Morphology of an interacting three-dimensional trapped Bose-Einstein condensate from many-particle variance anisotropy

Abstract

The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent a wave-packet is non-spherically symmetric. We examine an interacting three-dimensional trapped Bose-Einstein condensate at the limit of an infinite number of particles, and investigate its position, momentum, and angular-momentum anisotropies. Computing the variances of the three Cartesian components of the position, momentum, and angular-momentum operators we present simple scenarios where the anisotropy of a Bose-Einstein condensate is different at the many-body and mean-field levels of theory, despite having the same many-body and mean-field densities per particle. This suggests a way to classify correlations via the morphology of 100\% condensed bosons in a three-dimensional trap at the limit of an infinite number of particles. Implications are briefly discussed.

23 pages, 3 figures

References in corpus (11)

• Rigorous Derivation of the Gross-Pitaevskii Equation
• Variance as a sensitive probe of correlations enduring the infinite particle limit
• Entanglement in N-harmonium: bosons and fermions
• Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system
• Analytic solutions of topologically disjoint systems
• Overlap of exact and Gross-Pitaevskii wavefunctions in Bose-Einstein condensates of dilute gases
• Virial expansion coefficients in the harmonic approximation
• Analysis of a trapped Bose-Einstein condensate in terms of position, momentum, and angular-momentum variance
• Ultracold bosonic scattering dynamics off a repulsive barrier: coherence loss at the dimensional crossover
• Condensates in annuli: Dimensionality of the variance
• Variance of a Trapped Bose-Einstein Condensate