Laser probing of single-particle energy gap of a Bose gas in an optical lattice in the Mott insulator phase

TL;DR

This paper demonstrates how to directly measure the energy gap in a Mott insulator phase of a Bose gas in an optical lattice using output coupling experiments, revealing the transition to superfluidity.

Contribution

It applies the Green's function approach to the Bose-Hubbard model to show how the energy gap can be experimentally detected via momentum-resolved output current spectra.

Findings

Energy gap between particle and hole excitations identified

Two peaks in output current spectrum correspond to excitations

Method can detect the Mott insulator to superfluid transition

Abstract

We study single-particle excitations in the Mott insulator phase of a Bose gas in an optical lattice. The characteristic feature of the single-particle spectrum in the Mott insulator phase is the existence of an energy gap between the particle and hole excitations. We show that this energy gap can be directly probed by an output coupling experiment. We apply the general expression for the output current derived by Luxat and Griffin, which is given in terms of the single-particle Green's functions of a trapped Bose gas, to the Mott insulator phase using the Bose-Hubbard model. We find that the energy spectrum of the momentum-resolved output current exhibits two characteristic peaks corresponding to the particle and hole excitations, and thus it can be used to detect the transition point from the Mott insulator to superfluid phase where the energy gap disappears.