Experimental Determination of Bose-Hubbard Energies

TL;DR

This paper reports the first experimental measurement of both kinetic and interaction energies in a 3D Bose-Hubbard system at finite temperature, providing benchmarks for quantum many-body theories and methods for temperature estimation.

Contribution

It introduces novel experimental techniques to measure energies in the Bose-Hubbard model and compares results with theoretical predictions without fitting parameters.

Findings

Good agreement with Gutzwiller and cluster-Gutzwiller calculations

First experimental determination of both energies in a quantum many-body system

Potential application for temperature estimation in optical lattices

Abstract

We present the first experimental measurement of the ensemble averages of both the kinetic and interaction energies of the three-dimensional Bose--Hubbard model at finite temperature and various optical lattice depths across weakly to strongly interacting regimes, for an almost unit filling factor. The kinetic energy is obtained through Fourier transformation of a time-of-flight signal, and the interaction energy is measured using a newly developed atom-number-projection spectroscopy technique, by exploiting an ultra-narrow optical transition of two-electron atoms. The obtained experimental results can be used as benchmarks for state-of-the-art numerical methods of quantum many-body theory. As an illustrative example, we compare the measured energies with numerical calculations involving the Gutzwiller and cluster-Gutzwiller approximations, assuming realistic trap potentials and particle numbers at nonzero entropy (finite temperature); we obtain good agreement without fitting parameters. We also discuss the possible application of this method to temperature estimations for atoms in optical lattices using the thermodynamic relation. This study offers a unique advantage of cold atom system for `quantum simulators', because, to the best of our knowledge, it is the first experimental determination of both the kinetic and interaction energies of quantum many-body system.