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Journal of Modern Optics

Switching and self-trapping dynamics of Bose-Einstein solitons

S. Raghavan, Govind Prasad Agrawal

Published Jun 1, 2000• 25 citations
Publisher

Abstract

We investigate the dynamics of two weakly coupled Bose condensates in long cigar-shaped traps. The Bose condensates are characterized by attractive mean-field interaction and consequently can be studied in terms of bright solitons. We exploit the analogy with directional fibre couplers in nonlinear fibre optics to uncover interesting dynamical regimes like switching of condensates from one trap to another and self-trapping of condensates. We also discuss the analogy between two weakly coupled Bose condensates and the Josephson junction in superfluids and superconductors.

DOI
10.1080/09500340008232163

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The dynamics of a bright-bright vector soliton in a cigar-shaped Bose-Einstein condensate trapping in a harmonic potential is studied.The interaction between bright solitons in different species with small separation is derived.Unlike the interaction between solitons of the same species,it is independent of the phase difference between solitons.It may be of attraction or repulsion.In the former case,each soliton will oscillate about and pass through each other around the mass-center of the system,which will also oscillate harmonically due to the harmonic trapping potential.
The Gross-Pitaevskii equation for a Bose-Einstein condensate confined in an elongated cigar-shaped trap is reduced to an effective system of nonlinear equations depending on only one space coordinate along the trap axis. The radial distribution of the condensate density and its radial velocity are approximated by Gaussian functions with real and imaginary exponents, respectively, with parameters depending on the axial coordinate and time. The effective one-dimensional system is applied to a description of the ground state of the condensate, to dark and bright solitons, to the sound and radial compression waves propagating in a dense condensate, and to weakly nonlinear waves in repulsive condensate. In the low-density limit our results reproduce the known formulas. In the high-density case our description of solitons goes beyond the standard approach based on the nonlinear Schr\"odinger equation. The dispersion relations for the sound and radial compression waves are obtained in a wide region of values of the condensate density. The Korteweg--de Vries equation for weakly nonlinear waves is derived and the existence of bright solitons on a constant background is predicted for a dense enough condensate with a repulsive interaction between the atoms.
In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.