Superfluid Vortex Dynamics on Planar Sectors and Cones

We study the dynamics of vortices formed in a superfluid film adsorbed on the curved two-dimensional surface of a cone. To this aim, we observe that a cone can be unrolled to a sector on a plane with periodic boundary conditions on the straight sides. The sector can then be mapped conformally to the whole plane, leading to the relevant stream function. In this way, we show that a superfluid vortex on the cone precesses uniformly at fixed distance from the apex. The stream function also yields directly the interaction energy of two vortices on the cone. We then study the vortex dynamics on unbounded and bounded cones. In suitable limits, we recover the known results for dynamics on cylinders and planar annuli.Comment: 10 pages, 8 figure

Quantized superfluid vortex dynamics on cylindrical surfaces and planar annuli

Superfluid vortex dynamics on an infinite cylinder differs significantly from that on a plane. The requirement that a condensate wave function be single valued upon once encircling the cylinder means that such a single vortex cannot remain stationary. Instead, it acquires one of a series of quantized translational velocities around the circumference, the simplest being $\pm \hbar/(2MR)$, with $M$ the mass of the superfluid particles and $R$ the radius of the cylinder. A generalization to a finite cylinder automatically includes these quantum-mechanical effects through the pairing of the single vortex and its image in either the top or bottom end of the surface. The dynamics of a single vortex on this surface provides a hydrodynamic analog of Laughlin pumping. The interaction energy for two vortices on an infinite cylinder is proportional to the classical stream function $\chi({\bf r}_{12})$, and it crosses over from logarithmic to linear when the intervortex separation ${\bf r}_{12}$ becomes larger than the cylinder radius. An Appendix summarizes the connection to an earlier study of Ho and Huang for one or more vortices on an infinite cylinder. A second Appendix reviews the topologically equivalent planar annulus, where such quantized vortex motion has no offset, but Laughlin pumping may be more accessible to experimental observation.Comment: 16 pages, 7 figures; published version, with thoroughly revised Appendice

Twin peaks in rf spectra of Fermi gases at unitarity

We calculate the radio-frequency spectrum of balanced and imbalanced ultracold Fermi gases in the normal phase at unitarity. For the homogeneous case the spectrum of both the majority and minority components always has a single peak even in the pseudogap regime. We furthermore show how the double-peak structures observed in recent experiments arise due to the inhomogeneity of the trapped gas. The main experimental features observed above the critical temperature in the recent experiment of Schunck et al. [Science 316, 867, (2007)] are recovered with no fitting parameters.Comment: v3: version accepted for publication as a Rapid Communication in PRA. With respect to v2, minor changes in the text and in the inset of Fig.

p-Wave Polaron

We consider the properties of a single impurity immersed in a Fermi sea close to an interspecies p-wave Feshbach resonance. We calculate its dispersion and spectral response to a radiofrequency pulse. In the presence of a magnetic field, dipolar interactions split the resonance and lead to the appearance of two novel features with respect to the s-wave case: a third polaron branch in the excitation spectrum, in addition to the usual attractive and repulsive ones; and an anisotropic dispersion of the impurity characterized by different effective masses perpendicular and parallel to the magnetic field. The anisotropy can be tuned as a function of the field strength and the two effective masses may have opposite signs, or become smaller than the bare mass

Decay of polarons and molecules in a strongly polarized Fermi gas

The ground state of an impurity immersed in a Fermi sea changes from a polaron to a molecule as the interaction strength is increased. We show here that the coupling between these two states is strongly suppressed due to a combination of phase space effects and Fermi statistics, and that it vanishes much faster than the energy difference between the two states, thereby confirming the first order nature of the polaron-molecule transition. In the regime where each state is metastable, we find quasiparticle lifetimes which are much longer than what is expected for a usual Fermi liquid. Our analysis indicates that the decay rates are sufficiently slow to be experimentally observable.Comment: Version accepted in PRL. Added discussion of three-body losses to deeply bound molecular state

Superfluid vortex dynamics on an ellipsoid and other surfaces of revolution

We study the dynamics of quantized superfluid vortices on axisymmetric compact surfaces with no holes, where the total vortex charge must vanish and the condition of irrotational flow forbids distributed vorticity. A conformal transformation from the surface to the complex plane allows us to use familiar formalism to describe the motion of the quantized vortices and to find the total energy. The simplest case is a vortex dipole with unit vortex charges on an axisymmetric ellipsoid. We study two special symmetric vortex-dipole configurations along with a general asymmetric one.M.A.C. acknowledges support by the S ̃ao Paulo Research Foundation (FAPESP) under Grant No. 2013/07276-1. P.M. acknowledges support by the Spanish MINECO (Grants No. FIS2017-84114-C2-1-P and PID2020-113565GB-C21), by EU FEDER Quantumcat, and by the National Science Foundation under Grant No. NSF PHY-1748958.Peer ReviewedPostprint (author's final draft

Superfluid vortex dynamics in an elliptical boundary

Recent advances in cold atom platforms, providing experimental accessibility to real-time dynamics, have renewed interest in the motion of superfluid vortices in two-dimensional domains. Motivated by this development, we study the dynamics of a vortex in a two-dimensional incompressible superfluid inside an elliptical boundary. Employing the Joukowsky conformal map from a circle to an ellipse, we derive an analytical expression for the complex potential describing the hydrodynamic flow around the vortex. We integrate the resulting equations of motion, finding that the vortex moves along a nearly (but not exactly) elliptical trajectory. In addition, we obtain a simple closed expression for the vortex self-energy, which serves as the Hamiltonian of the system.Comment: 16 pages, 6 figure

Collective excitations of a trapped Bose-Einstein condensate in the presence of a 1D optical lattice

We study low-lying collective modes of a horizontally elongated 87Rb condensate produced in a 3D magnetic harmonic trap with the addition of a 1D periodic potential which is provided by a laser standing-wave along the horizontal axis. While the transverse breathing mode results unperturbed, quadrupole and dipole oscillations along the optical lattice are strongly modified. Precise measurements of the collective mode frequencies at different height of the optical barriers provide a stringent test of the theoretical model recently introduced [M.Kraemer et al. Phys. Rev. Lett. 88 180404 (2002)].Comment: 4 pages, 4 figure

Dynamics of a massive superfluid vortex in rk confining potentials

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 ¿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. In many cases, 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 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.Peer ReviewedPostprint (published version