Engineering generalized Gibbs ensembles with trapped ions

Generalized Gibbs ensembles (GGEs) have been introduced to describe stationary expectation values of local observables in integrable models with macroscopically many conservation laws. Recent advances showed that GGEs also describe more realistic nearly integrable systems which are weakly driven and open. In this case, integrability breaking perturbations determine the parameters of GGE. By tuning the coupling to the environment, it is thus possible to stabilize a broad range of tailored GGEs.
Here we pave the way for the first experimental observation of GGEs in a nearly integrable driven-dissipative setup with trapped ions. We present an implementation scheme for a particular choice of Lindblad operators and suggest experimental observables which detect that a GGE approximately describes the stabilized steady-state. To engineer single-, as well as two-body dissipation, we use a combination of couplings which can be engineered in an array of microtraps. We assess the performance of our implementation scheme and discuss the resources required to observe a deviation from a thermal ensemble in an experiment.