Quantum metrology in Lipkin-Meshkov-Glick critical systems

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.

11 pages, 5 figures

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Cited by in corpus (7)

• Entanglement and spin squeezing in non-Hermitian phase transitions
• Continuous-variable quantum probes for structured environments
• Enhancing parameter precision of optimal quantum estimation by direct quantum feedback
• Lattice quantum magnetometry
• Optimal and near-optimal probe states for quantum metrology of number conserving two-mode bosonic Hamiltonians
• Quantum Thermal Amplifiers with Engineered Dissipation
• Adiabatic Sensing Enhanced by Quantum Criticality