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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}
}
  • We extend the results of a previous paper on the Gross-Pitaevskii description of rotating Bose-Einstein condensates in two-dimensional traps to confining potentials of the form V(r)=r{sup s}, 2<s<{infinity}. Writing the coupling constant as 1/{epsilon}{sup 2}, we study the limit {epsilon}{yields}0. We derive rigorously the leading asymptotics of the ground state energy and the density profile when the rotation velocity {omega} tends to infinity as a power of 1/{epsilon}. The case of asymptotically homogeneous potentials is also discussed.
  • We consider bosonic atoms that rotate in an anharmonic trapping potential. Using numerical diagonalization of the Hamiltonian, we get evidence for various phases of the gas for different values of the coupling between the atoms and of the rotational frequency of the trap. These include vortex excitation of single and multiple quantization, the phase of center-of-mass excitation, and the unstable phase.
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  • After delineating the physical regimes that vortex lattices encounter in rotating Bose-Einstein condensates as the rotation rate {omega} increases, we derive the normal modes of the vortex lattice in two dimensions at zero temperature. Taking into account effects of the finite compressibility, we find an inertial mode of frequency {>=}2{omega}, and a primarily transverse Tkachenko mode, whose frequency goes from being linear in the wave vector in the slowly rotating regime, where {omega} is small compared with the lowest compressional mode frequency, to quadratic in the wave vector in the opposite limit. We calculate the correlation functions of vortex displacementsmore » and phase, density and superfluid velocities, and find that the zero-point excitations of the soft quadratic Tkachenko modes lead in a large system to a loss of long-range phase correlations, growing logarithmically with distance, and hence lead to a fragmented state at zero temperature. The vortex positional ordering is preserved at zero temperature, but the thermally excited Tkachenko modes cause the relative positional fluctuations to grow logarithmically with separation at finite temperature. The superfluid density, defined in terms of the transverse velocity autocorrelation function, vanishes at all temperatures. Finally we construct the long-wavelength single-particle Green's function in the rotating system and calculate the condensate depletion as a function of temperature.« less