Tkachenko modes and structural phase transitions of the vortex lattice of a twocomponent BoseEinstein condensate
Abstract
We consider a rapidly rotating twocomponent BoseEinstein condensate (BEC) containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the meanfield 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 singlecomponent triangular lattice. For a twocomponent 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 wavenumber 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 »
 Authors:
 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; BOSEEINSTEIN CONDENSATION; DENSITY; DISPERSION RELATIONS; EXCITATION; INTERACTIONS; MEANFIELD 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 twocomponent BoseEinstein 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 twocomponent BoseEinstein 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 twocomponent BoseEinstein 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 twocomponent BoseEinstein condensate},
author = {Keceli, M. and Oktel, M. Oe.},
abstractNote = {We consider a rapidly rotating twocomponent BoseEinstein condensate (BEC) containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the meanfield 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 singlecomponent triangular lattice. For a twocomponent 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 wavenumber 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 twocomponent BoseEinstein 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 firstorder phase transition characterized by a jump in the internal populations. Solving the timedependent GrossPitaevskii equation, we analyze the breakdown of adiabaticity, impact of nonlinear atomatom 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.

Continuum theory of Tkachenko modes in rotating BoseEinstein condensate
The present paper suggests the continuum theory of Tkachenko modes in a rotating twodimensional BoseEinstein 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 ThomasFermi 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. 
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Pinning and collective modes of a vortex lattice in a BoseEinstein condensate
We consider the ground state of vortices in a rotating BoseEinstein condensate that is loaded in a corotating twodimensional 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 »