Vortex mass, which is the inertia of a quantum vortex, has never been observed in superfluids and is a long-standing problem in low-temperature physics. The impact of the mass is considered negligible in typical experiments with superfluid $^{4}\mathrm{He}$. Recent developments of experimental techniques for manipulating quantum vortices in superfluid atomic gases have enabled us to test this problem more accurately. By introducing the vortex mass time and length as universal scales to many-body problems of massive quantum vortices, the theoretical description is formulated in the simplest manner and is universally applicable to different quantum fluids, including fermionic and multicomponent superfluids. There are two branches, the cyclotron and massless branches, for the circular motion of a pair of like-sign vortices. Finding a stable cyclotron branch for the motion of vortices is a clear evidence of vortex mass and superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$ is the specific example of a system where this phenomena could be observed. The impact of the mass on the massless branch is small but can be enhanced by taking the difference in the two-body dynamics of point vortices with different initial conditions. Our results imply that the vortex mass is a direct cause of the splitting instability of a doubly quantized vortex at absolute zero and that the vortex mass length characterizes the final state after the instability. It is also demonstrated that a pair of massive vortices with opposite circulations has a critical distance characterized by the vortex mass length, below which they are spontaneously annihilated without thermal fluctuations.
Vortex mass, which is the inertia of a quantum vortex, has never been observed in superfluids and is a long-standing problem in low-temperature physics. The impact of the mass is considered negligible in typical experiments with superfluid 4He. Recent developments of experimental techniques for manipulating quantum vortices in superfluid atomic gases have enabled us to test this problem more accurately. By introducing the vortex mass time and length as universal scales to many-body problems of massive quantum vortices, the theoretical description is formulated in the simplest manner and is universally applicable to different quantum fluids, including fermionic and multicomponent superfluids. There are two branches, the cyclotron and massless branches, for the circular motion of a pair of like-sign vortices. Finding a stable cyclotron branch for the motion of vortices is a clear evidence of vortex mass and superfluid 3He\ensuremath-B is the specific example of a system where this phenomena could be observed. The impact of the mass on the massless branch is small but can be enhanced by taking the difference in the two-body dynamics of point vortices with different initial conditions. Our results imply that the vortex mass is a direct cause of the splitting instability of a doubly quantized vortex at absolute zero and that the vortex mass length characterizes the final state after the instability. It is also demonstrated that a pair of massive vortices with opposite circulations has a critical distance characterized by the vortex mass length, below which they are spontaneously annihilated without thermal fluctuations.
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.
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.
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.
Quantum vortices are often endowed with an effective inertial mass, due, for example, to massive particles in their cores. Such ``massive vortices'' display new phenomena beyond the standard picture of superfluid vortex dynamics, where mass is neglected. In this work, we demonstrate that massive vortices are allowed to collide, as opposed to their massless counterparts. We propose a scheme to generate controllable, repeatable, deterministic collisional events in pairs of quantum vortices. We demonstrate two mass-driven fundamental processes: (i) the annihilation of two counter-rotating vortices and (ii) the merging of two corotating vortices, thus pointing out new mechanisms supporting incompressible-to-compressible kinetic-energy conversion, as well as doubly quantized vortex stabilization in flat superfluids.
The two-dimensional point vortex model was first introduced in the nineteenth century by Helmholtz and Kirchhoff. The methods of statistical physics were used to apply it to the problem of two-dimensional fluid flow and turbulence by Onsager in the 1940s, and it has provided many qualitative insights into the emergence of large scale vortices from turbulence. However, until recently there has been no quantitative comparison of its predictions with experimental measurements. Here we present the results of two sets of superfluid dynamics experiments for which the point vortex model provides quantitative insights. The first is in a planar quasi-two-dimensional atomic gas Bose-Einstein condensate cooled to nanokelvin temperatures [1]. The superfluid is confined and manipulated in a potential formed by laser light reflected from a Digital Micromirror Device (DMD) identical to those found in digital video projectors. Two different stirring procedures inject vortices into the gas. For the first stirring method the vortex number decays relatively quickly. However, the second stirring method leads to the formation of two macroscopic vortex clusters of opposite signs. The system quickly relaxes into a deeply negative temperature Onsager vortex state that persists in quasi-equilibrium for more than fifty cluster turnover times. The second experiment is in a superfluid helium thin film [2]. Optical stirring generates a macroscopic superfluid flow in the system that lifts the degeneracy in frequency of a number of third sound modes. These frequency splitting are subsequently observed to decay. Modelling the system using the point vortex model with a small amount of dissipation leads to a consistent interpretation of the measurements. We infer that a pinned persistent current slowly decays as a cluster of opposite sign vortices slowly annihilate the central charge. Improvements in the experimental apparatus are expected to lead to the capability of tracking the dynamics of a single vortex in real time. [1] Negative-Temperature Onsager Vortex Clusters in a Quantum Fluid, G. Gauthier, M. T. Reeves, X. Yu, A. S. Bradley, M. Baker, T. A. Bell, H. Rubinsztein-Dunlop, M. J. Davis, T. W. Neely, to appear in Science (2019). arXiv:1801.06951 [2] Coherent vortex dynamics in a strongly-interacting superfluid on a silicon chip, Yauhen P. Sachkou, Christopher G. Baker, Glen I. Harris, Oliver R. Stockdale, Stefan Forstner, Matthew T. Reeves, Xin He, David L. McAuslan, Ashton S. Bradley, Matthew J. Davis, Warwick P. Bowen. arXiv:1902.04409
Quantum vortices in superfluids may capture matter and deposit it inside their core. By doping vortices with foreign particles one can effectively visualize them and study them experimentally. To acquire a better understanding of the interaction between quantum vortices and matter, and clarify the details of recent experiments, the properties of doped vortices are investigated here theoretically in the regimes where the doping mass becomes close to the total mass of superfluid particles forming a vortex. Such formations are dynamically stable and, possessing both vorticity and enhanced inertia, demonstrate properties that are different from the pure vortex case. The goal of this paper is to define and investigate the universal aspects of heavily doped vortex behavior, which can be realized in different types of quantum mixtures. The proposed 3D model is based on a system of coupled semiclassical matter wave equations that are solved numerically in a wide range of physical parameters. The size, geometry and binding energy of dopants in different regimes are discussed. The coupled motion of a vortex–dopant complex and decoupling conditions are studied. The reconnection of vortices, taken as an example of a fundamental process responsible for the evolution of a quantum turbulent state, is modeled to illustrate the difference between the light and heavy doping cases.