Coherence properties of the two-dimensional Bose-Einstein condensate

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 previousl...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2004-10, Vol.70 (4), Article 043606
Main Authors: Gies, Christopher, Hutchinson, D. A. W.
Format: Article
Language:English
Subjects:
ATOMIC AND MOLECULAR PHYSICS
BOSE-EINSTEIN CONDENSATION
BOSE-EINSTEIN GAS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COHERENCE LENGTH
COMPARATIVE EVALUATIONS
EXCITATION
HARTREE-FOCK METHOD
HARTREE-FOCK-BOGOLYUBOV THEORY
MATHEMATICAL SOLUTIONS
ONE-DIMENSIONAL CALCULATIONS
SPECTRA
SPECTROSCOPY
THREE-DIMENSIONAL CALCULATIONS
TRAPPING
TWO-DIMENSIONAL CALCULATIONS
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Summary: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.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.70.043606