Wiseman-Milburn Control for the Lipkin-Meshkov-Glick Model

TL;DR

This paper demonstrates how Wiseman-Milburn feedback control can manipulate the quantum phase transition in the dissipative Lipkin-Meshkov-Glick model, shifting the critical point and enhancing transition detection via entanglement measures.

Contribution

It introduces a measurement-based feedback scheme to control the phase transition in the Lipkin-Meshkov-Glick model, showing how feedback shifts the critical point and improves transition detection.

Findings

Feedback shifts the critical point to smaller interactions.

Entanglement measures better locate the transition.

Finite-size effects blur expectation value signatures.

Abstract

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. Finite-size corrections blur these signatures in operator expectation values but entanglement measures such as concurrence can be used to locate the transition point more precisely. 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.