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Title: Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps

Abstract

We study a rotating Bose-Einstein condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of two-dimensional Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as 1/{epsilon}{sup 2} and we are interested in the limit {epsilon}{yields}0 (Thomas-Fermi limit) with the angular velocity {omega} depending on {epsilon}. We derive rigorously the leading asymptotics of the ground state energy and the density profile when {omega} tends to infinity as a power of 1/{epsilon}. If {omega}({epsilon})={omega}{sub 0}/{epsilon} a ''hole'' (i.e., a region where the density becomes exponentially small as 1/{epsilon}{yields}{infinity}) develops for {omega}{sub 0} above a certain critical value. If {omega}({epsilon})>>1/{epsilon} the hole essentially exhausts the container and a ''giant vortex'' develops with the density concentrated in a thin layer at the boundary. While we do not analyze the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const vertical bar log {epsilon} vertical bar <{omega}({epsilon}) < or approx. const/{epsilon}.

Authors:
; ;  [1];  [2];  [3]
  1. Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna (Austria)
  2. (Austria)
  3. (Austria) and Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna (Austria)
Publication Date:
OSTI Identifier:
20929681
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 4; Other Information: DOI: 10.1063/1.2712421; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANGULAR VELOCITY; BOSE-EINSTEIN CONDENSATION; BOUNDARY-VALUE PROBLEMS; COUPLING CONSTANTS; GROUND STATES; SYMMETRY BREAKING; THIN FILMS; THOMAS-FERMI MODEL; TRAPS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Correggi, M., Rindler-Daller, T., Yngvason, J., Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna, and Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna. Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps. United States: N. p., 2007. Web. doi:10.1063/1.2712421.
Correggi, M., Rindler-Daller, T., Yngvason, J., Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna, & Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna. Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps. United States. doi:10.1063/1.2712421.
Correggi, M., Rindler-Daller, T., Yngvason, J., Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna, and Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna. Sun . "Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps". United States. doi:10.1063/1.2712421.
@article{osti_20929681,
title = {Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps},
author = {Correggi, M. and Rindler-Daller, T. and Yngvason, J. and Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Vienna and Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna},
abstractNote = {We study a rotating Bose-Einstein condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of two-dimensional Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as 1/{epsilon}{sup 2} and we are interested in the limit {epsilon}{yields}0 (Thomas-Fermi limit) with the angular velocity {omega} depending on {epsilon}. We derive rigorously the leading asymptotics of the ground state energy and the density profile when {omega} tends to infinity as a power of 1/{epsilon}. If {omega}({epsilon})={omega}{sub 0}/{epsilon} a ''hole'' (i.e., a region where the density becomes exponentially small as 1/{epsilon}{yields}{infinity}) develops for {omega}{sub 0} above a certain critical value. If {omega}({epsilon})>>1/{epsilon} the hole essentially exhausts the container and a ''giant vortex'' develops with the density concentrated in a thin layer at the boundary. While we do not analyze the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const vertical bar log {epsilon} vertical bar <{omega}({epsilon}) < or approx. const/{epsilon}.},
doi = {10.1063/1.2712421},
journal = {Journal of Mathematical Physics},
number = 4,
volume = 48,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}