Coherence and instability in a driven Bose–Einstein condensate: a fully dynamical number-conserving approach

Rajamanickam Ravisankar, Rajaswathi Kannan, Ramaswamy Radha +2 more

Rajamanickam Ravisankar, K. Rajaswathi, Ramaswamy Radha +2 more

T. P. Billam, Peter Mason, SA Gardiner

T. P. Billam, S. A. Gardiner

We consider a Bose–Einstein condensate driven by periodic δ -kicks. In contrast to first-order descriptions, which predict rapid, unbounded growth of the noncondensate in resonant parameter regimes, the consistent treatment of condensate depletion in our fully time-dependent, second-order description acts to damp this growth, leading to oscillations in the (non)condensate population and the coherence of the system.

R. Lacaze, Pierre Lallemand, Yves Pomeau A +1 more

Peter Mason, S. A. Gardiner

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.