Investigating Lipkin-Meshkov-Glick Model and Criticality-Enhanced Metrology in a Coherent Ising Machine

TL;DR

This paper demonstrates how a coherent Ising machine can simulate the Lipkin-Meshkov-Glick model, capturing quantum phase transitions and enabling quantum-enhanced metrology near critical points.

Contribution

It introduces a scheme to simulate the LMG model with a CIM, revealing its phase diagram and critical behavior for quantum sensing applications.

Findings

CIM effectively captures the second-order quantum phase transition.

The phase diagram of the LMG model is reconstructed using CIM.

Quantum metrology precision diverges near the critical point.

Abstract

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., $N\rightarrow\infty$, 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.