Extracting the Mott gap from energy measurements in trapped atomic gases

TL;DR

This paper demonstrates that measuring the release-energy in trapped atomic gases can reveal the Mott gap, with the method being effective even under realistic confinement potentials, and shows how confinement affects the gap.

Contribution

It introduces a method to extract the Mott gap from energy measurements in confined atomic gases, accounting for different confinement types and going beyond simple approximations.

Findings

Release-energy curves show kinks indicating excitation gaps.

Harmonic confinement can renormalize the Mott gap.

Off-diagonal confinement closely matches the homogeneous case.

Abstract

We show that the measure of the so-called {\it release-energy}, which is an experimentally accessible quantity, makes it possible to assess the value of the Mott gap in the presence of the confinement potential that is unavoidable in the actual experimental setup. Indeed, the curve of the release-energy as a function of the total number of particles shows kinks that are directly related to the existence of excitation gaps. Calculations are presented within the Gutzwiller approach, but the final results go beyond this simple approximation and represent a genuine feature of the real system. In the case of harmonic confinement, the Mott gaps may be renormalized with respect to the uniform case. On the other hand, in the case of the recently proposed off-diagonal confinement, our results show an almost perfect agreement with the homogeneous case.