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arXiv:1401.8267 · Physical Review Letters

Phase Imprinting in Equilibrating Fermi Gases: The Transience of Vortex Rings and Other Defects

Peter Scherpelz, Karmela Padavić, Adam Rançon, Andreas Glatz, Igor S. Aranson, Kathryn Levin

Published Sep 16, 2014• 29 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.113.125301

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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 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 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.
Persistent currents in annular geometries have played an important role in disclosing the quantum phase coherence of superconductors and mesoscopic electronic systems.Ultracold atomic gases in multiply connected traps also exhibit long-lived supercurrents and have attracted much interest both for fundamental studies of superfluid dynamics and as prototypes for atomtronics circuits.Here, we report on the realization of supercurrents in homogeneous, tunable fermionic rings.We gain exquisite, rapid control over quantized persistent currents in all regimes of the BCS-BEC crossover through a universal phase-imprinting technique, attaining on-demand circulations w as high as 9. High-fidelity readout of the superfluid circulation state is achieved by exploiting an interferometric protocol, which also yields local information about the superfluid phase around the ring.In the absence of externally introduced perturbations, we find the induced metastable supercurrents to be as long-lived as the atomic sample.Conversely, we trigger and inspect the supercurrent decay by inserting a single small obstacle within the ring.For circulations higher than a critical value, the quantized current is observed to dissipate via the emission of vortices, i.e., quantized phase slips, which we directly image, in good agreement with numerical simulations.The critical circulation at which the superflow becomes unstable is found to depend starkly on the interaction strength, taking its maximum value for the unitary Fermi gas.Our results demonstrate fast and accurate control of quantized collective excitations in a macroscopic quantum system and establish strongly interacting fermionic superfluids as excellent candidates for atomtronics applications.
6 Li atoms following a one-sided phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, and its subsequent snaking and decay into a vortex ring. The latter eventually breaks at the boundary of the superuid, nally leaving behind a single, remnant solitonic vortex. The nodal surface is directly imaged and reveals its decay into a vortex ring via a puncture of the initial soliton plane. At intermediate stages we nd evidence for more exotic structures resembling -solitons. The observed evolution of the nodal surface represents dynamics that occurs at the length scale of the interparticle spacing, thus providing new experimental input for microscopic theories of strongly correlated fermions.
We investigate the stability of persistent currents in superfluid fermionic gases confined to a ring geometry. Our study, conducted at zero temperature using time-dependent density functional theory, cover interaction regimes from strong (unitary Fermi gas) to weak (Bardeen-Cooper-Schrieffer regime) couplings. Stability is tested against the presence of an external defect within the ring. The dissipation mechanism associated with vortex generation is present in all interaction regimes. Vortex emission is accompanied by Cooper pair breaking, which occurs even beyond the vortex core in the weakly interacting regime. The pair-breaking mechanism prevents the imprinting of a persistent current with a winding number above a threshold, which decreases as the system approach the BCS regime. Our study reveals the existence of two types of critical winding numbers above which currents cease to be persistent in Fermi superfluids: one related to the proliferation of quantum vortices and the other to the onset of the pair-breaking mechanism.
We use the time-dependent Gross-Pitaevskii equation to study the motion of a vortex ring produced by phase imprinting on an elongated cloud of cold atoms. Our approach models the experiments of Yefsah et al. [Nature (London) 499, 426 (2013)] on 6{}^{6}6Li in the Bose-Einstein-condensate regime where the fermions are tightly bound into bosonic dimers. We find ring oscillation periods which are much larger than the period of the axial harmonic trap. Our results lend further strength to Bulgac et al.'s arguments (arXiv:1306.4266) that the ``heavy solitons'' seen in those experiments are actually vortex rings. We numerically calculate the periods of oscillation for the vortex rings as a function of interaction strength, trap aspect ratio, and minimum vortex ring radius. In the presence of axial anisotropies the rings undergo complicated internal dynamics where they break into sets of vortex lines, then later combine into rings. These structures oscillate with a similar frequency to simple axially symmetric rings.