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

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

Rapidly rotating Bose-Einstein condensates in anharmonic potentials

Rapidly rotating Bose-Einstein condensates confined in anharmonic traps can exhibit a rich variety of vortex phases, including a vortex lattice, a vortex lattice with a hole, and a giant vortex. Using an augmented Thomas-Fermi variational approach to determine the ground state of the condensate in the rotating frame -- valid for sufficiently strongly interacting condensates -- we determine the transitions between these three phases for a quadratic-plus-quartic confining potential. Combining the present results with previous numerical simulations of small rotating condensates in such anharmonic potentials, we delineate the general structure of the zero temperature phase diagram.Comment: 5 pages, 5 figure

Vortices in Spatially Inhomogeneous Superfluids

We study vortices in a radially inhomogeneous superfluid, as realized by a trapped degenerate Bose gas in a uniaxially symmetric potential. We show that, in contrast to a homogeneous superfluid, an off-axis vortex corresponds to an anisotropic superflow whose profile strongly depends on the distance to the trap axis. One consequence of this superflow anisotropy is vortex precession about the trap axis in the absence of an imposed rotation. In the complementary regime of a finite prescribed rotation, we compute the minimum-energy vortex density, showing that in the rapid-rotation limit it is extremely uniform, despite a strongly inhomogeneous (nearly) Thomas-Fermi condensate density $\rho_s(r)$. The weak radially-dependent contribution ($\propto \nabla^2\ln\rho_s(r)$) to the vortex distribution, that vanishes with the number of vortices $N_v$ as $\frac{1}{N_v}$, arises from the interplay between vortex quantum discretness (namely their inability to faithfully support the imposed rigid-body rotation) and the inhomogeneous superfluid density. This leads to an enhancement of the vortex density at the center of a typical concave trap, a prediction that is in quantitative agreement with recent experiments (cond-mat/0405240). One striking consequence of the inhomogeneous vortex distribution is an azimuthally-directed, radially-shearing superflow.Comment: 22 RevTeX pages, 20 figures, Submitted to PR

Influence of equation of state on interpretation of electrical conductivity measurements in strongly coupled tungsten plasma

We study the influence of equation-of-state (EOS) model on the interpretation of electrical conductivity measurements in strongly coupled plasma of tungsten by Korobenko et al. (2002 Plasma Physics Reports 28(12) 1008--1016). Three different semiempirical EOS models for tungsten are used. Discrepancies in obtained thermodynamic parameters and specific resistivity values as compared with calculation results of Korobenko et al. are analysed.Comment: 11 pages, 5 Postscript figures, accepted for publication in J. Phys. A: Math. Ge

Two-component Bose-Einstein Condensates with Large Number of Vortices

We consider the condensate wavefunction of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of $^{87}$Rb or $^{23}$Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of $\sqrt{3}$, and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.Comment: 4 pages, 2 figures, RevTe

Theory of vortex-lattice melting in a one-dimensional optical lattice

We investigate quantum and temperature fluctuations of a vortex lattice in a one-dimensional optical lattice. We discuss in particular the Bloch bands of the Tkachenko modes and calculate the correlation function of the vortex positions along the direction of the optical lattice. Because of the small number of particles in the pancake Bose-Einstein condensates at every site of the optical lattice, finite-size effects become very important. Moreover, the fluctuations in the vortex positions are inhomogeneous due to the inhomogeneous density. As a result, the melting of the lattice occurs from the outside inwards. However, tunneling between neighboring pancakes substantially reduces the inhomogeneity as well as the size of the fluctuations. On the other hand, nonzero temperatures increase the size of the fluctuations dramatically. We calculate the crossover temperature from quantum melting to classical melting. We also investigate melting in the presence of a quartic radial potential, where a liquid can form in the center instead of at the outer edge of the pancake Bose-Einstein condensates.Comment: 17 pages, 17 figures, submitted to Phys. Rev. A, references update

Tkachenko oscillations and the compressibility of a rotating Bose gas

The elastic oscillations of the vortex lattice of a cold Bose gas (Tkachenko modes) are shown to play a crucial role in the saturation of the compressibility sum rule, as a consequence of the hybridization with the longitudinal degrees of freedom. The presence of the vortex lattice is responsible for a $q^2$ behavior of the static structure factor at small wavevectors $q$, which implies the absence of long range order in 2D configurations at zero temperature. Sum rules are used to calculate the Tkachenko frequency in the presence of harmonic trapping. Results are derived in the Thomas-Fermi regime and compared with experiments as well as with previous theoretical estimates.Comment: 4 pages, 2 figure

Coulomb Charging Effects in an Open Quantum Dot

Low-temperature transport properties of a lateral quantum dot formed by overlaying finger gates in a clean one-dimensional channel are investigated. Continuous and periodic oscillations superimposed upon ballistic conductance steps are observed, when the conductance G of the dot changes within a wide range 0<G<6e^2/h. Calculations of the electrostatics confirm that the measured periodic conductance oscillations correspond to successive change of the total charge of the dot by $e$. By modelling the transport it is shown that the progression of the Coulomb oscillations into the region G>2e^2/h may be due to suppression of inter-1D-subband scattering. Fully transmitted subbands contribute to coherent background of conductance, while sequential tunneling via weakly transmitted subbands leads to Coulomb charging of the dot.Comment: 12 pages, RevTeX, 15 eps figures included, submitted to Phys. Rev.

Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates

The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both the BdG and TDGP approaches allows one to unambiguously identify every observed mode.Comment: 5 pages, 4 figure