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New Journal of Physics

Interaction and motion of vortices in nonequilibrium quantum fluids

V. N. Gladilin, Michiel Wouters

Published Oct 13, 2017• 20 citations
Publisher

Abstract

We study numerically the motion of vortices in nonequilibrium Bose–Einstein condensates, that are described by a generalized Gross–Pitaevskii equation. We analyze how the vortex properties are modified when moving away under deviation from equilibrium. We find that far from equilibrium, the radial component dominates over the azimuthal one in the distribution of vortex currents at large distances from the vortex core. The modification of the current pattern has a strong effect on the vortex–antivortex interaction energy, that can become entirely repulsive. The vortex trajectories are also strongly affected by the driving and dissipation. Self acceleration of vortices is observed in the strong nonequilibrium case.

DOI
10.1088/1367-2630/aa83a1

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•Jan 1, 2000•1 citation
We study numerically the motion of vortices in nonequilibrium Bose–Einstein condensates, that are described by a generalized Gross–Pitaevskii equation. We analyze how the vortex properties are modified when moving away under deviation from equilibrium. We find that far from equilibrium, the radial component dominates over the azimuthal one in the distribution of vortex currents at large distances from the vortex core. The modification of the current pattern has a strong effect on the vortex–antivortex interaction energy, that can become entirely repulsive. The vortex trajectories are also strongly affected by the driving and dissipation. Self acceleration of vortices is observed in the strong nonequilibrium case.
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We study the dynamics of a single and a corotating vortex pair in a dipolar Bose–Einstein condensate in the framework of a dissipative Gross–Pitaevskii equation. This simple model enables us to simulate the effect of finite temperature on the vortex dynamics. We study the effect of dipolar interactions on the dynamics of a single vortex in the presence of phenomenological dissipation. In the case of a corotating vortex pair, initial asymmetry in the locations of the vortices can lead to different decay rates for the constituent vortices, as is the case for the condensates interacting via pure contact interactions. We observe that the anisotropic interaction between the component vortices manifests itself as the perceptible difference in the trajectories traversed by the vortices in the condensate at finite temperatures.
We explore vortices in non-equilibrium Dirac Bose-Einstein condensates (Dirac BEC) described by a stationary Dirac Gross-Pitaevskii equations (GPE). We find that the multi-component structure of Dirac equation enables the difference in phase winding of two condensates with respective phase winding number differing by one, ℓa−ℓb=±1\ell_a - \ell_b = \pm 1ℓa​−ℓb​=±1. We observe three classes of vortex states distinguished by their far-field behavior: A ring soliton on either of the two components in combination with a vortex on the other component, and, in the case of strong inter-component interactions, a vortex profile on both components. The latter are multiple core vortices due to the phase winding difference between the components. We also address the role of a Haldane gap on these vortices, which has a similar effect than inter-component by making the occupation on either sublattice more costly. We employ a numerical shooting method to reliably identify vortex solutions and use it to scan large parts of the phase space. We then use a classification algorithm on the integrated wavefunctions to establish a phase diagram of the different topological sectors.
We study the interaction and dynamics of two half-quantized vortices in two-component Bose-Einstein condensates. Using the Pad\'e approximation for the vortex core profile, we calculate the intervortex potential, whose asymptotic form for a large distance has been derived by Eto et al. [Phys. Rev. A 83, 063603 (2011)]. Through numerical simulations of the two-dimensional Gross-Pitaevskii equations, we reveal different kinds of dynamical trajectories of the vortices depending on the combinations of signs of circulations and the intercomponent density coupling. Under the adiabatic limit, we derive the equations of motion for the vortex coordinates, in which the motion is caused by the balance between Magnus force and the intervortex forces. The initial velocity of the vortex motion can be explained quantitatively by this point vortex approximation, but understanding the long-time behavior of the dynamics needs more consideration beyond our model.
In this paper, we examine the dynamical properties of vortices in atomic Bose-Einstein condensates in the presence of phenomenological dissipation, used as a basic model for the effect of finite temperatures. In the context of this so-called dissipative Gross-Pitaevskii model, we derive analytical results for the motion of single vortices and, importantly, for vortex dipoles, which have become very relevant experimentally. Our analytical results are shown to compare favorably to the full numerical solution of the dissipative Gross-Pitaevskii equation where appropriate. We also present results on the stability of vortices and vortex dipoles, revealing good agreement between numerical and analytical results for the internal excitation eigenfrequencies, which extends even beyond the regime of validity of this equation for cold atoms.
In this thesis we solve the Gross-Pitaevskii equation numerically in order to model the response of trapped Bose-Einstein condensed gases to perturbations by electromagnetic fields. First, we simulate output coupling of pulses from the condensate and compare our results to experiments. The excitation and separation of eigenmodes on flow through a constriction is also studied. We then move on to the main theme of this thesis: the important subject of quantised vortices in Bose condensates, and the relation between Bose-Einstein condensation and superfluidity. We propose methods of producing vortex pairs and rings by controlled motion of objects. Full three-dimensional simulations under realistic experimental conditions are performed in order to test the validity of these ideas. We link vortex formation to drag forces on the object, which in turn is connected with energy transfer to the condensate. We therefore argue that vortex formation by moving objects is intimately related to the onset of dissipation in superfluids. We discuss this idea in the context of a recent experiment, using simulations to provide evidence of vortex formation in the experimental scenario. Superfluidity is also manifest in the property of persistent currents, which is linked to vortex stability and dynamics. We simulate vortex line and ring motion, and find in both cases precessional motion and thermodynamic instability to dissipation. Strictly speaking, the Gross-Pitaevskii equation is valid only for temperatures far below the BEC transition. We end the thesis by describing a simple finite-temperature model to describe mean-field coupling between condensed and non-condensed components of the gas. We show that our hybrid Monte-Carlo/FFT technique can describe damping of the lowest energy excitations of the system. Extensions to this model and future research directions are discussed in the conclusion. (author)