Extracting the Mott gap from energy measurements in trapped atomic gases

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.