Wiseman–Milburn control for the Lipkin–Meshkov–Glick model

We apply a measurement-based closed-loop control scheme to the dissipative Lipkin–Meshkov–Glick model. Specifically, we use the Wiseman–Milburn feedback master equation to control its quantum phase transition. For the steady state properties of the Lipkin–Meshkov–Glick system under feedback we show that the considered control scheme changes the critical point of the phase transition. We show that entanglement measures such as concurrence allow one to unambiguously locate precursors of quantum-critical behaviour in the finite-size regime, unlike conventionally used operator expectation values. We find that with feedback, the position of the critical point can be shifted to smaller spin–spin interactions, which is potentially useful for setups with limited control on these. (paper)