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Number-conserving approaches to n-component Bose-Einstein condensates.

Mason, P. and Gardiner, S.A. (2014) 'Number-conserving approaches to n-component Bose-Einstein condensates.', Physical review A : atomic, molecular and optical physics., 89 (4). 043617.


We develop the number-conserving approach, which has previously been used in a single-component Bose-Einstein condensed dilute atomic gas, to describe consistent coupled condensate and noncondensate number dynamics, to an n -component condensate. The resulting system of equations is comprised, for each component, of a generalized Gross-Pitaevskii equation coupled to modified Bogoliubov–de Gennes equations. Lower order approximations yield general formulations for multicomponent Gross-Pitaevskii equations, and systems of multicomponent Gross-Pitaevskii equations coupled to multicomponent modified number-conserving Bogoliubov–de Gennes equations. The analysis is left general, such that, in the n -component condensate, there may or may not be mutually coherent components. An expansion in powers of the ratio of noncondensate-to-condensate particle numbers for each coherent set is used to derive the self-consistent, second-order, dynamical equations of motion. The advantage of the analysis developed in this article is in its applications to dynamical instabilities that appear when two (or more) components are in conflict and where a significant noncondensed fraction of atoms is expected to appear.

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Publisher statement:Reprinted with permission from the American Physical Society: Peter Mason and Simon A. Gardiner, Physical Review A, 89, 043617, 2014. © 2014 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.
Date accepted:No date available
Date deposited:19 May 2014
Date of first online publication:April 2014
Date first made open access:No date available

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