On the anomalous density of a dilute homogeneous Bose gas

TL;DR

This paper develops a Hartree-Fock-Bogoliubov theory for dilute Bose gases, revealing that the anomalous density's sign depends on the condensate phase and can be inferred from sound velocity and condensed fraction measurements.

Contribution

The authors introduce a phase-inclusive Hartree-Fock-Bogoliubov framework that clarifies the observability and measurement of the anomalous density in Bose-Einstein condensates.

Findings

The sign of the anomalous density is phase-dependent and unobservable directly.

The absolute value of the anomalous density can be inferred from sound velocity and condensed fraction.

Theoretical predictions for the anomalous density in a uniform Bose gas are provided.

Abstract

Measurement of numerical values of the anomalous density, $\sigma$, which plays important role in Bose -- Einstein condensation, and, especially, determination of its sign, has been a long standing problem. We develop Hartree -- Fock -- Bogoliubov theory taking account arbitrary phase of the condensate wave function. We show that, the sign of $\sigma$ directly related to the phase, and, hence is not observable. Despite this, its absolute value can be extracted from measurements of the sound velocity and condensed fraction. We present theoretical prediction for $\vert \sigma \vert$ for a BEC in a uniform box.