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arXiv:2406.00289 · Physical Review Research

Dynamic generation of superflow in a fermionic ring through phase imprinting

Ke-Ji Chen, Wei Yi, Fan Wu

Published Jan 7, 2025• 2 citations
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Abstract

We study the dynamic generation of persistent current by phase imprinting fermionic atoms in a ring geometry at zero temperature. Mediated by the pairing interaction, the Fermi condensate dynamically acquires a quantized current by developing azimuthal phase slips, as well as density and pairing-order-parameter depletions. Resorting to the Bogolioubov–de Gennes formalism, we investigate the time evolution of the transferred total angular momentum and the quantized superfluid current throughout the phase-imprinting process. This enables a detailed self-consistent analysis of the impact of interaction, as well as different initial pairing states, on the superflow formation, in contrast to previous theoretical analysis based on the Gross-Pitaevskii equation with artificially imposed phases. In particular, we show that, as the interaction strength increases, the azimuthal density distribution becomes less susceptible to the phase imprinting potential, leading to a smaller quantized current under the same imprinting parameters. Our results offer microscopic insights into the dynamic development of superflow in the phase-imprinting process, and are helpful for the ongoing experimental effort.

DOI
10.1103/physrevresearch.7.013022

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We study the dynamic generation of persistent current by phase imprinting fermionic atoms in a ring geometry at zero temperature. Mediated by the pairing interaction, the Fermi condensate dynamically acquires a quantized current by developing azimuthal phase slips, as well as density and pairing-order-parameter depletions. Resorting to the Bogolioubov–de Gennes formalism, we investigate the time evolution of the transferred total angular momentum and the quantized superfluid current throughout the phase-imprinting process. This enables a detailed self-consistent analysis of the impact of interaction, as well as different initial pairing states, on the superflow formation, in contrast to previous theoretical analysis based on the Gross-Pitaevskii equation with artificially imposed phases. In particular, we show that, as the interaction strength increases, the azimuthal density distribution becomes less susceptible to the phase imprinting potential, leading to a smaller quantized current under the same imprinting parameters. Our results offer microscopic insights into the dynamic development of superflow in the phase-imprinting process, and are helpful for the ongoing experimental effort.
Abstract Phase imprinting enables the dynamic generation of superflow in bosonic atoms, effectively overcoming traditional limitations such as vortex number constraints and heating effects. However, the mechanisms underlying superflow formation remain insufficiently understood. In this work, we reveal these mechanisms by studying the time evolution of the transferred total angular momentum and the quantized current throughout the phase imprinting process, achieved through numerically solving the time-dependent Schrödinger and Gross–Pitaevskii equations. We demonstrate that the Bose gas dynamically acquires angular momentum through the density depletion induced by the phase imprinting potential, whereas quantized currents emerge from azimuthal phase slips accompanied by complete density depletions. Regarding the impact of system parameters, such as interactions, we find that interactions hinder superflow formation, as the azimuthal density distribution becomes less susceptible to the phase imprinting potential. Our findings offer microscopic insights into the dynamic development of superflow during the phase imprinting process and provide valuable guidance for ongoing experimental efforts.
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.
Abstract We present a kinetic description of superfluid currents in ring-shaped Bose-Einstein condensates based on the Wigner phase-space formalism. Starting from the Gross-Pitaevskii equation in a toroidal geometry, we derive a Vlasov-type equation for the angular Wigner function, in which the mean-field interaction generates an effective force proportional to the density gradient. Within this framework, we obtain the dispersion relation of collective modes and recover the Bogoliubov spectrum in the long-wavelength limit. We show that the Landau criterion for superfluidity can be interpreted as the absence of resonant phase-space trajectories satisfying the condition ω=qvℓ\omega = q v_\ell ω=qvℓ​ ω = q v ℓ . In a ring geometry, the quantization of angular momentum leads to a discrete set of velocities, which suppresses the availability of resonant states and strongly inhibits Landau damping. In contrast, in the continuous limit R→∞R \rightarrow \infty R→∞ R → ∞ , the spectrum becomes quasi-continuous and the standard Landau damping mechanism is recovered, establishing a direct connection between kinetic resonances and the energetic criterion for superfluidity. We further analyze the role of Bogoliubov depletion by considering a finite-width angular momentum distribution. Although resonant states formally exist in this case, we show that, for flow velocities below the sound velocity, the phase-space distribution does not provide the gradients required for energy transfer, and the superfluid current remains dynamically stable. Our results provide a unified phase-space interpretation of superfluidity, highlighting the role of angular momentum quantization and the structure of the distribution function in determining the stability of persistent currents. Graphic abstract Phase-space interpretation of superfluid stability in a ring Bose-Einstein condensate. For flow velocities below the sound velocity, resonant phase-space trajectories are unavailable and the superflow remains stable, whereas above the sound velocity resonant coupling becomes possible, leading to kinetic instability
We have produced persistent currents of ultracold fermionic atoms trapped in a ring, with lifetimes greater than 10 sec in the strongly interacting regime. These currents remain stable well into the BCS regime at sufficiently low temperature. We drive a circulating BCS superfluid into the normal phase and back by changing the interaction strength and find that the probability for quantized superflow to reappear is remarkably insensitive to the time spent in the normal phase and the minimum interaction strength. After ruling out spontaneous current formation for our experimental conditions, we argue that the reappearance of superflow is due to weak damping of normal currents in this limit. These results establish that ultracold fermionic atoms with tunable interactions can be used to create matter-wave circuits similar to those previously created with weakly interacting bosonic atoms.
Abstract Considerable progress in experimental studies of atomic gases in a toroidal geometry opens up novel prospects for the investigation of fundamental properties of superfluid states and creation of new configurations for atomtronic circuits. In particular, a setting with Bose–Einstein condensates loaded in a dual-ring trap suggests a possibility to consider the dynamics of tunneling between condensates with different angular momenta. Accordingly, we address the tunneling in a pair of coaxial three-dimensional (3D) ring-shaped condensates separated by a horizontal potential barrier. A truncated (finite-mode) Galerkin model and direct simulations of the underlying 3D Gross–Pitaevskii equation are used for the analysis of tunneling superflows driven by an initial imbalance in atomic populations of the rings. The superflows through the corresponding Bose–Josephson junction are strongly affected by persistent currents in the parallel rings. Josephson oscillations of the population imbalance and angular momenta in the rings are obtained for co-rotating states and non-rotating ones. On the other hand, the azimuthal structure of the tunneling flow demonstrates formation of Josephson vortices (fluxons) with zero net current through the junction for hybrid states , built of counter-rotating persistent currents in the coupled rings.
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.