Reduced dimensionality and spatial entanglement in highly anisotropic Bose-Einstein condensates
arXiv:1310.6621 · doi:10.1103/PhysRevA.90.013605
Abstract
We investigate the reduced dimensionality of highly anisotropic Bose-Einstein condensates (BECs) in connection to the entanglement between its spatial degrees of freedom. We argue that the reduced-dimensionality of the BEC is physically meaningful in a regime where spatial correlations are negligible. We handle the problem analytically within the mean-field approximation for general quasi-one-dimensional and -two-dimensional geometries, and obtain the optimal reduced-dimension, pure-state description of the condensate mean field. We give explicit solutions to the case of harmonic potentials, which we compare against exact numerical integration of the three-dimensional Gross-Pitaevskii equation.
15 pages, 3 figures. Minor changes in text to be in agreement with published version
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