Thermometry of cold atoms in optical lattices via artificial gauge fields

Artificial gauge fields are a unique way of manipulating the motional state of cold atoms. Here we propose the use of artificial gauge fields -- obtained e.g. via lattice shaking -- to perform primary noise thermometry of cold atoms in optical lattices - not requiring any form of prior calibration. The proposed thermometric scheme relies on fundamental fluctuation-dissipation relations, connecting the global response to the variation of the applied gauge field and the fluctuation of quantities related to the momentum distribution (such as the average kinetic energy or the average current). We demonstrate gauge-field thermometry for several physical situations, including free fermions and strongly interacting bosons. The proposed approach is extremely robust to quantum fluctuations - even in the vicinity of a quantum phase transition - when it relies on the thermal fluctuations of an emerging classical field, associated with the onset of Bose condensation or chiral order.