A driven dissipative quantum phase transition

Experiments with ultracold atomic gases have achieved an enormous level of control in the simulation of many- body physics and other models of interest in condensed matter, such as the insulator-superfluid transition. Recent theoretical efforts have now extended the focus to a quantum control of open-system many-body dynamics, enabling for example, the dissipative preparation of entangled states and phases, dissipative quantum computation and novel out-of-equilibrium physics. As a response to this drive, in a recent experiment, a complete toolbox for the simulation of open quantum systems was demonstrated with trapped ions. Here, we propose to use such simulator to study a novel type of phase transition in a driven dissipative many-body system. This work will constitute a first and conceptual experimental step towards novel classes of non-equilibrium many-body quantum physics. This demonstration of a combination of coherent and dissipative many-body dynamics is expected to open the door to novel scenarios of many-body physics, such as combined coherent and dissipative dynamical quantum maps, which have been hardly experimentally accessible to date.