Vortices in spatially inhomogeneous superfluids

Abstract

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 rapidrotation limit it is extremely uniform, despite a strongly inhomogeneous (nearly) Thomas-Fermi condensate density ρs(r). The weak radially-dependent contribution (∝ ∇ 2 ln ρs(r)) to the vortex distribution, that vanishes with the number of vortices Nv as 1 Nv , 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. One striking consequence of the inhomogeneous vortex distribution is an azimuthally-directed, radially-shearing superflow.

BEC-BCS Crossover in “Magnetized” Feshbach-Resonantly Paired Superfluids

“…1. We find [15] that above expressions for h m (δ) and h c2 (δ) receive only small O(γ) correction for δ < −γ 1/2 ǫ F . Hence in contrast to the BCS side, where the system undergoes phase separation for an arbitrary small m = 0, on the BEC side the transition at h m (δ) is into a uniform magnetized superfluid (SF M ) that persists over a finite range of m and is a coherent superposition of a singlet molecular condensate and fully spin-polarized Fermi gas.…”

Three-dimensional vortex structure of a fast rotating Bose-Einstein condensate with harmonic-plus-quartic confinement

“…In particular, the vortex merging leading to the formation of the central hole in a condensate is proved to be highly three-dimensional. Quantitative measurements of the intervortex spacing give a new validation of the theoretical study of Sheehy and Radzihovsky [26,27] predicting vortex lattice inhomogeneity from local density profile. An interesting question remaining for future numerical investigations is whether or not the condensate trapped in a quadratic-plus-quartic potential enters the lowest Landau level regime for Ω ≃ Ω h .…”

“…4 to recent theory of Sheehy and Radzihovsky [26,27]. They expressed the vortex density n v (r) as a function of the local superfluid density ρ s (r):…”

“…6 the TF fit for the integrated density profile (ρ s (r) =ρ z TF (r)) and the characteristic length for the vortex-core ξ v defined as [26] …”

Unconventional interaction between vortices in a polarized Fermi gas

“…However, an important problem yet to be explored is the possible influence of strong spatial inhomogeneities caused by the presence of the trap on the form of the vortex lattice, as studied by Sheehy and Radzihovsky in the context of trapped Bose gases. [60,61] They have provided an explanation for the striking uniformity of the vortex lattices seen in experiments in spite of the strong spatial variation of the local superfluid density imposed by the trap. Moreover, they have shown that an interplay of an inhomogeneous trap potential and vortex discreteness leads to a vortex density that is largest in the center of the trap, a counterintuitive result from the energetic point of view because both the kinetic energy cost and the repulsive interaction between vortices are proportional to the local superfluid density and are therefore largest in the center of the trap.…”