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Bulletin of the American Physical Society

Quantum simulation of non-equilibrium dynamical maps with trapped ions

Philipp Schindler, Marcus M uller, Daniel Nigg, Thomas Monz, Julio T. Barreiro, Esteban A. Martinez, Markus Hennrich, Sebastian Diehl, P. Zoller, R. Blatt

Published Mar 19, 2013• 0 citations
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Trapped ions excited to high-lying electronic states combine strongly coupled collective vibrational and electronic degrees of freedom with long-ranged interparticle interactions. These ingredients enable the quantum simulation of biochemical processes, associated with the dynamics of excitons in non-perturbative parameter regimes. The key feature of such a quantum simulator are electronic-state-dependent molecular potential surfaces which can be strongly coupled. This allows to shed light on a variety of mechanisms underlying exciton transport. We illustrate this in a system of three trapped ions, which is amenable to an ab initio treatment. Given that ion traps can be routinely prepared with hundreds of ions, these quantum simulators can immediately realise scenarios which are inaccessible by current numerical methods.
Open quantum many-body systems with controllable dissipation can exhibit novel features in their dynamics and steady states. A paradigmatic example is the dissipative transverse field Ising model. It has been shown recently that the steady state of this model with all-to-all interactions is genuinely non-equilibrium near criticality, exhibiting a modified time-reversal symmetry and violating the fluctuation-dissipation theorem. Experimental study of such non-equilibrium steady-state phase transitions is however lacking. Here we propose realistic experimental setups and measurement schemes for current trapped-ion quantum simulators to demonstrate this phase transition, where controllable dissipation is engineered via a continuous weak optical pumping laser. With extensive numerical calculations, we show that strong signatures of this dissipative phase transition and its non-equilibrium properties can be observed with a small system size across a wide range of system parameters. In addition, we show that the same signatures can also be seen if the dissipation is instead achieved via Floquet dynamics with periodic and probabilistic resetting of the spins. Dissipation engineered in this way may allow the simulation of more general types of driven-dissipative systems or facilitate the dissipative preparation of useful many-body entangled states.