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

Abstract

We develop the number-conserving approach that 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 comprises, for each component, of a generalised Gross-Pitaevskii equation coupled to modified Bogoliubov-de Gennes equations. Lower-order approximations yield general formulations for multi-component Gross-Pitaevskii equations, and systems of multi-component Gross-Pitaevskii equations coupled to multi-component 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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• Fluctuation and interaction induced instability of dark solitons in single and binary condensates
• Kinetic Model of Trapped Finite Temperature Binary Condensates
• Particle-Number-Conserving Bogoliubov Approximation for Bose-Einstein Condensates Using Extended Catalytic States
• A Non-Equilibrium Kinetic Theory for Trapped Binary Condensates
• Properties of a trapped multiple-species bosonic mixture at the infinite-particle-number limit: A solvable model
• Fragmentation of a trapped multiple-species bosonic mixture
• Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature. II. The general case