Quasi-long-range order in trapped two-dimensional Bose gases

TL;DR

This paper investigates how algebraic decay of correlations persists in trapped two-dimensional Bose gases, revealing that power-law behavior remains significant over a substantial part of the trap and is influenced by the normal component.

Contribution

The study extends the spin wave description to trapped gases, providing analytical expressions for correlations and revealing the impact of trap size and normal component on decay exponents.

Findings

Algebraic decay persists up to 20% of the Thomas-Fermi radius.

Trap-averaged correlations decay algebraically with larger exponents.

Normal component significantly influences the observed scaling exponents.

Abstract

We study the fate of algebraic decay of correlations in a harmonically trapped two-dimensional degenerate Bose gas. The analysis is inspired by recent experiments on ultracold atoms where power-law correlations have been observed despite the presence of the external potential. We generalize the spin wave description of phase fluctuations to the trapped case and obtain an analytical expression for the one-body density matrix within this approximation. We show that algebraic decay of the central correlation function persists to lengths of about 20% of the Thomas--Fermi radius. We establish that the trap-averaged correlation function decays algebraically with a strictly larger exponent weakly changing with trap size and find indications that the recently observed enhanced scaling exponents receive significant contributions from the normal component of the gas. We discuss radial and angular correlations and propose a local correlation approximation which captures the correlations very well. Our analysis goes beyond the usual local density approximation and the developed summation techniques constitute a powerful tool to investigate correlations in inhomogeneous systems.