Quantum metrology in Lipkin-Meshkov-Glick critical systems

TL;DR

This paper investigates how critical phenomena in Lipkin-Meshkov-Glick systems can be exploited to enhance quantum parameter estimation and thermometry, providing exact and approximate results for quantum Fisher information and measurement strategies.

Contribution

It offers the first detailed analysis of quantum Fisher information in LMG models, demonstrating how criticality improves measurement precision and thermometric range.

Findings

Exact quantum Fisher information for small LMG chains

Criticality enhances estimation precision

Level crossings extend thermometric range

Abstract

The Lipkin-Meshkov-Glick (LMG) model describes critical systems with interaction beyond the first-neighbor approximation. Here we address the characterization of LMG systems, i.e. the estimation of anisotropy, and show how criticality may be exploited to improve precision. In particular, we provide exact results for the Quantum Fisher Information of small-size LMG chains made of $N=2, 3$ and $4$ lattice sites and analyze the same quantity in the thermodynamical limit by means of a zero-th order approximation of the system Hamiltonian. We then show that the ultimate bounds to precision may be achieved by tuning the external field and by measuring the total magnetization of the system. We also address the use of LMG systems as quantum thermometers and show that: i) precision is governed by the gap between the lowest energy levels of the systems, ii) field-dependent level crossing provides a resource to extend the operating range of the quantum thermometer.