Thermometry Precision in Strongly Correlated Ultracold Lattice Gases

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.