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arXiv:1107.0627 · Physical Review A

Jetlike tunneling from a trapped vortex

Eliahu Cohen, Stefan Muenzel, O. V. Farberovich, Jason W. Fleischer, V. Fleurov, Avy Soffer

Published Oct 17, 2013• 6 citations
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Abstract

We analyze tunneling from vortex states in elliptically shaped traps. Using the hydrodynamic representation of the Gross-Pitaevskii (nonlinear Schr\"odinger) equation, we derive analytically and demonstrate numerically an interesting type of quantum fluid flow: a jetlike singularity formed by the interaction between the vortex and the asymmetric trap. For strongly elongated traps and high enough vorticity, the ellipticity overwhelms the circular rotation, resulting in the ejection of jets in narrow, well-defined directions. These jets are formed due to a convergence of trajectories starting from the top of the potential barrier and meeting at a certain point on the exit line. Under proper conditions they will appear in any coherent wave system with angular momentum and noncircular symmetry, such as superfluids, Bose-Einstein condensates, and light.

DOI
10.1103/physreva.88.043833

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We consider a Bose-Einstein condensate confined in a ``Mexican hat'' or sombrero potential, with a quartic minus quadratic radial dependence. We find conditions under which the ground state is annular in shape, with a hole in the center of the condensate. Rotation leads to the appearance of stable multiply quantized vortices, giving rise to a superfluid flow around the ring. The collective modes of the system are explored both numerically and analytically using the Gross-Pitaevskii and hydrodynamic equations. Potential experimental schemes to detect vorticity are proposed and evaluated, which include measuring the splitting of collective-mode frequencies, observing expansion following release from the trap, and probing the momentum distribution of the condensate.
One of the key issues related to superfluidity is the existence of quantized vortices. Following recent experiments on Bose–Einstein condensates exhibiting vortices, we investigate the behavior of the wave function which solves the Gross–Pitaevskii equation. For a rotating Bose–Einstein condensate in a harmonic trap, we give a simplified expression of the Gross–Pitaevskii energy in the Thomas–Fermi regime, which only depends on the number and shape of the vortex lines. This allows us to study in detail the structure of the line of a single quantized vortex, which has a U or S shape. S type vortices exist for all values of the angular velocity Ω but are not minimizers of the energy while U vortices are minimizers and exist only for Ω sufficiently large. Finally, we study the drag created by the movement of a detuned laser beam in a condensate and the nucleation of vortices in the low density region close to the boundary layer of the cloud.
We consider a Bose-Einstein condensate confined in a 'Mexican hat' or sombrero potential, with a quartic minus quadratic radial dependence. We find conditions under which the ground state is annular in shape, with a hole in the center of the condensate. Rotation leads to the appearance of stable multiply quantized vortices, giving rise to a superfluid flow around the ring. The collective modes of the system are explored both numerically and analytically using the Gross-Pitaevskii and hydrodynamic equations. Potential experimental schemes to detect vorticity are proposed and evaluated, which include measuring the splitting of collective-mode frequencies, observing expansion following release from the trap, and probing the momentum distribution of the condensate.