the ion number will be increased to up to 20 ions.
We will implement discrete dissipative time-crystals as Floquet systems by applying the operations described above in a stroboscopic manner or by periodic modulation of laser frequency and amplitude. We will monitor quantum trajectories of the time-crystal by photon counting and photon correlation measurement of light scattered by auxiliary ions. Guided by the measurement outcome, we will apply active feedback on laser control parameters to stabilize and actively control system dynamics. Alternatively, and as outlook, we will investigate homodyne detection as a means to observe phase transitions in trajectories.