Superfluid and Mott Insulating shells of bosons in harmonically confined optical lattices

TL;DR

This paper investigates the coexistence of superfluid and Mott insulating shells in harmonically confined optical lattices, analyzing their excitation spectra, superfluid properties, and phase transitions.

Contribution

It introduces a detailed analysis of superfluid regions between Mott shells, including excitation spectra and the behavior of low-energy sound modes, extending understanding of phase coexistence.

Findings

Superfluid shells exhibit low energy sound modes with spatially varying velocities.

Superfluid order parameter differs from Gross-Pitaevskii form except near boundaries.

Berezinskii-Kosterlitz-Thouless transition and vortex pairs are discussed in thin superfluid shells.

Abstract

Weakly interacting atomic or molecular bosons in quantum degenerate regime and trapped in harmonically confined optical lattices, exhibit a wedding cake structure consisting of insulating (Mott) shells. It is shown that superfluid regions emerge between Mott shells as a result of fluctuations due to finite hopping. It is found that the order parameter equation in the superfluid regions is not of the Gross-Pitaeviskii type except near the insulator to superfluid boundaries. The excitation spectra in the Mott and superfluid regions are obtained, and it is shown that the superfluid shells posses low energy sound modes with spatially dependent sound velocity described by a local index of refraction directly related to the local superfluid density. Lastly, the Berezinskii-Kosterlitz-Thouless transition and vortex-antivortex pairs are discussed in thin (wide) superfluid shells (rings) limited by three (two) dimensional Mott regions.