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Title: Virial theorems for vortex states in a confined Bose-Einstein condensate

Abstract

We derive a class of virial theorems which provide stringent tests of both analytical and numerical calculations of vortex states in a confined Bose-Einstein condensate. In the special case of harmonic confinement we arrive at the somewhat surprising conclusion that the linear moments of the particle density, as well as the linear momentum, must vanish even in the presence of off-center vortices which lack axial or reflection symmetry. Illustrations are provided by some analytical results in the limit of a dilute gas, and by a numerical calculation of a class of single and double vortices at intermediate couplings. The effect of anharmonic confinement is also discussed.

Authors:
; ;  [1];  [2]
  1. Department of Physics, University of Crete, and Research Center of Crete, Heraklion (Greece)
  2. (United Kingdom)
Publication Date:
OSTI Identifier:
20786555
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.053609; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; BOSE-EINSTEIN CONDENSATION; CONFINEMENT; DENSITY; LINEAR MOMENTUM; REFLECTION; SYMMETRY; VIRIAL THEOREM; VORTICES

Citation Formats

Papanicolaou, N., Komineas, S., Cooper, N. R., and Theory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE. Virial theorems for vortex states in a confined Bose-Einstein condensate. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Papanicolaou, N., Komineas, S., Cooper, N. R., & Theory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE. Virial theorems for vortex states in a confined Bose-Einstein condensate. United States. doi:10.1103/PHYSREVA.72.0.
Papanicolaou, N., Komineas, S., Cooper, N. R., and Theory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE. Tue . "Virial theorems for vortex states in a confined Bose-Einstein condensate". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786555,
title = {Virial theorems for vortex states in a confined Bose-Einstein condensate},
author = {Papanicolaou, N. and Komineas, S. and Cooper, N. R. and Theory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE},
abstractNote = {We derive a class of virial theorems which provide stringent tests of both analytical and numerical calculations of vortex states in a confined Bose-Einstein condensate. In the special case of harmonic confinement we arrive at the somewhat surprising conclusion that the linear moments of the particle density, as well as the linear momentum, must vanish even in the presence of off-center vortices which lack axial or reflection symmetry. Illustrations are provided by some analytical results in the limit of a dilute gas, and by a numerical calculation of a class of single and double vortices at intermediate couplings. The effect of anharmonic confinement is also discussed.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
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  • We use entanglement to investigate the transition from vortex-liquid phase to vortex-lattice phase in a weakly interacting rotating Bose-Einstein condensate. For the torus geometry, the ground-state entanglement spectrum is analyzed to distinguish these two phases. The low-lying part of the ground-state entanglement spectrum, as well as the behavior of its lowest level, changes clearly when the transition occurs. For the sphere geometry, the entanglement gap in the conformal limit is also studied. We also show that the decrease in entanglement between particles can be regarded as a signal of the transition.
  • We analyze the scattering of vortex pairs (the particular case of 2D dark solitons) by a single quantum vortex in a Bose–Einstein condensate with repulsive interaction between atoms. For this purpose, an asymptotic theory describing the dynamics of such 2D soliton-like formations in an arbitrary smoothly nonuniform flow of a ultracold Bose gas is developed. Disregarding the radiation loss associated with acoustic wave emission, we demonstrate that vortex–antivortex pairs can be put in correspondence with quasiparticles, and their behavior can be described by canonical Hamilton equations. For these equations, we determine the integrals of motion that can be used tomore » classify various regimes of scattering of vortex pairs by a single quantum vortex. Theoretical constructions are confirmed by numerical calculations performed directly in terms of the Gross–Pitaevskii equation. We propose a method for estimating the radiation loss in a collision of a soliton-like formation with a phase singularity. It is shown by direct numerical simulation that under certain conditions, the interaction of vortex pairs with a core of a single quantum vortex is accompanied by quite intense acoustic wave emission; as a result, the conditions for applicability of the asymptotic theory developed here are violated. In particular, it is visually demonstrated by a specific example how radiation losses lead to a transformation of a vortex–antivortex pair into a vortex-free 2D dark soliton (i.e., to the annihilation of phase singularities).« less