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Title: Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate

Abstract

We consider a rapidly rotating two-component Bose-Einstein condensate (BEC) containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the mean-field quantum Hall regime, taking into account the coupling of these modes with density excitations. Using an analytic form for the density of the vortex lattice, we numerically calculate the elastic constants for different lattice geometries. We also apply this method to calculate the elastic constant for the single-component triangular lattice. For a two-component BEC, there are two kinds of Tkachenko modes, which we call acoustic and optical in analogy with phonons. For all lattice types, acoustic Tkachenko mode frequencies have quadratic wave-number dependence at long wavelengths, while the optical Tkachenko modes have linear dependence. For triangular lattices the dispersion of the Tkachenko modes are isotropic, while for other lattice types the dispersion relations show directional dependence consistent with the symmetry of the lattice. Depending on the intercomponent interaction there are five distinct lattice types, and four structural phase transitions between them. Two of these transitions are second order and are accompanied by the softening of an acoustic Tkachenko mode. The remaining two transitions are first order and while one of themmore » is accompanied by the softening of an optical mode, the other does not have any dramatic effect on the Tkachenko spectrum. We also find an instability of the vortex lattice when the intercomponent repulsion becomes stronger than the repulsion within components.« less

Authors:
;  [1]
  1. Department of Physics, Bilkent University, 06800 Ankara (Turkey)
Publication Date:
OSTI Identifier:
20974627
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.023611; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; DENSITY; DISPERSION RELATIONS; EXCITATION; INTERACTIONS; MEAN-FIELD THEORY; OPTICAL MODES; OSCILLATIONS; PHASE TRANSFORMATIONS; SYMMETRY; WAVELENGTHS

Citation Formats

Keceli, M., and Oktel, M. Oe.. Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.023611.
Keceli, M., & Oktel, M. Oe.. Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate. United States. doi:10.1103/PHYSREVA.73.023611.
Keceli, M., and Oktel, M. Oe.. Wed . "Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate". United States. doi:10.1103/PHYSREVA.73.023611.
@article{osti_20974627,
title = {Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate},
author = {Keceli, M. and Oktel, M. Oe.},
abstractNote = {We consider a rapidly rotating two-component Bose-Einstein condensate (BEC) containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the mean-field quantum Hall regime, taking into account the coupling of these modes with density excitations. Using an analytic form for the density of the vortex lattice, we numerically calculate the elastic constants for different lattice geometries. We also apply this method to calculate the elastic constant for the single-component triangular lattice. For a two-component BEC, there are two kinds of Tkachenko modes, which we call acoustic and optical in analogy with phonons. For all lattice types, acoustic Tkachenko mode frequencies have quadratic wave-number dependence at long wavelengths, while the optical Tkachenko modes have linear dependence. For triangular lattices the dispersion of the Tkachenko modes are isotropic, while for other lattice types the dispersion relations show directional dependence consistent with the symmetry of the lattice. Depending on the intercomponent interaction there are five distinct lattice types, and four structural phase transitions between them. Two of these transitions are second order and are accompanied by the softening of an acoustic Tkachenko mode. The remaining two transitions are first order and while one of them is accompanied by the softening of an optical mode, the other does not have any dramatic effect on the Tkachenko spectrum. We also find an instability of the vortex lattice when the intercomponent repulsion becomes stronger than the repulsion within components.},
doi = {10.1103/PHYSREVA.73.023611},
journal = {Physical Review. A},
number = 2,
volume = 73,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
  • We study the dynamics of a two-component Bose-Einstein condensate where the two components are coupled via an optical lattice. In particular, we focus on the dynamics as one drives the system through a critical point of a first-order phase transition characterized by a jump in the internal populations. Solving the time-dependent Gross-Pitaevskii equation, we analyze the breakdown of adiabaticity, impact of nonlinear atom-atom scattering, and role of a harmonic trapping potential. Our findings demonstrate that the phase transition is resilient to both contact interaction between atoms and external trapping confinement.
  • The present paper suggests the continuum theory of Tkachenko modes in a rotating two-dimensional Bose-Einstein condensate taking into account density inhomogeneity and compressibility of the condensate. The theory is based on the solution of coupled hydrodynamic equations for vortex and liquid motion with proper boundary conditions, which were derived for the condensate described by the Thomas-Fermi approximation. Compressibility becomes essential at rapid rotation with angular velocity close to the trap frequency. The theory is in reasonable agreement with experimental observation of Tkachenko modes.
  • In a rapidly rotating Bose-Einstein condensate (BEC) the condensate wave function is analogous to that of a type II superconductor close to the critical magnetic field H{sub c2}. This wave function is a superposition of the lowest Landau levels (LLL) of a charged particle in a magnetic field and corresponds to a vortex lattice. This leads to the inverted-parabola density profile of the BEC in the parabolic trap similar to slower rotation outside the LLL regime. Then one can apply the continuum theory of the Tkachenko modes (transverse sound modes in the vortex lattice) suggested for slower rotation, but withmore » another shear modulus also known for type II superconductors at H{sub c2}. The theory yields a simple expression for the Tkachenko eigenfrequencies of the BEC cloud. The comparison with experiment shows that the experimental conditions have not yet reached the LLL regime.« less
  • The continuum theory of Tkachenko modes in a rotating 2D Bose-Einstein condensate (BEC) is considered taking into account density inhomogeneity and compressibility of the condensate. Two regimes of rotation are discussed: (i) the Vortex Line Lattice (VLL) regime, in which the vortex array consists of thin vortex lines with the core size much less than the intervortex distance; (ii) the Lowest-Landau Level (LLL) regime, in which vortex cores overlap and the BEC wave function is a superposition of states at the lowest Landau level. The theory is in good agreement with experimental observation of Tkachenko modes in the VLL regime.more » But theoretical frequencies in the LLL regime are essentially higher than those observed for very rapidly rotating BEC. This provides evidence that the experiment has not yet reached the LLL regime.« less
  • We consider the ground state of vortices in a rotating Bose-Einstein condensate that is loaded in a corotating two-dimensional optical lattice. Due to the competition between vortex interactions and their potential energy, the vortices arrange themselves in various patterns, depending on the strength of the optical potential and the vortex density. We outline a method to determine the phase diagram for arbitrary vortex filling factor. Using this method, we discuss several filling factors explicitly. For increasing strength of the optical lattice, the system exhibits a transition from the unpinned hexagonal lattice to a lattice structure where all the vortices aremore » pinned by the optical lattice. The geometry of this fully pinned vortex lattice depends on the filling factor and is either square or triangular. For some filling factors there is an intermediate half-pinned phase where only half of the vortices is pinned. We also consider the case of a two-component Bose-Einstein condensate, where the possible coexistence of the above-mentioned phases further enriches the phase diagram. In addition, we calculate the dispersion of the low-lying collective modes of the vortex lattice and find that, depending on the structure of the ground state, they can be gapped or gapless. Moreover, in the half-pinned and fully pinned phases, the collective mode dispersion is anisotropic. Possible experiments to probe the collective mode spectrum, and in particular the gap, are suggested.« less