1,102,505 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
Quantization of generally covariant systems with extrinsic time
A generally covariant system can be deparametrized by means of an
``extrinsic'' time, provided that the metric has a conformal ``temporal''
Killing vector and the potential exhibits a suitable behavior with respect to
it. The quantization of the system is performed by giving the well ordered
constraint operators which satisfy the algebra. The searching of these
operators is enlightned by the methods of the BRST formalism.Comment: 10 pages. Definite published versio
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
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
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