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arXiv:0704.2427 · Physical Review Letters

Stationary and Nonstationary Fluid Flow of a Bose-Einstein Condensate Through a Penetrable Barrier

Peter Engels, C. R. Atherton

Published Oct 19, 2007• 224 citations
arXivHTMLPDF

Abstract

We experimentally study the fluid flow induced by a broad, penetrable barrier moving through an elongated dilute gaseous Bose-Einstein condensate. The barrier is created by a laser beam swept through the condensate, and the resulting dipole potential can be either attractive or repulsive. We examine both cases and find regimes of stable and unstable fluid flow: At slow speeds of the barrier, the fluid flow is steady due to the superfluidity of the condensate. At intermediate speeds, we observe an unsteady regime in which the condensate gets filled with dark solitons. At faster speeds, soliton formation completely ceases, and a remarkable absence of excitation in the condensate is seen again.

DOI
10.1103/physrevlett.99.160405

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We experimentally study the fluid flow induced by a broad, penetrable barrier moving through an elongated dilute gaseous Bose-Einstein condensate. The barrier is created by a laser beam swept through the condensate, and the resulting dipole potential can be either attractive or repulsive. We examine both cases and find regimes of stable and unstable fluid flow: At slow speeds of the barrier, the fluid flow is steady due to the superfluidity of the condensate. At intermediate speeds, we observe an unsteady regime in which the condensate gets filled with dark solitons. At faster speeds, soliton formation completely ceases, and a remarkable absence of excitation in the condensate is seen again.
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We investigate vortex shedding from a moving penetrable obstacle in a highly oblate Bose-Einstein condensate. The penetrable obstacle is formed by a repulsive Gaussian laser beam that has the potential barrier height lower than the chemical potential of the condensate. The moving obstacle periodically generates vortex dipoles and the vortex shedding frequency fv{f}_{v}fv​ linearly increases with the obstacle velocity vvv as ${f}_{v}=a(v\ensuremath{-}{v}_{c})$, where vc{v}_{c}vc​ is a critical velocity. Based on the periodic shedding behavior, we demonstrate deterministic generation of a single vortex dipole by applying a short linear sweep of a laser beam. This method will allow further controlled vortex experiments such as dipole-dipole collisions.
We investigate by numerical simulations the pattern formation after an oscillating attractive-repulsive obstacle inserted into the flow of a Bose-Einstein condensate. For slow oscillations we observe a complex emission of vortex dipoles. For moderate oscillations organized lined up vortex dipoles are emitted. For high frequencies no dipoles are observed but only lined up dark fragments. The results shows that the drag force turns negative for sufficiently high frequency. We also successfully model the ship waves in front of the obstacle. In the limit of very fast oscillations all the excitations of the system tend to vanish.
We numerically model experiments on the superfluid critical velocity of an elongated, harmonically trapped Bose-Einstein condensate as reported by [P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007)]. These experiments swept an obstacle formed by an optical dipole potential through the long axis of the condensate at constant velocity. Their results found an increase in the resulting density fluctuations of the condensate above an obstacle velocity of v≈0.3v\approx 0.3v≈0.3 mm/s, suggestive of a superfluid critical velocity substantially less than the average speed of sound. However, our analysis shows that the that the experimental observations of Engels and Atherton are in fact consistent with a superfluid critical velocity equal to the local speed of sound. We construct a model of energy transfer to the system based on the local density approximation to explain the experimental observations, and propose and simulate experiments that sweep potentials through harmonically trapped condensates at a constant fraction of the local speed of sound. We find that this leads to a sudden onset of excitations above a critical fraction, in agreement with the Landau criterion for superfluidity.
The one-dimensional flow of a continuous beam of Bose-Einstein condensed atoms in the presence of an obstacle is studied as a function of the beam velocity and of the type of perturbing potential (representing the interaction of the obstacle with the atoms of the beam). We identify the relevant regimes: stationary/time-dependent and superfluid/dissipative; the absence of drag is used as a criterion for superfluidity. There exists a critical velocity below which the flow is superfluid. For attractive obstacles, we show that this critical velocity can reach the value predicted by Landau's approach. Besides, for penetrable obstacles, it is shown that superfluidity is recovered at large beam velocity. Finally, enormous differences in drag occur when switching from repulsive to attractive potential.
We consider the dynamics of two coupled miscible Bose-Einstein condensates, when an obstacle is dragged through them. The existence of two different speeds of sound provides the possibility for three dynamical regimes: when both components are subcritical, we do not observe nucleation of coherent structures; when both components are supercritical they both form dark solitons in one dimension (1D) and vortices or rotating vortex dipoles in two dimensions; in the intermediate regime, we observe the nucleation of a structure in the form of a dark-antidark soliton in 1D; the 2D analog of such a structure, a vortex-lump, is also observed.