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Journal of Optoelectronics·laser

Effect of nonlinear spatial modulation on the evolution of two-component Bose-Einstein condensate solitons

Yi Lin

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Effect of the nonlinear spatial modulation on the evolution of twocomponent linear coupling Bose-Einstein condensate bright solitons trapped in a harmonic potential has been investigated numerically.It is indicated that the atomic density envelope of the soltions is changed with the spatial variation of s-wave scattering length,and the soliton exists in stable state under appropriate conditions.The evolution of solitons depends on the sign and value of the coefficient of the nonlinear spatial modulation.

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Effect of the nonlinear spatial modulation on the evolution of twocomponent linear coupling Bose-Einstein condensate bright solitons trapped in a harmonic potential has been investigated numerically.It is indicated that the atomic density envelope of the soltions is changed with the spatial variation of s-wave scattering length,and the soliton exists in stable state under appropriate conditions.The evolution of solitons depends on the sign and value of the coefficient of the nonlinear spatial modulation.
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The evolution characteristics of a matter-wave bright soliton are investigated by means of the variational approach in the presence of spatially varying nonlinearity.It is found that the atom density envelope of the soliton is changed as a result of the spatial variation of the s-wave scattering length.The stable soliton can exist in appropriate initial conditions.The movement of the soliton depends on the sign and value of the coefficient of spatially modulated nonlinearity.These theoretical predictions are confirmed by the full numerical simulations of the one-dimensional Gross-Pitaevskii equation.
We study the formation of bright solitons in a Bose-Einstein condensate of 7Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment [Nature (London) 417, 150 (2002)]]. The numerical simulations are performed by using the Gross-Pitaevskii equation with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results. We find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior.
We investigate the effect of higher-order interactions induced by shape-dependent confinement in the modulational instability (MI) of a binary mixture of Bose-Einstein condensates. For this, we present and compute both analytically and numerically a system of coupled Gross-Pitaevskii equations with residual nonlinearity that rule the dynamics of the mixture. Using the linear stability approach, we obtain the instability criteria of the mixture and find that the MI can be excited in miscible condensates and altered in immiscible condensates due to the effect of residual nonlinearity. Direct numerical calculations are performed to support the analytical predictions, and a good agreement is found. The space-time evolution of the condensate density is displayed in both cases when the mixture is miscible and immiscible, showing the generation of bright solitons for modes predicted to be unstable.
We introduce vector solitary waves in two-component Bose–Einstein condensates with spatially modulated nonlinearity coefficients and a harmonic trapping potential. Using the self-similarity method, novel vector solitary waves are built with the help of Whittaker function, including multipole solutions and necklace rings. The stability of vortex soliton pairs is examined by direct numerical simulation; the results show that a new class of stable low-order vortex soliton pairs with n = 2 and m ≤ 3 can be supported by the spatially modulated interaction in the harmonic trap. Higher order vector-vortex soliton is found unstable over prolonged distances.
The transmissions of matter-wave solitons through linear and nonlinear inhomogeneities induced by the spatial variations of the trap and the scattering length in Bose-Einstein condensates are investigated. The enhanced transmission of a soliton through a linear trap by a modulation of the scattering length, is exhibited. The theory is based on the perturbed inverse scattering transform for solitons, and we show that radiation effects are important. Numerical simulations of the Gross-Pitaevskii equation confirm the theoretical predictions.