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arXiv:cond-mat/0205624 · Physical Review A

Dynamics of a matter-wave bright soliton in an expulsive potential

Lincoln D. Carr, Yvan Castin

Published Dec 12, 2002• 146 citations
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Abstract

The stability regimes and nonlinear dynamics of bright solitons created in a harmonic potential which is transversely attractive and longitudinally expulsive are presented. This choice of potential is motivated by the recent creation of a matter-wave bright soliton from an attractive Bose-Einstein condensate [L. Khaykovich et al., Science 296, 1290 (2002)]. The critical branches for collapse due to the three-dimensional character of the gas and explosion caused by the expulsive potential are derived based on variational studies. Weak excitations of the soliton due to sudden changes in the trapping potential and/or or the scattering length are shown to damp exponentially by the emission of a small fraction of particles. It is shown that higher-order solitons can also be created in present experiments by an abrupt change of a factor of 4 in the scattering length. Finally, it is demonstrated that quantum evaporation occurs by nonlinear tunneling of particles out of the soliton, leading eventually to its explosion.

DOI
10.1103/physreva.66.063602

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The stability regimes and nonlinear dynamics of bright solitons created in a harmonic potential which is transversely attractive and longitudinally expulsive are presented. This choice of potential is motivated by the recent creation of a matter-wave bright soliton from an attractive Bose-Einstein condensate [L. Khaykovich et al., Science 296, 1290 (2002)]. The critical branches for collapse due to the three-dimensional character of the gas and explosion caused by the expulsive potential are derived based on variational studies. Weak excitations of the soliton due to sudden changes in the trapping potential and/or or the scattering length are shown to damp exponentially by the emission of a small fraction of particles. It is shown that higher-order solitons can also be created in present experiments by an abrupt change of a factor of 4 in the scattering length. Finally, it is demonstrated that quantum evaporation occurs by nonlinear tunneling of particles out of the soliton, leading eventually to its explosion.
We theoretically investigate the dynamics of a matter-wave soliton created in a harmonic potential, which is attractive in the transverse direction but expulsive in the longitudinal direction. This Bose-Einstein-condensate (BEC) bright soliton made of 7Li^{7}\mathrm{Li}7Li atoms has been observed in a recent experiment [Khaykovich et al., Science 296, 1290 (2002)]. We show that the nonpolynomial Schr\"odinger equation, an effective one-dimensional equation we derived from the three-dimensional Gross-Pitaevskii equation, is able to reproduce the main experimental features of this BEC soliton in an expulsive potential.
Matter-wave bright solitons of 7^77Li gas in an expulsive potential
A Lagrangian based method is used to derive an analytical model for studying the dynamics of matter-wave bright soliton created in a harmonic potential which is attractive in the transverse direction and expulsive in the longitudinal direction. By means of sech trial functions and a Ritz optimization procedure, evolution eqautions are constructed for width, amplitude and nonlinear frequency chirp of the propagating soliton of the atomic condensate. Our eqaution for the width is an exact agreement with that of Carr and Castin [Phys.Rev.A66,063602(2002)][ Phys. Rev. A {\bf{66}}, 063602 (2002)][Phys.Rev.A66,063602(2002)], obtained by more detailed analysis. In agreement with the experiment of Paris group [Science296,1290(2002)][ Science {\bf{296}}, 1290 (2002)][Science296,1290(2002)], the expulsive potential is found to cause the soliton to explode for N∣as∣=0.98N|a_s|=0.98N∣as​∣=0.98, NNN being the number of atoms in the condensate and asa_sas​, the scattering length of the atom-atom interaction.
A Lagrangian based method is used to derive an analytical model for studying the dynamics of matter-wave bright soliton created in a harmonic potential which is attractive in the transverse direction and expulsive in the longitudinal direction.By means of sech trial functions and a Ritz optimization procedure, evolution equations are constructed for width, amplitude and nonlinear frequency chirp of the propagating soliton of the atomic condensate.Our equation for the width is an exact agreement with that of Carr and Castin, obtained by more detailed analysis.In agreement with the experiment of Paris group, the expulsive potential is found to cause the soliton to explode for N |a s | = 0.98, N being the number of atoms in the condensate and as -the scattering length of the atom-atom interaction.
We investigate the dynamics of Bose-Einstein condensate bright solitons made of alkali-metal atoms with negative scattering length and under harmonic confinement in the transverse direction. Contrary to the one-dimensional (1D) case, the 3D bright soliton exists only below a critical attractive interaction that depends on the extent of confinement. Such a behavior is also found in multisoliton condensates with box boundary conditions. We obtain numerical and analytical estimates of the critical strength beyond which the solitons do not exist. By using an effective 1D nonpolynomial nonlinear Schr\"odinger equation, which accurately takes into account the transverse dynamics of cigarlike condensates, we numerically simulate the dynamics of the ``soliton train'' reported in a recent experiment [Nature (London) 417, 150 (2002)]. Then, analyzing the macroscopic quantum tunneling of the bright soliton on a Gaussian barrier, we find that its interference in the tunneling region is strongly suppressed with respect to nonsolitonic case; moreover, the tunneling through a barrier breaks the shape invariance of the matter wave. Finally, we show that the collapse of the soliton is induced by the scattering on the barrier or by the collision with another matter wave when the density reaches a critical value, for which we derive an accurate analytical formula.
We present a family of exact solutions of the one-dimensional nonlinear Schro dinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.