Alexander L. Fetter

Rotating vortex lattice in a Bose-Einstein condensate trapped in combined quadratic and quartic radial potentials

A dense vortex lattice in a rotating dilute Bose-Einstein condensate is studied with the Thomas-Fermi approximation. The upper critical angular velocity Omega_{c2} occurs when the intervortex separation b becomes comparable with the vortex core radius xi. For a radial harmonic trap, the loss of confinement as Omega approaches omega_perp implies a singular behavior. In contrast, an additional radial quartic potential provides a simple model for which Omega_{c2} is readily determined. Unlike the case of a type-II superconductor at fixed temperature, the onset of Omega_{c2} arises not only from decreasing b but also from increasing xi caused by the vanishing of the chemical potential as Omega approaches Omega_{c2}.

Rapid rotation of a Bose-Einstein condensate in a harmonic plus quartic trap

A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic trap with quadratic and quartic radial confinement is studied analytically with the Thomas-Fermi approximation and numerically with the full time-independent Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed {omega} to exceed the radial harmonic frequency {omega}{sub perpendicular}. In the regime {omega} > or approx. {omega}{sub perpendicular}, the condensate contains a dense vortex array (approximated as solid-body rotation for the analytical studies). At a critical angular velocity {omega}{sub h}, a central hole appears in the condensate. Numerical studies confirm the predicted value of {omega}{sub h}, even for interaction parameters that are not in the Thomas-Fermi limit. The behavior is also investigated at larger angular velocities, where the system is expected to undergo a transition to a giant vortex (with pure irrotational flow)

Kelvin mode of a vortex in a nonuniform Bose-Einstein condensate

In a uniform fluid, a quantized vortex line with circulation h/M can support long-wavelength helical traveling waves {proportional_to}e{sup i(kz-{omega}{sub k}t)} with the well-known Kelvin dispersion relation {omega}{sub k}{approx_equal}(({Dirac_h}/2{pi})k{sup 2}/2M)ln(1/k{xi}), where {xi} is the vortex-core radius. This result is extended to include the effect of a nonuniform harmonic trap potential, using a quantum generalization of the Biot-Savart law that determines the local velocity V of each element of the vortex line. The normal-mode eigenfunctions form an orthogonal Sturm-Liouville set. Although the lines curvature dominates the dynamics, the transverse and axial trapping potential also affect the normal modes of a straight vortex on the symmetry axis of an axisymmetric Thomas-Fermi condensate. The leading effect of the nonuniform condensate density is to increase the amplitude along the axis away from the trap center. Near the ends, however, a boundary layer forms to satisfy the natural Sturm-Liouville boundary conditions. For a given applied frequency, the next-order correction renormalizes the local wave number k(z) upward near the trap center, and k(z) then increases still more toward the ends.

Vortex stabilization in a small rotating asymmetric Bose-Einstein condensate

We use a variational method to investigate the ground-state phase diagram of a small, asymmetric Bose-Einstein condensate with respect to the dimensionless interparticle interaction strength

Oscillations of a Bose-Einstein Condensate Rotating in a Harmonic Plus Quartic Trap

\ensuremath{\gamma}

Vortex Precession in a Rotating Nonaxisymmetric Trapped Bose-Einstein Condensate

and the applied external rotation speed

Bose gas: Theory and Experiment

\ensuremath{\Omega}.

Oscillations of a rapidly rotating annular Bose-Einstein condensate

For a given

Rotating trapped Bose-Einstein condensates

\ensuremath{\gamma},

Vortices in rotating trapped dilute Bose–Einstein condensates

the transition lines between no-vortex and vortex states are shifted toward higher