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arXiv:cond-mat/9710238 · Physical Review Letters

Creation of Dark Solitons and Vortices in Bose-Einstein Condensates

Ralph Dum, J. I. Cirac, Maciej Lewenstein, P. Zoller

Published Apr 6, 1998• 212 citations
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Abstract

We propose and analyze a scheme to create dark solitons and vortices in Bose-Einstein condensates. This is achieved starting from a condensate in the internal state $|a〉$ and transferring the atoms to the internal state $|b〉$ via a Raman transition induced by laser light. By scanning adiabatically the Raman detuning, dark solitons and vortices are created.

DOI
10.1103/physrevlett.80.2972

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We propose and analyze a scheme to create dark solitons and vortices in Bose-Einstein condensates. This is achieved starting from a condensate in the internal state ∣a〉|a〉∣a〉 and transferring the atoms to the internal state ∣b〉|b〉∣b〉 via a Raman transition induced by laser light. By scanning adiabatically the Raman detuning, dark solitons and vortices are created.
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We present a widely accessible and experimentally realizable technique for the controlled creation of dark-bright solitons and soliton lattices in one-dimensional atomic Bose-Einstein condensates. The method is based on preparing the condensate in a dark state of a ΛΛΛ-coupled three-level system. Numerical simulations of the corresponding two-component system reveal that individual dark-bright solitons created through this scheme can survive over experimentally accessible timescales, even when the coupling laser fields are switched off. Meanwhile, the fate of soliton lattices upon the quench of the fields depends on the scattering lengths. When they are all equal, the lattice is found to persist on timescales comparable to the condensate lifetime, even though the analysis of dynamical stability reveals that they possess unstable modes. In this case the resulting destabilization is not found to be detrimental, as it leads to recurrent dynamics. However, for unequal scattering lengths the lattice structure gets destroyed once the instability sets in, which happens after a few tens of milliseconds after the quench of the optical fields.
The generation of dark solitons in Bose-Einstein condensates has been an area of interest since the first experimental condensates were produced. The ubiquity of solitons in the natural world makes them an important phenomenon to understand. Despite excellent theoretical work in two dimensional dark solitons, few experiments have had the opportunity to investigate this regime. The work presented investigates the generation of dark solitons in a Rb-87 Bose-Einstein condensate. The evolution and decay of these topological excitations are investigated. The decay of the dark solitons is found to vary with the phase-step used to generate them. Dark solitons created with a phase-step width of 0.60 ±0.15 μm are found to decay into vortices after 10 ms. Dark solitons generated with larger phase-steps are found not to exhibit this vortex decay, instead dissipating over 10-15 ms back into the condensate. The first experimental generation of two dimensional Jones-Roberts solitons is reported in this work. These dark solitons differ from the standard planar dark soliton in that they are finite in extent and are \nfound to be more dynamically stable. The Jones-Roberts solitons are observed for 40 ms with no observed change in energy. \n
We theoretically propose a new method of making quantum turbulence from many dark solitons in atomic Bose-Einstein condensates. We solve numerically the two-dimensional Gross-Pitaevskii equation. We set initially many solitons so that they can form a square grid. A dark soliton is known to be stable in one-dimensional systems, but unstable in two- or three-dimensional systems and decay to vortices. Our simulation shows that these solitons decay to a lot of vortices which move around in the system and eventually lead to two-dimensional quantum turbulence. The probability distribution function of the superfluid velocity obeys a Gaussian distribution in the low-velocity region and a power-law distribution in the high-velocity region. The decay of the total number of vortices obeys a power-law for a relatively long period. This scenario may be experimentally realized through interference of Bose-Einstein condensates in a trap potential.