CoQuaDis

In this WP we develop the theory for driven-dissipative spin-boson models and emergent collective behaviour in their dynamics, stationary and non-stationary phases. We will pursue different settings and control mechanisms, including periodically driven Floquet systems and quantum systems with (time-delayed) feedback that can be implemented in the SU trapped ion experiment. We will develop numerical code based on tensor networks and perform analytical calculations, based on advanced mean-field approaches that are able to capture quantum correlations. A focus will be set on deriving a faithful description of dissipative processes (local vs. global master equation), which are obtained by integrating out bosonic degrees of freedom. We will also study how collective dynamics is detected from the open system output by analysing dynamical phase and phase transitions of quantum trajectories.

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.

The goal of this WP is to exploit collective dynamics in dissipative spin-boson models for the purpose of parameter estimation and possible augmentation due to quantum effects. Starting point will be time-crystal phases with which we will estimate the strength of an externally applied effective magnetic field coupling to the spins. We will focus on a range of experimental protocols, including in-situ measurement of output and repeated measurements in stationary spin state. We will characterise achievable sensitivities and signal-to-noise ratios and identify optimal working points. Proof-of-principle experiments will be conducted within the trapped ion system, and we will benchmark the attainable key figures of merit. We will also conduct a study on implementation of time-keeping using stochastic clocks based on time-crystals.