Thermometry Precision in Strongly Correlated Ultracold Lattice Gases

TL;DR

This paper investigates the fundamental limits and practical methods for precise temperature measurement in strongly correlated ultracold lattice gases, combining quantum metrology and correlation analysis.

Contribution

It introduces a quantum metrology framework to determine the ultimate temperature estimation bounds and proposes an optimal measurement method using Faraday spectroscopy.

Findings

Quantum Fisher information sets the lowest temperature estimation bound.

Faraday spectroscopy can approach optimal temperature measurement at low temperatures.

The methods are applicable to strongly correlated quantum systems.

Abstract

The precise knowledge of the temperature of an ultracold lattice gas simulating a strongly correlated system is a question of both, fundamental and technological importance. Here, we address such question by combining tools from quantum metrology together with the study of the quantum correlations embedded in the system at finite temperatures. Within this frame we examine the spin-$1/2$ XY chain, first estimating, by means of the quantum Fisher information, the lowest attainable bound on the temperature precision. We then address the estimation of the temperature of the sample from the analysis of correlations using a quantum non demolishing Faraday spectroscopy method. Finally, we demonstrate that for sufficiently low temperatures the proposed measurements are optimal to estimate accurately the temperature of the sample.