Entanglement-based perturbation theory for highly anisotropic Bose-Einstein condensates

Tacla, Alexandre B. and Caves, Carlton M. (2011) Entanglement-based perturbation theory for highly anisotropic Bose-Einstein condensates. Physical Review a, 84 5: . doi:10.1103/PhysRevA.84.053606

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Author Tacla, Alexandre B.
Caves, Carlton M.
Title Entanglement-based perturbation theory for highly anisotropic Bose-Einstein condensates
Journal name Physical Review a   Check publisher's open access policy
ISSN 1050-2947
1094-1622
Publication date 2011-11
Sub-type Article (original research)
DOI 10.1103/PhysRevA.84.053606
Open Access Status File (Publisher version)
Volume 84
Issue 5
Total pages 12
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2012
Language eng
Abstract We investigate the emergence of three-dimensional behavior in a reduced-dimension Bose-Einstein condensate trapped by a highly anisotropic potential. We handle the problem analytically by performing a perturbative Schmidt decomposition of the condensate wave function between the tightly confined (transverse) direction(s) and the loosely confined (longitudinal) direction(s). The perturbation theory is valid when the nonlinear scattering energy is small compared to the transverse energy scales. Our approach provides a straightforward way, first, to derive corrections to the transverse and longitudinal wave functions of the reduced-dimension approximation and, second, to calculate the amount of entanglement that arises between the transverse and longitudinal spatial directions. Numerical integration of the three-dimensional Gross-Pitaevskii equation for different cigar-shaped potentials and experimentally accessible parameters reveals good agreement with our analytical model even for relatively high nonlinearities. In particular, we show that even for such stronger nonlinearities the entanglement remains remarkably small, which allows the condensate to be well described by a product wave function that corresponds to a single Schmidt term.
Keyword State
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
 
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