Coherence properties of the two-dimensional Bose-Einstein condensate

TL;DR

This paper investigates the coherence properties and excitation spectrum of a two-dimensional trapped Bose gas at finite temperature using the Hartree-Fock-Bogoliubov method, providing theoretical predictions for experimental observations.

Contribution

It extends the HFB-Popov approach to two-dimensional systems, analyzing unique features like low-lying excitations and coherence, and predicts observable signatures of quasicondensation.

Findings

Calculated the Bragg response and coherence length in 2D Bose gases.

Compared 2D results with 1D and 3D cases.

Predicted experimental signatures of quasicondensate phase.

Abstract

We present a detailed finite-temperature Hartree-Fock-Bogoliubov (HFB) treatment of the two-dimensional trapped Bose gas. We highlight the numerical methods required to obtain solutions to the HFB equations within the Popov approximation, the derivation of which we outline. This method has previously been applied successfully to the three-dimensional case and we focus on the unique features of the system which are due to its reduced dimensionality. These can be found in the spectrum of low-lying excitations and in the coherence properties. We calculate the Bragg response and the coherence length within the condensate in analogy with experiments performed in the quasi-one-dimensional regime [Richard et al., Phys. Rev. Lett. 91, 010405 (2003)] and compare to results calculated for the one-dimensional case. We then make predictions for the experimental observation of the quasicondensate phase via Bragg spectroscopy in the quasi-two-dimensional regime.