2004/01/23 by V. I. Yukalov, K. -P. Marzlin, Karl-Peter Marzlin +1 · 3 citations
Mathematics · Physics and Astronomy · #Bose–Einstein condensate #Coherent states #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Harmonic #Mathematics #Mode (computer interface) #Parametric statistics #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Resonance (particle physics) #Stability (learning theory) #Strong Light-Matter Interactions #Topology (electrical circuits) #cond-mat.soft
paper · pdf · doi:10.1103/physreva.69.023620
published as Phys. Rev. A 69, 023620 (2004) · One reference modified
arxiv created 2004/01/23 · openalex publication_date 2004/02/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Trapped atoms cooled down to temperatures below the Bose-Einstein condensation temperature are considered. Stationary solutions to the Gross-Pitaevskii equation (GPE) define the topological coherent modes, representing nonground-state Bose-Einstein condensates. These modes can be generated by means of alternating fields whose frequencies are in resonance with the transition frequencies between two collective energy levels corresponding to two different topological modes. The theory of resonant generation of these modes is generalized in several aspects: Multiple-mode formation is described; a shape-conservation criterion is derived, imposing restrictions on the admissible spatial dependence of resonant fields; evolution equations for the case of three coherent modes are investigated; the complete stability analysis is accomplished; the effects of harmonic generation and parametric conversion for the topological coherent modes are predicted. All considerations are realized both by employing approximate analytical methods as well as by numerically solving the GPE. Numerical solutions confirm all conclusions following from analytical methods.