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arXiv:cond-mat/0408165 · Physical Review A

Dynamics of a Bose-Einstein-condensate bright soliton in an expulsive potential

Luca Salasnich

Published Nov 22, 2004• 53 citations
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Abstract

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 $^{7}\mathrm{Li}$ 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.

DOI
10.1103/physreva.70.053617

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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.
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.
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 analyze the dynamics of a bright soliton in Bose–Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential. Under a safe range of parameters in which the Gross–Pitaevskii (GP) equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomic scattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity.
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.
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.
The Bose-Einstein condensate (BEC) of a dilute gas of bosons is well described by the three-dimensional Gross-Pitaevskii equation (3D GPE), that is a nonlinear Schrödinger equation. By imposing a transverse confinement the BEC can travel only in the cylindrical axial direction. We show that in this case the BEC with attractive interaction admits a 3D bright soliton solution which generalizes the text-book one, that is valid in the one-dimensional limit (1D GPE). Contrary to the 1D case, the 3D bright soliton exists only below a critical number of Bosons that depends on the extent of confinement. Finally, we find that the 3D bright soliton collapses if its density excedes a critical value. Our results are obtained by using a nonpolynomial Schrödinger equation (NPSE), an effective one-dimensional equation derived from the 3D GPE.