Thermometry of arbitrary quantum systems via non-equilibrium work distributions

Estimating the temperature of a cold quantum system is difficult. Usually, one measures a well-understood thermal state and uses that prior knowledge to infer its temperature. In contrast, we introduce a method of thermometry that assumes no knowledge of the state of a system and is potentially non-destructive. Our method uses a universal temperature-dependence of the non-equilibrium dynamics of an initially thermal system coupled to a qubit probe that follows from the Tasaki-Crooks theorem for non-equilibrium work distributions. We provide examples, for a cold atom system, for which our thermometry protocol may retain accuracy and precision at subnanokelvin temperatures.