Subnanokelvin thermometry of an interacting d-dimensional homogeneous Bose gas

We propose experimentally feasible means for nondestructive thermometry of homogeneous Bose-Einstein condensates in different spatial dimensions (d is an element of {1 , 2, 3}). Our impurity-based protocol suggests that the fundamental error bound on thermometry at the subnanokelvin domain depends highly on the dimension, in that the higher the dimension the better the precision. Furthermore, suboptimal thermometry of the condensates by using measurements that are experimentally feasible is explored. We specifically focus on measuring position and momentum of the impurity that belong to the family of Gaussian measurements. We show that, generally, experimentally feasible measurements are far from optimal, except in one dimension, where position measurements are indeed optimal. This makes realistic experiments perform very well at few nanokelvin temperatures for all dimensions, and at subnanokelvin temperatures in the one-dimensional scenario. These results take a significant step towards experimental realization of probe-based quantum thermometry of Bose-Einstein condensates, as it deals with them in one, two, and three dimensions and uses feasible measurements applicable in current experimental setups.