Bogoliubov approach to superfluidity of atoms in an optical lattice

TL;DR

This paper applies Bogoliubov theory to analyze superfluidity in atoms within optical lattices, deriving an explicit superfluid density expression and linking quantum depletion to the superfluid fraction, with implications for observing phase transitions.

Contribution

It introduces a new explicit formula for superfluid density in optical lattices and connects quantum depletion with superfluidity, enhancing understanding of the Mott-insulator transition.

Findings

Superfluid density can be explicitly calculated from phase rigidity.

Quantum depletion correlates with the superfluid fraction.

Band filling by depletion signals approach to insulator phase.

Abstract

We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This enables us to explore the connection between the quantum depletion of the condensate and the quasi-momentum distribution on the one hand and the superfluid fraction on the other. The approach to the insulator phase may be characterized through the filling of the band by quantum depletion, which should be directly observable via the matter wave interference patterns. We complement these findings by self-consistent Hartree-Fock-Bogoliubov-Popov calculations for one-dimensional lattices including the effects of a parabolic trapping potential.