3,229 research outputs found
Vortex lattice stability and phase coherence in three-dimensional rapidly rotating Bose condensates
We establish the general equations of motion for the modes of a vortex
lattice in a rapidly rotating Bose-Einstein condensate in three dimensions,
taking into account the elastic energy of the lattice and the vortex line
bending energy. As in two dimensions, the vortex lattice supports Tkachenko and
gapped sound modes. In contrast, in three dimensions the Tkachenko mode
frequency at long wavelengths becomes linear in the wavevector for any
propagation direction out of the transverse plane. We compute the correlation
functions of the vortex displacements and the superfluid order parameter for a
homogeneous Bose gas of bounded extent in the axial direction. At zero
temperature the vortex displacement correlations are convergent at large
separation, but at finite temperatures, they grow with separation. The growth
of the vortex displacements should lead to observable melting of vortex
lattices at higher temperatures and somewhat lower particle number and faster
rotation than in current experiments. At zero temperature a system of large
extent in the axial direction maintains long range order-parameter correlations
for large separation, but at finite temperatures the correlations decay with
separation.Comment: 10 pages, 2 figures, Changes include the addition of the particle
density - vortex density coupling and the correct value of the shear modulu
Tkachenko modes of vortex lattices in rapidly rotating Bose-Einstein condensates
We calculate the in-plane modes of the vortex lattice in a rotating Bose
condensate from the Thomas-Fermi to the mean-field quantum Hall regimes. The
Tkachenko mode frequency goes from linear in the wavevector, , for lattice
rotational velocities, , much smaller than the lowest sound wave
frequency in a finite system, to quadratic in in the opposite limit. The
system also supports an inertial mode of frequency . The
calculated frequencies are in good agreement with recent observations of
Tkachenko modes at JILA, and provide evidence for the decrease in the shear
modulus of the vortex lattice at rapid rotation.Comment: 4 pages, 2 figure
Vortex lattices in rapidly rotating Bose-Einstein condensates: modes and correlation functions
After delineating the physical regimes which vortex lattices encounter in
rotating Bose-Einstein condensates as the rotation rate, , 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 , and a primarily transverse
Tkachenko mode, whose frequency goes from being linear in the wave vector in
the slowly rotating regime, where 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 displacements 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.Comment: 11 pages Latex, no figure
Dislocation-Mediated Melting in Superfluid Vortex Lattices
We describe thermal melting of the two-dimensional vortex lattice in a
rotating superfluid by generalizing the Halperin and Nelson theory of
dislocation-mediated melting. and derive a melting temperature proportional to
the renormalized shear modulus of the vortex lattice. The rigid-body rotation
of the superfluid attenuates the effects of lattice compression on the energy
of dislocations and hence the melting temperature, while not affecting the
shearing. Finally, we discuss dislocations and thermal melting in inhomogeneous
rapidly rotating Bose-Einstein condensates; we delineate a phase diagram in the
temperature -- rotation rate plane, and infer that the thermal melting
temperature should lie below the Bose-Einstein transition temperature.Comment: 9 pages, 2 figure
Dissipationless Phonon Hall Viscosity
We study the acoustic phonon response of crystals hosting a gapped
time-reversal symmetry breaking electronic state. The phonon effective action
can in general acquire a dissipationless "Hall" viscosity, which is determined
by the adiabatic Berry curvature of the electron wave function. This Hall
viscosity endows the system with a characteristic frequency, \omega_v; for
acoustic phonons of frequency \omega, it shifts the phonon spectrum by an
amount of order (\omega/\omega_v)^2 and it mixes the longitudinal and
transverse acoustic phonons with a relative amplitude ratio of \omega/\omega_v
and with a phase shift of +/- \pi/2, to lowest order in \omega/\omega_v. We
study several examples, including the integer quantum Hall states, the quantum
anomalous Hall state in Hg_{1-y}Mn_{y}Te quantum wells, and a mean-field model
for p_x + i p_y superconductors. We discuss situations in which the acoustic
phonon response is directly related to the gravitational response, for which
striking predictions have been made. When the electron-phonon system is viewed
as a whole, this provides an example where measurements of Goldstone modes may
serve as a probe of adiabatic curvature of the wave function of the gapped
sector of a system.Comment: 14 page
Tkachenko modes as sources of quasiperiodic pulsar spin variations
We study the long wavelength shear modes (Tkachenko waves) of triangular
lattices of singly quantized vortices in neutron star interiors taking into
account the mutual friction between the superfluid and the normal fluid and the
shear viscosity of the normal fluid. The set of Tkachenko modes that propagate
in the plane orthogonal to the spin vector are weakly damped if the coupling
between the superfluid and normal fluid is small. In strong coupling, their
oscillation frequencies are lower and are undamped for small and moderate shear
viscosities. The periods of these modes are consistent with the observed
~100-1000 day variations in spin of PSR 1828-11.Comment: 7 pages, 3 figures, uses RevTex, v2: added discussion/references,
matches published versio
Tkachenko modes in a superfluid Fermi gas at unitarity
We calculate the frequencies of the Tkachenko oscillations of a vortex
lattice in a harmonically trapped superfluid Fermi gas. We use the
elasto-hydrodynamic theory by properly accounting for the elastic constants,
the Thomas-Fermi density profile of the atomic cloud, and the boundary
conditions. Thanks to the Fermi pressure, which is responsible for larger cloud
radii with respect to the case of dilute Bose-Einstein condensed gases, large
vortex lattices are achievable in the unitary limit of infinite scattering
length, even at relatively small angular velocities. This opens the possibility
of experimentally observing vortex oscillations in the regime where the
dispersion relation approaches the Tkachenko law for incompressible fluids and
the mode frequency is almost comparable to the trapping frequencies.Comment: 5 pages, 1 figure; minor changes, now published as Phys. Rev. A 77,
021602(R) (2008
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