Thermometry precision in strongly correlated ultracold lattice gases

The precise knowledge of the temperature of an ultracold lattice gas simulating a strongly correlated<br/>system is a question of both fundamental and technological importance. Here, we address such<br/>question by combining tools from quantum metrology together with the study of the quantum<br/>correlations embedded in the system at finite temperatures. Within this frame we examine the spin-<br/>1 2 XY chain, first estimating, by means of the quantum Fisher information, the lowest attainable<br/>bound on the temperature precision. We then address the estimation of the temperature of the sample<br/>from the analysis of correlations using a quantum non demolishing Faraday spectroscopy method.<br/>Remarkably, our results show that the collective quantum correlations can become optimal<br/>observables to accurately estimate the temperature of our model in a given range of temperatures.