110 research outputs found
Manifestation of a gap due to the exchange energy in a spinor condensate
We investigate the dynamic response of population transfer between two
components of a finite temperature spinor Bose condensed gas to a
time-dependent coupling potential. Comparison between results obtained in the
Bogoliubov-Popov approximation (BPA) and in the generalized random phase
approximation (GRPA) shows noticeable discrepancies. In particular, the
inter-component current response function calculated in the GRPA displays a
gapped spectrum due to the exchange interaction energy whereas the
corresponding density response function is gapless. We argue that the GRPA is
superior since, contrary to the BPA, it preserves the SU(2) symmetry and the
f-sum rule associated to the spinor gas. In order to validate the
approximation, we propose an experimental setup that allows the observation of
the predicted gap.Comment: 5 pages, 2 figure
Tkachenko modes and structural phase transitions of the vortex lattice of a two component Bose-Einstein condensate
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.Comment: 24 pages, 13 figures, typos corrected, references added, final
versio
Pairing and Vortex Lattices for Interacting Fermions in Optical Lattices with a Large Magnetic Field
We study the structure of pairing order parameter for spin-1/2 fermions with
attractive interactions in a square lattice under a uniform magnetic field.
Because the magnetic translation symmetry gives a unique degeneracy in the
single-particle spectrum, the wave function has both zero and finite momentum
components co-existing, and their relative phases are determined by a
self-consistent mean-field theory. We present a microscopic calculation that
can determine the vortex lattice structure in the superfluid phase for
different flux densities. Phase transition from a Hofstadter insulator to a
superfluid phase is also discussed.Comment: 4 pages, 3 figures, one table, published versio
Phase Boundary of the Boson Mott Insulator in a Rotating Optical Lattice
We consider the Bose-Hubbard model in a two dimensional rotating optical
lattice and investigate the consequences of the effective magnetic field
created by rotation. Using a Gutzwiller type variational wavefunction, we find
an analytical expression for the Mott insulator(MI)-Superfluid(SF) transition
boundary in terms of the maximum eigenvalue of the Hofstadter butterfly. The
dependence of phase boundary on the effective magnetic field is complex,
reflecting the self-similar properties of the single particle energy spectrum.
Finally, we argue that fractional quantum Hall phases exist close to the MI-SF
transition boundaries, including MI states with particle densities greater than
one.Comment: 5 pages,3 figures. High resolution figures available upon reques
Spectrum of a particle on a polyhedron enclosing a synthetic magnetic monopole
Cataloged from PDF version of article.We consider a single particle hopping on a tight binding lattice formed by the vertices of a regular polyhedron and discuss the effect of a magnetic monopole enclosed in the polyhedron. The presence of the monopole induces phases on the hopping terms, given by Peierls substitution. By requiring the flux through each face of a regular polyhedron to be the same, Dirac's quantization condition is obtained in this discrete setting. For each regular polyhedron, we calculate the energy spectrum for an arbitrary value of the flux through a Dirac string coming in from one of the faces. We find that the energy levels are degenerate only when the flux through the Dirac string corresponds to a quantized monopole. We show that the degeneracies in the presence of the monopole can be classified using the double group of the symmetry of the polyhedron and label all energy levels with corresponding irreducible representations
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