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Universal Behavior of Perturbation-Induced Defects in Trapped Superfluids

Peter Scherpelz, Karmela Padavić, A. M. Murray, Andreas Glatz, Igor S. Aranson, Kathryn Levin

Published Sep 30, 2014• 0 citations
OpenAlex

Abstract

We investigate equilibration processes shortly after sudden perturbations are applied to ultracold trapped superfluids. We show the similarity of imprinting and localized density depletion perturbations, both of which initially are found to produce phase walls. These planar defects are associated with a sharp gradient in the phase. Importantly they relax following a quite general sequence. Our studies, based on simulations of the complex time-dependent Ginzburg-Landau equation, address the challenge posed by these experiments: how a superfluid eventually eliminates a spatially extended planar defect. The processes involved are necessarily more complex than equilibration involving simpler line vortices. An essential mechanism for relaxation involves repeated formation and loss of vortex rings near the trap edge.

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We investigate equilibration processes shortly after sudden perturbations are applied to ultracold trapped superfluids. We show the similarity of imprinting and localized density depletion perturbations, both of which initially are found to produce phase walls. These planar defects are associated with a sharp gradient in the phase. Importantly they relax following a quite general sequence. Our studies, based on simulations of the complex time-dependent Ginzburg-Landau equation, address the challenge posed by these experiments: how a superfluid eventually eliminates a spatially extended planar defect. The processes involved are necessarily more complex than equilibration involving simpler line vortices. An essential mechanism for relaxation involves repeated formation and loss of vortex rings near the trap edge.
We investigate equilibration processes shortly after sudden perturbations are applied to ultracold trapped superfluids. We show the similarity of phase imprinting and localized density depletion perturbations, both of which initially are found to produce ``phase walls.'' These planar defects are associated with a sharp gradient in the phase. Importantly they relax following a quite general sequence. Our studies, based on simulations of the complex time-dependent Ginzburg-Landau equation, address the challenge posed by these experiments: how a superfluid eventually eliminates a spatially extended planar defect. The processes involved are necessarily more complex than equilibration involving simpler line vortices. An essential mechanism for relaxation involves repeated formation and loss of vortex rings near the trap edge.
We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases, which were obtained independently and are in good agreement with recent experimental results. Our focus is on the sequence and evolution of defects using the fermionic time-dependent Ginzburg-Landau equation, which contains dissipation necessary for equilibration. In contrast to other simulations, we introduce small, experimentally unavoidable symmetry breaking, particularly that associated with thermal fluctuations and with the phase-imprinting tilt angle, and we illustrate their dramatic effects. As appears consistent with experiment, the former causes vortex rings in confined geometries to move to the trap surface and rapidly decay into more stable vortex lines. The latter aligns the precessing and relatively long-lived vortex filaments, rendering them difficult to distinguish from solitons.
We investigate the role of vortices in the decay of persistent current states of annular atomic superfluids by solving numerically the Gross–Pitaevskii equation, and we directly compare our results with the 6Li experiment at LENS data. We theoretically model the optical phase-imprinting technique employed to experimentally excite finite-circulation states in the Bose–Einstein condensation regime, accounting for imperfections of the optical gradient imprinting profile. By comparing simulations of this realistic protocol to an ideal imprinting, we show that the introduced density excitations arising from imperfect imprinting are mainly responsible for limiting the maximum reachable winding number wmax in the superfluid ring. We also investigate the effect of a point-like obstacle with variable potential height V0 on the decay of circulating supercurrents. For a given obstacle height, a critical circulation wc exists, such that for an initial circulation w0 larger than wc the supercurrent decays through the emission of vortices, which cross the superflow and thus induce phase slippage. Higher values of the obstacle height V0 further favor the entrance of vortices, thus leading to lower values of wc. Furthermore, the stronger vortex-defect interaction at higher V0 leads to vortices that propagate closer to the center of the ring condensate. The combination of both these effects leads to an increase in the supercurrent decay rate for increasing w0, in agreement with experimental observations.
We follow the time evolution of a superfluid Fermi gas of resonantly interacting ^{6}Li atoms after a phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, its subsequent snaking, and its decay into a vortex ring, which, in turn, breaks to finally leave behind a single solitonic vortex. In intermediate stages, we find evidence for an exotic structure resembling the Φ soliton, a combination of a vortex ring and a vortex line. Direct imaging of the nodal surface reveals its undulation dynamics and its decay via the puncture of the initial soliton plane. The observed evolution of the nodal surface represents dynamics beyond superfluid hydrodynamics, calling for a microscopic description of unitary fermionic superfluids out of equilibrium.
We study the relaxation dynamics of an isolated zero temperature quasi-two-dimensional superfluid Bose-Einstein condensate that is imprinted with a spatially random distribution of quantum vortices. Following a period of vortex annihilation the remaining vortices self-organize into two macroscopic coherent "Onsager vortex" clusters that are stable indefinitely--despite the absence of driving or external dissipation in the dynamics. We demonstrate that this occurs due to a novel physical mechanism--the evaporative heating of the vortices--that results in a negative-temperature phase transition in the vortex degrees of freedom. At the end of our simulations the system is trapped in a nonthermal state. Our computational results provide a pathway to observing Onsager vortex states in a superfluid Bose gas.
We study the spontaneous formation of vortices during the superfluid condensation in a trapped fermionic gas subjected to a rapid thermal quench via evaporative cooling. Our work is based on the numerical solution of the time-dependent crossover Ginzburg-Landau equation coupled to the heat diffusion equation. We quantify the evolution of condensate density and vortex length as a function of a crossover phase parameter from BCS to BEC. The more interesting phenomena occur somewhat nearer to the BEC regime and should be experimentally observable; during the propagation of the cold front, the increase in condensate density leads to the formation of supercurrents toward the center of the condensate as well as possible condensate volume oscillations.