Precision Measurements of Temperature and Chemical Potential of Quantum Gases

TL;DR

This paper analyzes the fundamental limits of measuring temperature and chemical potential in quantum gases, highlighting how Bose-Einstein condensation can enhance measurement sensitivity and how interactions affect this precision.

Contribution

It provides a comprehensive calculation of quantum Fisher information for fermionic and bosonic gases, including near phase transitions and under various interaction models, revealing new insights into measurement limits.

Findings

Bose-Einstein condensation can enable sub-shot noise sensitivity.

Interactions slightly reduce measurement sensitivity in weakly interacting gases.

Sensitivity varies near different condensation scenarios and dimensions.

Abstract

We investigate the sensitivity with which the temperature and the chemical potential characterizing quantum gases can be measured. We calculate the corresponding quantum Fisher information matrices for both fermionic and bosonic gases. For the latter, particular attention is devoted to the situation close to the Bose-Einstein condensation transition, which we examine not only for the standard scenario in three dimensions, but also for generalized condensation in lower dimensions, where the bosons condense in a subspace of Hilbert space instead of a unique ground state, as well as condensation at fixed volume or fixed pressure. We show that Bose Einstein condensation can lead to sub-shot noise sensitivity for the measurement of the chemical potential. We also examine the influence of interactions on the sensitivity in three different models, and show that mean-field and contact interactions deteriorate the sensitivity but only slightly for experimentally accessible weak interactions.