Abstract
The concept of generalized Gibbs ensembles (GGEs) has been introduced to describe steady states of integrable models. Recent advances show that GGEs can also be stabilized in nearly integrable quantum systems when driven by external fields and open. Here, we present a weakly dissipative dynamics that drives towards a steady-state GGE and is realistic to implement in systems of trapped ions. We outline the engineering of the desired dissipation by a combination of couplings which can be realized with ion-trap setups and discuss the experimental observables needed to detect a deviation from a thermal state. We present a novel mixed-species motional mode engineering technique in an array of micro-traps and demonstrate the possibility to use sympathetic cooling to construct many-body dissipators. Our work provides a blueprint for experimental observation of GGEs in open systems and opens a new avenue for quantum simulation of driven-dissipative quantum many-body problems.
Highlights
Providing a compact description of complicated manybody systems is a challenging task
Recent advances show that generalized Gibbs ensembles (GGEs) can be stabilized in nearly integrable quantum systems when driven by external fields and open
We present a weakly dissipative dynamics that drives towards a steady-state GGE and is realistic to implement in systems of trapped ions
Summary
Providing a compact description of complicated manybody systems is a challenging task. Lp denotes the Liouville operator corresponding to perturbations which weakly break the integrability, and as a consequence the conservation laws, while driving and cooling the system Such a setup is much more versatile because it does not require the fine-tuned perfect integrability and at the same time allows for the engineering of GGEs through a particular choice of perturbations. The resulting dynamics stabilizes a steady state approximately described by a generalized Gibbs ensemble, despite different integrability breaking terms. The operators (2) j with support are sufficiently structured to stabilize clearly nonthermal states approximated by GGEs and at the same time require a manageable amount of resources to be realized on trapped-ion platforms, as discussed in Secs. We go on to establish that this model does stabilize a steady state approximately described by a GGE ensemble, despite different sources of integrability breaking
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