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arXiv:2208.03172 · Physical Review A

Dynamics of a massive superfluid vortex in rk confining potentials

Andrea Richaud, Pietro Massignan, Vittorio Penna, Alexander L. Fetter

Published Dec 13, 2022• 22 citations
arXivHTMLPDF

Abstract

We study the motion of a superfluid vortex in condensates having different background density profiles, ranging from parabolic to uniform. The resulting effective point-vortex model for a generic power-law potential $\ensuremath{\propto}{r}^{k}$ can be experimentally realized with recent advances in optical-trapping techniques. Our analysis encompasses both empty-core and filled-core vortices. In the latter case, the vortex acquires a mass due to the presence of distinguishable atoms located in its core. The axisymmetry allows us to reduce the coupled dynamical equations of motion to a single radial equation with an effective potential ${V}_{\mathrm{eff}}$. In many cases, ${V}_{\mathrm{eff}}$ has a single minimum, where the vortex precesses uniformly. The dynamics of the vortex and the localized massive core arises from the dependence of the energy on the radial position of the vortex and from the ${r}^{k}$ trap potential. We find that a positive vortex with small mass orbits in the positive direction, but the sense of precession can reverse as the core mass increases. Early experiments and theoretical studies on two-component vortices found some qualitatively similar behavior.

DOI
10.1103/physreva.106.063307

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We study the motion of a superfluid vortex in condensates having different background density profiles, ranging from parabolic to uniform. The resulting effective point-vortex model for a generic power-law potential \ensuremath∝rk\ensuremath{\propto}{r}^{k}\ensuremath∝rk can be experimentally realized with recent advances in optical-trapping techniques. Our analysis encompasses both empty-core and filled-core vortices. In the latter case, the vortex acquires a mass due to the presence of distinguishable atoms located in its core. The axisymmetry allows us to reduce the coupled dynamical equations of motion to a single radial equation with an effective potential Veff{V}_{\mathrm{eff}}Veff​. In many cases, Veff{V}_{\mathrm{eff}}Veff​ has a single minimum, where the vortex precesses uniformly. The dynamics of the vortex and the localized massive core arises from the dependence of the energy on the radial position of the vortex and from the rk{r}^{k}rk trap potential. We find that a positive vortex with small mass orbits in the positive direction, but the sense of precession can reverse as the core mass increases. Early experiments and theoretical studies on two-component vortices found some qualitatively similar behavior.
Abstract We study the motion of superfluid vortices with filled massive cores. Previous point-vortex models already pointed out the impact of the core mass on the vortex dynamical properties, but relied on an assumption that is questionable in many physical systems where the immiscibility condition is barely satisfied: the fact that the massive core always lays at the very bottom of the effective confining potential constituted by the hosting vortex. Here, we relax this assumption and present a new point-vortex model where quantum vortices are harmonically coupled to their massive cores. We thoroughly explore the new dynamical regimes offered by this improved model; we then show that the functional dependence of the system normal modes on the microscopic parameters can be correctly interpreted only within this new generalized framework. Our predictions are benchmarked against the numerical simulations of coupled Gross–Pitaevskii equations for a realistic mixture of atomic Bose–Einstein condensates.
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 ${\ensuremath{\rho}}_{s}(r)$. The weak radially dependent contribution $[\ensuremath{\propto}{\ensuremath{\nabla}}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\rho}}_{s}(r)]$ to the vortex distribution, that vanishes with the number of vortices Nv{N}_{v}Nv​ as 1∕Nv1∕{N}_{v}1∕Nv​, arises from the interplay between vortex quantum discreteness (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.
Abstract We consider the dynamical properties of quantum vortices with filled massive cores, hence the term “massive vortices”. While the motion of massless vortices is described by first-order motion equations, the inclusion of core mass introduces a second-order time derivative in the motion equations and thus doubles the number of independent dynamical variables needed to describe the vortex. The simplest possible system where this physics is present, i.e. a single massive vortex in a circular domain, is thoroughly discussed. We point out that a massive vortex can exhibit various dynamical regimes, as opposed to its massless counterpart, which can only precess at a constant rate. The predictions of our analytical model are validated by means of numerical simulations of coupled Gross-Pitaevskii equations, which indeed display the signature of the core inertial mass. Eventually, we discuss a nice formal analogy between the motion of massive vortices and that of massive charges in two-dimensional domains pierced by magnetic fields.
We study the massive point-vortex model introduced in Richaud et al. [A. Richaud, V. Penna, R. Mayol, and M. Guilleumas, Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core.
In this thesis, we analytically and numerically study two different scenarios of vortex dynamics in a two-dimensional superfluid. The first system we explore is an expanding cluster of like-sign vortices, which recently suggested it could explain observations in a superfluid optomechanics experiment. We employ a recent theoretical model that approximates large collections of vortices as a fluid and present an analytic solution for its dynamics. Analysis suggests that as a cluster expands due to thermal friction, it forms a Rankine vortex (i.e., a top-hat distribution) that expands self-similarly in time regardless of initial vorticity distribution. Numerical simulations of point vortices confirm this universal expanding regime and further demonstrates vortex lattice formation that goes beyond the vortex fluid theory. We analyse correlations that emerge in the resulting lattices and observe decaying disorder as the cluster expands. Furthermore, we analyse experimental data from a quasi-two-dimensional 87Rb Bose-Einstein condensate, which supports the vortex fluid theory’s predictions.The second scenario considers the dynamics of a scattering event where a single quantum vortex interacts with a uniform, circular pinning potential in a steady two-dimensional superfluid flow. We first develop an approximate hydrodynamical model to understand the interaction between the vortex and the pinning potential in the conservative regime and find it is in good agreement with the mean-field Gross-Pitaevskii equation in the low-velocity limit. We further solve the Gross-Pitaevskii equation for higher background velocities to study how the vortex moves around pinning sites, interacts with it, and ultimately becomes pinned. We uncover four different regimes of vortex pinning, each marked with a characteristic emission of sound energy. Finally, we study how vortices become unpinned from a pinning site, revealing large vortex dipoles form to stabilise the system.Our work in this thesis takes significant steps towards advancing knowledge of both the collective dynamics of vortices and their individual interaction with defects upon surface substrates. Our numerical and analytical results opens up new avenues of exploration be it further understanding dissipation mechanisms in two-dimensional superfluids, or elucidating the nature of vortex pinning in systems such as neutron stars.
We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of the parabolic trap there is a logarithmic correction in the dependence of the precession frequency $\ensuremath{\omega}$ on the chemical potential $\ensuremath{\mu}$, this is no longer true for a general potential $V(r)\ensuremath{\propto}{r}^{p}$. Our calculations suggest that for p>2p>2p>2, the precession frequency scales with $\ensuremath{\mu}$ as $\ensuremath{\omega}\ensuremath{\sim}{\ensuremath{\mu}}^{\ensuremath{-}2/p}$. This theoretical prediction is corroborated by numerical computations, not only at the level of spectral (Bogolyubov--de Gennes) stability analysis by identifying the relevant precession mode dependence on $\ensuremath{\mu}$ but also through direct numerical computations of the vortex evolution in the large-$\ensuremath{\mu}$, so-called Thomas-Fermi, limit. Additionally, the dependence of the precession frequency on the distance to the trap center of an initially displaced vortex is examined, and the corresponding predictions are tested against numerical results.