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Register a new userWatching dark solitons decay into vortex rings in a Bose-Einstein condensate
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We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.
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In a shaken Bose-Einstein condensate, confined in a vibrating trap, there can appear different nonlinear coherent modes. Here we concentrate on two types of such coherent modes, vortex ring solitons and vortex rings. In a cylindrical trap, vortex ring solitons can be characterized as nonlinear Hermite-Laguerre modes, whose description can be done by means of optimized perturbation theory. The energy, required for creating vortex ring solitons, is larger than that needed for forming vortex rings. This is why, at a moderate excitation energy, vortex rings appear before vortex ring solitons. The generation of vortex rings is illustrated by numerical simulations for trapped $^{87}$Rb atoms.
Quasi-one-dimensional solitons that may occur in an elongated Bose-Einstein condensate become unstable at high particle density. We study two basic modes of instability and the corresponding bifurcations to genuinely three-dimensional solitary waves such as axisymmetric vortex rings and non-axisymmetric solitonic vortices. We calculate the profiles of the above structures and examine their dependence on the velocity of propagation along a cylindrical trap. At sufficiently high velocity, both the vortex ring and the solitonic vortex transform into an axisymmetric soliton. We also calculate the energy-momentum dispersions and show that a Lieb-type mode appears in the excitation spectrum for all particle densities.
We present a method for numerically building a vortex knot state in the superfluid wave-function of a Bose-Einstein condensate. We integrate in time the governing Gross-Pitaevskii equation to determine evolution and stability of the two (topologically) simplest vortex knots which can be wrapped over a torus. We find that the velocity of a vortex knot depends on the ratio of poloidal and toroidal radius: for smaller ratio, the knot travels faster. Finally, we show how unstable vortex knots break up into vortex rings.
We study the dynamics of bright solitons in a Bose-Einstein condensate (BEC) confined in a highly asymmetric trap. While working within the f ramework of a variational approach we carry out the stability analysis o f BEC solitons against collapse. When the number of atoms in the soliton exceeds a critical number $N_c$, it undergoes the so called primary col lapse. We find an analytical expression for $N_c$ in terms of appropriat e experimental quantities that are used to produce and confine the conde nsate. We further demonstrate that, in the geometry of the problem consi dered, the width of the soliton varies inversely as the number of consti tuent atoms.
Understanding quantum dynamics in a two-dimensional Bose-Einstein condensate (BEC) relies on understanding how vortices interact with each others microscopically and with local imperfections of the potential which confines the condensate. Within a system consisting of many vortices, the trajectory of a vortex-antivortex pair is often scattered by a third vortex, an effect previously characterised. However, the natural question remains as to how much of this effect is due to the velocity induced by this third vortex and how much is due to the density inhomogeneity which it introduces. In this work, we describe the various qualitative scenarios which occur when a vortex-antivortex pair interacts with a smooth density impurity whose profile is identical to that of a vortex but lacks the circulation around it.
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