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arXiv:1704.08410 · Physical Review A

Vortex mass in a superfluid

Tapio Simula

Published Feb 6, 2018• 44 citations
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Abstract

We consider the inertial mass of a vortex in a superfluid. We obtain a vortex mass that is well defined and is determined microscopically and self-consistently by the elementary excitation energy of the kelvon quasiparticle localized within the vortex core. The obtained result for the vortex mass is found to be consistent with experimental observations on superfluid quantum gases and vortex rings in water. We propose a method to measure the inertial rest mass and Berry phase of a vortex in superfluid Bose and Fermi gases.

DOI
10.1103/physreva.97.023609

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We consider the inertial mass of a vortex in a superfluid. We obtain a vortex mass that is well defined and is determined microscopically and self-consistently by the elementary excitation energy of the kelvon quasiparticle localized within the vortex core. The obtained result for the vortex mass is found to be consistent with experimental observations on superfluid quantum gases and vortex rings in water. We propose a method to measure the inertial rest mass and Berry phase of a vortex in superfluid Bose and Fermi gases.
Vortex mass is a key concept in the study of superfluid dynamics, referring to the inertia of vortices in a superfluid, which affects their motion and behavior. Despite being an important quantity, the vortex mass has never been observed experimentally, and remains an unresolved issue in this field. As of now, a large body of research assumes that the vortex mass is a local parameter. In contrast, we present a calculation that suggests a logarithmic dependence on the system size, agreeing with some earlier predictions in the context of Bose gases. We analyze the problem using an effective field theory that describes ultracold atomic Fermi gases over the BEC-BCS crossover at both zero and nonzero temperatures. Our study reveals a strong dependence of the vortex mass on the scattering length; in particular, the vortex mass grows rapidly when moving toward the BCS side. Furthermore, we find that the system-size dependence of the vortex mass results in values an order of magnitude larger than those predicted by other models for realistic system sizes. This implies that the vortex mass could be observable in a wider parameter range than was previously expected. This is particularly relevant considering recent advances in experimental techniques that place the observation of vortex mass in superfluid Fermi gases within reach.
We study quasiparticle dynamics in a Bose-Einstein condensate with a vortex by following the center of mass motion of a Bogoliubov wave packet, and find important Berry-phase effects due to the background flow. We show that the Berry phase invalidates the usual canonical relation between the mechanical momentum and position variables, leading to important modifications of quasiparticle statistics and thermodynamic properties of the condensates. Applying these results to a vortex in an infinite uniform superfluid, we find that the total transverse force acting on the vortex is proportional to the superfluid density. We propose an experimental setup to directly observe Berry phase effects through measuring local thermal atoms' momentum distribution around a vortex.
Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov quasiparticles localized in the core. These bound states form the normal component, which is nonzero even in the low-temperature limit. In the collisionless regime ω 0 τ≫1 the normal component trapped by the vortex is unbound from the normal component in a bulk superfluid/superconductor and adds to the inertial mass of the moving vortex. In a d-wave superconductor the vortex mass has an additional factor of (B c2/B)1/2 due to the gap nodes.
We consider superfluid hydrodynamics of two-dimensional Bose-Einstein condensates. Interpreting the curvature of the macroscopic condensate wave function as an effective gravity in such a superfluid universe, we argue for a superfluid equivalence principle: that the gravitational mass of a quantized vortex should be equal to the inertial vortex mass. In this model, gravity and electromagnetism have the same origin and are emergent properties of the superfluid universe, which itself emerges from the underlying collective structure of more elementary particles, such as atoms. The Bose-Einstein condensate is identified as the elusive dark matter of the superfluid universe with vortices and phonons, respectively, corresponding to massive charged particles and massless photons. Implications of this cosmological picture of superfluids to the physics of dense vortex matter are considered.
Quantum vortices are commonly described as funnel-like objects around which the superfluid swirls, and their motion is typically modeled in terms of massless particles. Here we show that in Fermi superfluids the normal component confined in the vortex core provides the vortex with a finite inertial mass. This inertia imparts an unambiguous signature to the dynamic behavior of vortices, specifically manifesting as small-amplitude transverse oscillations which remarkably follow the prediction of a simple point-like model supplemented by an effective mass. We demonstrate this phenomenon through large-scale time-dependent simulations of Fermi superfluids across a wide range of interaction parameters, at both zero and finite temperatures, and for various initial conditions. Our findings pave the way for the exploration of inertial effects in superfluid vortex dynamics.
We consider geometric phases of mobile quantum vortices in superfluid Bose--Einstein condensates (BECs). Haldane and Wu [Phys. Rev. Lett. 55, 2887 (1985)] showed that the geometric phase, ${\ensuremath{\gamma}}_{\mathcal{C}}=2\ensuremath{\pi}{N}_{\mathcal{C}}$, of such a vortex is determined by the number of condensate atoms NC{N}_{\mathcal{C}}NC​ enclosed by the vortex trajectory. Considering an experimentally realistic freely orbiting vortex leads to an apparent disagreement with this prediction. We resolve it using the superfluid electrodynamics picture, which allows us to identify two additional contributions to the measured geometric phase: (i) A topologically protected edge current of vortices at the condensate boundary and (ii) a superfluid displacement current. Our results generalize to and pave the way for experimental measurements of vortex geometric phases using scalar and spinor BECs and superfluid Fermi gases.