Topological objects in twocomponent BoseEinstein condensates
Abstract
We study the topological objects in twocomponent BoseEinstein condensates. We compare two competing theories of twocomponent BoseEinstein condensates, the popular GrossPitaevskii theory, and the recently proposed gauge theory of twocomponent BoseEinstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of twocomponent BoseEinstein condensates, with the U(1) gauge symmetry, is remarkably similar to the Skyrme theory. Just like the Skyrme theory this theory admits the nonAbelian vortex, the helical vortex, and the vorticity knot. We construct the lightest knot solution in twocomponent BoseEinstein condensates numerically, and discuss how the knot can be constructed in the spin(1/2) condensate of {sup 87}Rb atoms.
 Authors:
 Center for Theoretical Physics, College of Natural Sciences, Seoul National University, Seoul 151742 (Korea, Republic of) and C. N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11790 (United States)
 (Korea, Republic of)
 Publication Date:
 OSTI Identifier:
 20786340
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.063603; (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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMS; BOSEEINSTEIN CONDENSATION; COMPARATIVE EVALUATIONS; GAUGE INVARIANCE; RUBIDIUM 87; SKYRME POTENTIAL; SPIN; TOPOLOGY; U1 GROUPS; VORTICES
Citation Formats
Cho, Y. M., Khim, Hyojoong, Zhang, Pengming, and School of Physics, College of Natural Sciences, Seoul National University, Seoul 151742. Topological objects in twocomponent BoseEinstein condensates. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.
Cho, Y. M., Khim, Hyojoong, Zhang, Pengming, & School of Physics, College of Natural Sciences, Seoul National University, Seoul 151742. Topological objects in twocomponent BoseEinstein condensates. United States. doi:10.1103/PHYSREVA.72.0.
Cho, Y. M., Khim, Hyojoong, Zhang, Pengming, and School of Physics, College of Natural Sciences, Seoul National University, Seoul 151742. Thu .
"Topological objects in twocomponent BoseEinstein condensates". United States.
doi:10.1103/PHYSREVA.72.0.
@article{osti_20786340,
title = {Topological objects in twocomponent BoseEinstein condensates},
author = {Cho, Y. M. and Khim, Hyojoong and Zhang, Pengming and School of Physics, College of Natural Sciences, Seoul National University, Seoul 151742},
abstractNote = {We study the topological objects in twocomponent BoseEinstein condensates. We compare two competing theories of twocomponent BoseEinstein condensates, the popular GrossPitaevskii theory, and the recently proposed gauge theory of twocomponent BoseEinstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of twocomponent BoseEinstein condensates, with the U(1) gauge symmetry, is remarkably similar to the Skyrme theory. Just like the Skyrme theory this theory admits the nonAbelian vortex, the helical vortex, and the vorticity knot. We construct the lightest knot solution in twocomponent BoseEinstein condensates numerically, and discuss how the knot can be constructed in the spin(1/2) condensate of {sup 87}Rb atoms.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 6,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}

We study the generation of twomode entanglement in a twocomponent BoseEinstein condensate trapped in a doublewell potential. The dynamics of the system is shown to be equivalent to that of two coupled harmonic oscillators in the low excitation regime. Strong entanglement between the two components can be achieved if the interspecies interaction is sufficiently strong. In particular, the condensate constitutes a symmetric Gaussian system and hence its entanglement of formation can be measured directly by fluctuations in the quadratures of the two constituent components.

Twocomponent gap solitons in two and onedimensional BoseEinstein condensates
We introduce two and onedimensional (1D) models of a binary BEC (BoseEinstein condensate) in a periodic potential, with repulsive interactions. We chiefly consider the most fundamental case of the interspecies repulsion with zero intraspecies interactions. The same system may also model a mixture of two mutually repulsive fermionic species. Existence and stability regions for gap solitons (GSs) supported by the interplay of the interspecies repulsion and periodic potential are identified. Twocomponent GSs are constructed by means of the variational approximation (VA) and in a numerical form. The VA provides an accurate description for the GS which is a compound statemore » 
Spontaneous spatial symmetry breaking in twocomponent BoseEinstein condensates
We discuss the general features of spontaneous spatial symmetry breaking in trapped twocomponent alkalimetal{endash}atom BoseEinstein condensates, and give qualitative guidelines for when it will occur. We further show that the HartreeFock equations admit symmetrybroken solutions for as few as two trapped atoms, discussing the particular system of one {sup 85}Rb atom and one {sup 87}Rb atom. It is also shown that the critical value of the interspecies scattering length for a mixture of Na and Rb in an isotropic trap depends strongly on the number of atoms in a manner not described by the standard ThomasFermi phase separation condition. {copyright}more » 
Manyparticle entanglement in twocomponent BoseEinstein condensates
We investigate schemes to dynamically create manyparticle entangled states of a twocomponent BoseEinstein condensate in a very short time proportional to 1/N, where N is the number of condensate particles. For small N we compare exact numerical calculations with analytical semiclassical estimates and find very good agreement for N{>=}50. We also estimate the effect of decoherence on our scheme, study possible scenarios for measuring the entangled states, and investigate experimental imperfections. 
Twocomponent BoseEinstein condensates in periodic potential
Coupled nonlinear Schroedinger (CNLS) equations with an external elliptic function potential model with high accuracy a quasionedimensional interacting twocomponent BoseEinstein condensate (BEC) trapped in a standing wave generated by a few laser beams. The construction of stationary solutions of the twocomponent CNLS equation with a periodic potential is detailed and their stability properties are studied by direct numerical simulations. Some of these solutions allow reduction to the Manakov system. From a physical point of view the trivial phase solutions can be interpreted as exact Bloch states at the edge of the Brillouin zone. Some of them are stable while othersmore »