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The Dynamics of a Tilted Vortex in a Trapped Quantum Fluid

Chuanzhou Zhu, Mark E. Siemens, Mark T. Lusk

Published Feb 19, 2021• 0 citations
OpenAlex

Abstract

The nonequilibrium dynamics of vortices in 2D quantum fluids are shown to obey a kinetic equation in which vortex tilt (ellipticity) is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a trapped, tilted vortex is analytically found to move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself, allowing experimental measurement of vortex tilt via path observation. A combination of analysis and simulation is then used to show that nonlinear interactions cause the vortex tilt to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex tilt and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate local vortex structure is expected to prove useful in designing few-vortex systems in which tilt is a ubiquitous, as-yet-unharnessed feature.

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The nonequilibrium dynamics of vortices in 2D quantum fluids are shown to obey a kinetic equation in which vortex tilt (ellipticity) is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a trapped, tilted vortex is analytically found to move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself, allowing experimental measurement of vortex tilt via path observation. A combination of analysis and simulation is then used to show that nonlinear interactions cause the vortex tilt to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex tilt and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate local vortex structure is expected to prove useful in designing few-vortex systems in which tilt is a ubiquitous, as-yet-unharnessed feature.
The nonequilibrium dynamics of vortices in two-dimensional quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a harmonically trapped fluid can be analyzed analytically to show that single vortices will move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself. This allows the vortex ellipticity to be estimated through observation of its trajectory. A combination of analysis and numerical simulation is then used to show that nonlinear interactions cause the vortex orientation to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex ellipticity and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate and control local vortex structure and vortex trajectory is expected to prove useful in designing few-vortex systems in which ellipticity is a ubiquitous, as-yet-unharnessed feature.
The motion of quantized vortices on two-dimensional inhomogeneous density backgrounds with boundaries is considered numerically and asymptotically. We show that a Hamiltonian group relation together with the method of images and an approximation for the density background is useful to understand vortex motion. We analyze the vortex motion on a variety of background configurations motivated by experiments on trapped Bose-Einstein condensates including linear and quadratic traps. We show that close to the center of the condensate cloud in the Thomas-Fermi regime the vortex is moving predominantly due to the image vortex that is effectively shifted because of the large density depletion of the condensate at the boundary. Close to the boundary the vortex moves mostly due to a large background density gradient across the vortex core. The vortex velocity is a nonlinear combination of these effects and of the global shape of the background density. We find the complete families of the traveling coherent structures in an infinitely long two-dimensional channel and derive an approximation of the velocity of a single vortex moving close to the center of the channel in the Thomas-Fermi regime.
If a quantum fluid is driven with enough angular momentum, at equilibrium the ground state of the system is given by a lattice of quantized vortices whose density is prescribed by the quantization of circulation. We report on the first experimental study of the Feynman-Onsager relation in a nonequilibrium polariton fluid, free to expand and rotate. Upon initially imprinting a lattice of vortices in the quantum fluid, we track the vortex core positions on picosecond timescales. We observe an accelerated stretching of the lattice and an outward bending of the linear trajectories of the vortices, due to the repulsive polariton interactions. Access to the full density and phase fields allows us to detect a small deviation from the Feynman-Onsager rule in terms of a transverse velocity component, due to the density gradient of the fluid envelope acting on the vortex lattice.
The mechanisms behind the motion of vortices has recently been re-examined. The findings have given a more detailed and complete view as to how vortices move in Bose-Einstein condensation. Specifically, vortex propagation is not seen as purely the result of a density gradient which would arise because of the gradient of the trapping potential, but is also made up of a contribution from the boundary eects. I will consider the motion of vortices in an asymptotically inhomogeneous condensate under various trapping potentials. By first considering a linear potential trap and then a semi-infinite quadratic trap, the eects that govern the motion can be separated. It will be shown that for large density gradient backgrounds the motion can be analysed from the energy-momentum dispersion relationship, whereas for low density gradient backgrounds the motion is dominated by an eective shift in the image term caused by the eects of the boundary. Finally, a separate case of the motion of vortices in an infinitely long two-dimensional channel will be presented where the interaction strength plays a key role in the dynamics.
We analyze tunneling from vortex states in elliptically shaped traps. Using the hydrodynamic representation of the Gross-Pitaevskii (nonlinear Schr\"odinger) equation, we derive analytically and demonstrate numerically an interesting type of quantum fluid flow: a jetlike singularity formed by the interaction between the vortex and the asymmetric trap. For strongly elongated traps and high enough vorticity, the ellipticity overwhelms the circular rotation, resulting in the ejection of jets in narrow, well-defined directions. These jets are formed due to a convergence of trajectories starting from the top of the potential barrier and meeting at a certain point on the exit line. Under proper conditions they will appear in any coherent wave system with angular momentum and noncircular symmetry, such as superfluids, Bose-Einstein condensates, and light.
Abstract We analytically study the dynamics of a solitonic vortex (SV) in a superfluid confined in a non-axisymmetric harmonic trap. The study provides a framework for analyzing the role of the trap anisotropy in the oscillation of SVs observed in recent experiments on atomic Bose and Fermi superfluids. The emergence of common and statistics-dependent features is traced in a unified approach to both types of fluid. Our description, built in the hydrodynamic formalism, is based on a Lagragian approach which incorporates the vortex location as dynamical parameters of a variational ansatz. Previous operative Hamiltonian pictures are recovered through a canonically traced procedure. Our results improve the understanding of the experimental findings. Some of the observed features are shown to be specific to the tri-axial anisotropy of the trap. In particular, we characterize the nontrivial dependence of the oscillation frequency on the trapping transversal to the vortical line. The study reveals also the crucial role played by the nonlinear character of the dynamics in the observed oscillation: for the considered experimental conditions, the frequency, and, in turn, the effective inertial mass of the vortex, are found to significantly depend on the amplitude of the generated motion. It is also uncovered how the coupling with collective modes of the fluid induces a non-negligible shift in the oscillation frequency. The appearance of fine-structure features in the SV trajectory is predicted.