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arXiv:cond-mat/0312084

Interconversion of dark soliton and Josephson vortex in a quasi-1D long Bose Josephson junction

V. M. Kaurov, Anatoly B. Kuklov

Published Dec 3, 2003• 0 citations
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Abstract

Dark soliton (DS) and Josephson vortex (JV) in quasi-1D long Bose Josephson junction (BJJ) can be interconverted by tuning Josephson coupling. Rates of the interconversion as well as of the thermally activated phase-slip effect, resulting in the JV switching its vorticity, have been evaluated. The role of quantum phase-slip in creating superposition of JVs with opposite vorticities as a qubit is discussed as well. Utilization of the JV for controlled and coherent transfer of atomic Bose-Einstein condensate (BEC) is suggested.

DOI
10.48550/arxiv.cond-mat/0312084

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Dark soliton (DS) and Josephson vortex (JV) in quasi-1D long Bose Josephson junction (BJJ) can be interconverted by tuning Josephson coupling. Rates of the interconversion as well as of the thermally activated phase-slip effect, resulting in the JV switching its vorticity, have been evaluated. The role of quantum phase-slip in creating superposition of JVs with opposite vorticities as a qubit is discussed as well. Utilization of the JV for controlled and coherent transfer of atomic Bose-Einstein condensate (BEC) is suggested.
The Josephson vortex (JV) between two long parallel coupled atomic Bose-Einstein condensates (BECs) is considered analytically and numerically in the quasi-one-dimensional limit. Its closed analytical solution is presented. It is found that, upon increasing the Josephson coupling, the JV transforms spontaneously into a dark soliton and vice versa. We suggest how the JV and its transformation can be detected. We also propose that the JV can be utilized for controlled and coherent transfer of atomic BECs and as a possible mobile qubit.
We show that Josephson vortices in a quasi-one-dimensional atomic Bose Josephson junction can be controllably manipulated by imposing a difference of chemical potentials on the atomic Bose-Einstein condensate waveguides forming the junction. This effect, which has its origin in the Berry phase structure of a vortex, turns out to be very robust in the whole range of the parameters where such vortices can exist. We also propose that a Josephson vortex can be created by the phase imprinting technique and can be identified by a specific tangential feature in the interference picture produced by expanding clouds released from the waveguides.
Dilute atomic Bose-Einstein condensates support intriguing macroscopic excitations in the form of quantized vortices and dark solitons. In this thesis we present extensive quantitative studies of the dynamics of these phenomena in the limit of zero temperature, performed by numerical simulation of the Gross- Pitaevskii equation. We show that vortices and dark solitons are inherently unstable to acceleration through the condensate, leading to the emission of sound waves. Indeed, for a single vortex/soliton, the power emitted is proportional to the square of the local acceleration. However, due to the finite size of the condensate, the vortex/soliton reinteracts with the emitted sound. This coupling has an important effect on the ensuing dynamics, and we illustrate how it can be engineered to induce net decay, stabilise, or even drive energy into the vortex/soliton. Under the harmonic confinement typically employed to trap the condensates, the acceleration-induced decay is stabilised by reabsorption of the emitted sound. However, by modifying the trap geometry, e.g. by adding an inner dimple in which the soliton resides or an optical lattice potential, it is possible to break this equilibrium and so induce a net decay of the vortex/soliton in a controllable manner. The decay rate can be considerable and should be observable under current experimental conditions. The dynamical stability of quantized vortices is also relevant to the field of turbulence in superfluid Helium, where the motion of the vortices is induced by the surrounding distribution of vortices rather than density. We extend these results to this field, and additionally consider the interactions between two and three vortices, which are also found to involve sound emission. By exciting the sound field of the condensate it is possible to drive parametrically energy into a dark soliton. In a real dissipative environment, this can be used to stabilise the soliton decay. Finally, we illustrate the links between dark solitons and vortices: a dark soliton embedded in a three-dimensional system is prone to decay into vortex rings, while a vortex in a quasi-one-dimensional geometry cannot be supported and exists as a hybrid between a vortex and dark soliton, known as a solitonic vortex.
We study the relation between Josephson dynamics and topological excitations in a dilute Bose-Einstein condensate confined in a double-well trap. We show that the phase slips responsible for the self-trapping regime are created by vortex rings entering and annihilating inside the weak-link region or created at the center of the barrier and expanding outside the system. Large amplitude oscillations just before the onset of self-trapping are also strictly connected with the dynamics of vortex rings at the edges of the inter-well barrier. Our results extend and analyze the dynamics of the vortex-induced phase slippages suggested a few decades ago in relation to the "ac" Josephson effect of superconducting and superfluid helium systems.
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.