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arXiv:1803.01138 · Journal of Physics A Mathematical and Theoretical

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

Sven Zimmermann, Wassilij Kopylov, Gernot Schaller

Published Jul 11, 2018• 5 citations
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Abstract

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. 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.

DOI
10.1088/1751-8121/aad2c3

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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. 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.
Critical behaviour in phase transitions is a resource for enhanced precision metrology. The reason is that the function, known as Fisher information, is superextensive at critical points, and, at the same time, quantifies performances of metrological protocols. Therefore, preparing metrological probes at phase transitions provides enhanced precision in measuring the transition control parameter. We focus on the Lipkin-Meshkov-Glick model that exhibits excited state quantum phase transitions at different magnetic fields. Resting on the model spectral properties, we show broad peaks of the Fisher information, and propose efficient schemes for precision magnetometry. The Lipkin-Meshkov-Glick model was first introduced for superconductivity and for nuclear systems, and recently realised in several condensed matter platforms. The above metrological schemes can be also exploited to measure microscopic properties of systems able to simulate the Lipkin-Meshkov-Glick model.
We investigate the Lipkin-Meshkov-Glick model coupled to a thermal bath. Since the isolated model itself exhibits a quantum phase transition, we explore the critical signatures of the open system. Starting from a system-reservoir interaction written in positive-definite form, we find that the position of the critical point remains unchanged, in contrast to the popular mean-field prediction. Technically, we employ the polaron transform to be able to study the full crossover regime from the normal to the symmetry-broken phase, which allows us to investigate the fate of quantum-critical points subject to dissipative environments. The signatures of the phase transition are reflected in observables such as magnetization, stationary mode occupation, or waiting-time distributions.
We propose a cavity QED setup which implements a dissipative Lipkin-Meshkov-Glick model---an interacting collective spin system. By varying the external model parameters the system can be made to undergo both first- and second-order quantum phase transitions, which are signified by dramatic changes in cavity output field properties, such as the probe laser transmission spectrum. The steady-state entanglement between pairs of atoms is shown to peak at the critical points and can be experimentally determined by suitable measurements on the cavity output field. The entanglement dynamics also exhibits pronounced variations in the vicinities of the phase transitions.
Quantum criticality has received extensive attention due to its ability to significantly enhance quantum sensing. But its realization and control in many-body quantum systems remain challenging. We present an effective scheme to simulate the Lipkin-Meshkov-Glick (LMG) model using a coherent Ising machine (CIM) composed of a network of degenerate optical parametric oscillators (DOPO). In our work, the spin variables of the LMG model are mapped onto the phases of DOPO pulses, and the spin-spin interactions are realized by all-to-all couplings among them. Through our investigation of the critical behavior in the antiferromagnetically coupled LMG model in the thermodynamic limit, i.e., N→∞N\rightarrow\inftyN→∞, and its application in quantum sensing near the critical point, we verify that the CIM does not only effectively capture the second-order quantum phase transition (QPT) at the critical point but also reconstructs its complete phase diagram under ferromagnetic coupling. Furthermore, we demonstrate how the critical dynamics of this simulation platform can be utilized for quantum-enhanced metrology, achieving a measurement precision that diverges near the critical point of the LMG model. These results highlight the capability of the CIM as a flexible experimental platform for investigating the QPT in the fundamental quantum magnetic models, providing valuable insights into quantum simulation and critical phenomena.