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arXiv:cond-mat/0205409 · Physical Review A

Persistent currents in a circular array of Bose-Einstein condensates

Gheorghe Sorin Paraoanu

Published Feb 14, 2003• 48 citations
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Abstract

A ring-shaped array of Bose-Einstein condensed atomic gases can display circular currents if the relative phase of neighboring condensates becomes locked to certain values. It is shown that, irrespective of the mechanism responsible for generating these states, only a restricted set of currents are stable, depending on the number of condensates, on the interaction and tunneling energies, and on the total number of particles. Different instabilities due to quasiparticle excitations are characterized, and possible experimental setups for testing the stability prediction are also discussed.

DOI
10.1103/physreva.67.023607

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A ring-shaped array of Bose-Einstein condensed atomic gases can display circular currents if the relative phase of neighboring condensates becomes locked to certain values. It is shown that, irrespective of the mechanism responsible for generating these states, only a restricted set of currents are stable, depending on the number of condensates, on the interaction and tunneling energies, and on the total number of particles. Different instabilities due to quasiparticle excitations are characterized, and possible experimental setups for testing the stability prediction are also discussed.
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We study the stability of persistent currents in a coherently coupled quasi-two-dimensional Bose-Einstein condensate confined in a ring trap at T=0T=0T=0. By numerically solving Gross-Pitaevskii equations and by analyzing the excitation spectrum obtained from diagonalization of the Bogoliubov--de Gennes matrix, we describe the mechanisms responsible for the decay of the persistent currents depending on the values of the interaction coupling constants and the Rabi frequency. When the unpolarized system decays due to an energetic instability in the density channel, the spectrum may develop a rotonlike minimum, which gives rise to the finite wavelength excitation necessary for vortex nucleation at the inner surface. When decay in the unpolarized system is driven by spin-density excitations, the finite wavelength naturally arises from the existence of a gap in the excitation spectrum. In the polarized phase of the coherently coupled condensate, there is a hybridization of the excitation modes that leads to complex decay dynamics. In particular, close to the phase transition, a state of broken rotational symmetry is found to be stationary and stable.
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.
Motivated by a recent experiment [Beattie, Moulder, Fletcher, and Hadzibabic, Phys. Rev. Lett. 110, 025301 (2013)], we study the superflow of atomic spinor Bose-Einstein condensates optically trapped in a ring-shaped geometry. Within a dissipative mean-field approach we simulate a two-component condensate in conditions adapted to the experiment. In qualitative agreement with the experimental findings, we observe stable superflow if the spin-population imbalance is above some well-defined threshold value. Below the stability threshold the persistent currents with higher-order circulation decay in quantized steps, and the vortex lines escape from the center of the ring through dynamically created ``weak links'' in the condensate annulus. These regions with reduced density of one spin component are filled by atoms of the other component. The vortices then leave the ring-shaped high-density region of the condensate and finally decay into elementary excitations.
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 consider large rings of weakly coupled Bose-Einstein condensates, analyzing their transition to chaotic dynamics and loss of coherence. Initially, a ring is considered to be in an eigenstate, i.e., in a commensurate configuration with equal site fillings and equal phase differences between neighboring sites. Such a ring should exhibit a circulating current whose value will depend on the initial, nonzero phase difference. The appearance of such currents is a signature of an established coherence along the ring. If phase difference falls between $\ensuremath{\pi}/2$ and $3\ensuremath{\pi}/2$ and interparticle interaction in condensates exceeds a critical interaction value uc{u}_{c}uc​, the coherence is supposed to be quickly destroyed because the system enters a chaotic regime due to inherent instabilities. This is, however, only part of the story. It turns out that chaotic dynamics and resulting averaging of circular current to zero are generally offset by a critical timescale tc{t}_{c}tc​, which is almost two orders of magnitude larger than the one expected from the linear stability analysis. We study the critical timescale in detail in a broad parameter range.