Superfluidity and Interference Pattern of Ultracold Bosons in Optical Lattices

TL;DR

This paper investigates the superfluid behavior of ultracold bosons in optical lattices using the Bose-Hubbard model, highlighting the superfluid fraction as a key indicator of the Mott-insulator transition.

Contribution

It introduces a microscopic definition of superfluid fraction based on phase response and compares it with other physical observables in small 1D systems.

Findings

Superfluid fraction clearly signals the Mott-insulator transition.

Interference pattern visibility does not directly indicate superfluidity.

Exact numerical calculations confirm the superfluid fraction's effectiveness.

Abstract

We present a study of the superfluid properties of atomic Bose gases in optical lattice potentials using the Bose-Hubbard model. To do this, we use a microscopic definition of the superfluid fraction based on the response of the system to a phase variation imposed by means of twisted boundary conditions. We compare the superfluid fraction to other physical quantities, i.e., the interference pattern after ballistic expansion, the quasi-momentum distribution, and number fluctuations. We have performed exact numerical calculations of all these quantities for small one-dimensional systems. We show that the superfluid fraction alone exhibits a clear signature of the Mott-insulator transition. Observables like the fringe visibility, which probe only ground state properties, do not provide direct information on superfluidity and the Mott-insulator transition.