Sub-nK thermometry of an interacting $d$-dimensional homogeneous Bose gas

TL;DR

This paper proposes a feasible impurity-based thermometry method for homogeneous Bose-Einstein condensates across 1D, 2D, and 3D, showing that higher dimensions allow for more precise temperature measurements in the sub-nano Kelvin range.

Contribution

It introduces a non-destructive thermometry protocol applicable in multiple dimensions and analyzes the effectiveness of feasible Gaussian measurements, highlighting the optimality of position measurements in 1D.

Findings

Higher dimension improves thermometry precision.

Position measurements are optimal in 1D.

Feasible measurements perform well at nano Kelvin temperatures.

Abstract

We propose experimentally feasible means for non-destructive thermometry of homogeneous Bose Einstein condensates in different spatial dimensions ($d\in\{1,2,3\}$). Our impurity based protocol suggests that the fundamental error bound on thermometry at the sub nano Kelvin domain depends highly on the dimension, in that the higher the dimension the better the precision. Furthermore, sub-optimal 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 1D, where position measurements are indeed optimal. This makes realistic experiments perform very well at few nano Kelvin temperatures for all dimensions, and at sub nano Kelvin temperatures in the one dimensional scenario. These results take a significant step towards experimental realisation 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.