Criterion for bosonic superfluidity in an optical lattice

TL;DR

This paper proposes a new criterion based on visibility to accurately identify superfluidity in optical lattices, highlighting limitations of previous methods and implications for experimental observations.

Contribution

It introduces a visibility-based criterion for superfluidity detection and discusses temperature effects on trapped lattice bosons, challenging existing experimental interpretations.

Findings

Visibility must be 1 within O(N^{-2/3}) for superfluidity.

Zero-temperature visibility is higher than in current experiments.

Normal states may exist at low temperatures, enabling quantum critical studies.

Abstract

We show that the current method of determining superfluidity in optical lattices based on a visibly sharp bosonic momentum distribution $n({\bf k})$ can be misleading, for even a normal Bose gas can have a similarly sharp $n({\bf k})$. We show that superfluidity in a homogeneous system can be detected from the so-called visibility $(v)$ of $n({\bf k})$ $-$ that $v$ must be 1 within $O(N^{-2/3})$, where $N$ is the number of bosons. We also show that the T=0 visibility of trapped lattice bosons is far higher than what is obtained in some current experiments, suggesting strong temperature effects and that these states can be normal. These normal states allow one to explore the physics in the quantum critical region.