Dynamics of a vortex dipole in a holographic superfluid

Abstract

We use holography to investigate the dynamics of a vortex-anti-vortex dipole in a strongly coupled superfluid in 2+1 dimensions. The system is evaluated in numerical real-time simulations in order to study the evolution of the vortices as they approach and eventually annihilate each other. A tracking algorithm with sub-plaquette resolution is introduced which permits a high-precision determination of the vortex trajectories. With the increased precision of the trajectories it becomes possible to directly compute the vortex velocities and accelerations. We find that in the holographic superfluid the vortices follow universal trajectories independent of their initial separation, indicating that a vortex-anti-vortex pair is fully characterized by its separation. Subtle non-universal effects in the vortex motion at early times of the evolution can be fully attributed to artifacts due to the numerical initialization of the vortices. We also study the dependence of the dynamics on the temperature of the superfluid.

Vortex motion quantifies strong dissipation in a holographic superfluid

“…The imprinting of two separate phase fields for the vortices by simply adding their phases at all points across the lattice is in fact incompatible with a true two-vortex solution of the equations of motion. The deviation of the phase field from an actual solution can be shown to lead to an outward velocity of the superfluid that acts on the vortices accordingly [24]. Similar effects have also been observed for soliton solutions in GP simulations [99,100].…”

“…The motion of a vortex dipole as we consider it here has been explored separately in holographic and DGPE simulations in [23,24] and [60], respectively. More generally, the motion of vortices in a two-dimensional system and their interactions with each other and with background excitations has been studied in depth, both theoretically and experimentally, also in the vicinity of the BKT transition, in thin films of superfluid helium [1, 7, 26, 28-30, 42, 43, 61-67], in superconductors, e. g., [68], as well as in ultracold atomic gases [2,3,33,41,[51][52][53][69][70][71].…”

“…Here, we address this longstanding problem for the holographic model of a superfluid in two spatial dimensions [12][13][14][15]. This system has been studied extensively, with particular focus on linear [13,14,16,17] and nonlinear excitations such as vortices [18][19][20][21][22][23][24]. So far it was unknown how the holographic superfluid compares to experimentally realized superfluids like ultracold atomic gases [25] or liquid helium [26].…”

“…We determine the trajectories on the grid with subplaquette resolution in a quasi-continuous manner by a combination of two tracking methods, cf. [24]: a two-dimensional Gaussian fit to the density depression around the vortex cores and a Newton-Raphson algorithm for tracking the zeros in the superfluid density. The precision of this procedure allows us to match the DGPE vortex trajectories in space and time by adjusting the dissipation constant γ and time rescaling parameter τ.…”

“…With the knowledge of the DGPE parameters, we can fit solutions of the HVI equations for the motion of point vortices to the dipole trajectories to obtain friction coefficients of the holographic superfluid. We do this in a regime where effects due to the preparation of the initial vortex configuration (in particular a slight initial outward bending of the trajectories [24]) have died out but the vortices are still far enough apart.…”