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

Vortex Lattice Inhomogeneity in Spatially Inhomogeneous Superfluids

A trapped degenerate Bose gas exhibits superfluidity with spatially nonuniform superfluid density. We show that the vortex distribution in such a highly inhomogeneous rotating superfluid is nevertheless nearly uniform. The inhomogeneity in vortex density, which diminishes in the rapid-rotation limit, is driven by the discrete way vortices impart angular momentum to the superfluid. This effect favors highest vortex density in regions where the superfluid density is most uniform (e.g., the center of a harmonically trapped gas). A striking consequence of this is that the boson velocity deviates from a rigid-body form exhibiting a radial-shear flow past the vortex lattice.Comment: 5 RevTeX pgs,2 figures, published versio

Giant Vortex Lattice Deformations in Rapidly Rotating Bose-Einstein Condensates

We have performed numerical simulations of giant vortex structures in rapidly rotating Bose-Einstein condensates within the Gross-Pitaevskii formalism. We reproduce the qualitative features, such as oscillation of the giant vortex core area, formation of toroidal density hole, and the precession of giant vortices, observed in the recent experiment [Engels \emph{et.al.}, Phys. Rev. Lett. {\bf 90}, 170405 (2003)]. We provide a mechanism which quantitatively explains the observed core oscillation phenomenon. We demonstrate the clear distinction between the mechanism of atom removal and a repulsive pinning potential in creating giant vortices. In addition, we have been able to simulate the transverse Tkachenko vortex lattice vibrations.Comment: 5 pages, 6 figures; revised description of core oscillation, new subfigur

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

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

Pinning and collective modes of a vortex lattice in a Bose-Einstein condensate

We consider the ground state of vortices in a rotating Bose-Einstein condensate that is loaded in a corotating two-dimensional 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 are pinned by the optical lattice. The geometry of this fully pinned vortex lattice depends on the filling factor and is either square or triangular. For some filling factors there is an intermediate half-pinned phase where only half of the vortices is pinned. We also consider the case of a two-component Bose-Einstein condensate, where the possible coexistence of the above-mentioned phases further enriches the phase diagram. In addition, we calculate the dispersion of the low-lying collective modes of the vortex lattice and find that, depending on the structure of the ground state, they can be gapped or gapless. Moreover, in the half-pinned and fully pinned phases, the collective mode dispersion is anisotropic. Possible experiments to probe the collective mode spectrum, and in particular the gap, are suggested.Comment: 29 pages, 4 figures, changes in section

Transients influencing rocket engine ignition and popping Interim report

Engine design and operating parameters studied for effects on rocket engine ignition and poppin

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

Soft Pomeron and Lower-Trajectory Intercepts

We present a preliminary report on the determination of the intercepts and couplings of the soft pomeron and of the rho/omega and f/a trajectories from the largest data set available for all total cross sections and real parts of the hadronic amplitudes. Factorization is reasonably satisfied by the pomeron couplings, which allows us to make predictions on gamma gamma and gamma p total cross sections. In addition we show that these data cannot discriminate between fits based on a simple Regge pomeron-pole and on an asymptotic log^2s-type behaviour, implying that the effect of unitarisation is negligible. Also we examine the range of validity in energy of the fit, and the bounds that these data place on the odderon and on the hard pomeron.Comment: 13 pages, LaTeX, 14 figures. Presented by K. Kang at a 4th Workshop on Quantum Chromodynamics, June 1 - 6, 1998, The American University of Paris, Paris, France, and at the 4th Workshop on Small-x and Diffractive Physics, September 17 - 20, 1998, Fermi National Accelerator Laboratory, Batavia, I

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