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The averaged lagrangian of solitons of Bose-Einstein condensation

M.R. Zhumaev, Mirzo Zokirovich Sharipov, N. N. Mirzhonova

Published Mar 30, 2018• 0 citations
OpenAlex

Abstract

The effect of the fluctuation interaction of atoms forming a condensate on solitons of the Bose-Einstein condensation is considered. A short derivation of the Gross-Pitaevsky equation is given. The averaged Lagrangian of solitons of the Bose-Einstein condensation is determined. The obtained results give an opportunity to investigate the solitons dynamics under the action of various perturbations.

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The effect of the fluctuation interaction of atoms forming a condensate on solitons of the Bose-Einstein condensation is considered. A short derivation of the Gross-Pitaevsky equation is given. The averaged Lagrangian of solitons of the Bose-Einstein condensation is determined. The obtained results give an opportunity to investigate the solitons dynamics under the action of various perturbations.
Numerical analysis of the one-, two-, and three-dimensional soliton solutions for the modified Gross-Pitaevski equation with regard to the nonlocality of interaction between atoms of a condensate is performed. In calculations of the parameter of interaction nonlocality, the Lennard-Jones potential for collisions between Li atoms in the triplet state was used. It is shown that the nonlocality stabilizes the three-dimensional solitons with sizes in a certain range. The lifetimes of solitons, which are determined by two-and three-particle collisions between atoms, are estimated.
A modified Gross-Pitaevskii equation for a Bose-Einstein condensate with nonlocal interaction between atoms is used to analyze and calculate the characteristics of internal modes of bright solitons (eigen-modes of small perturbations of the condensate). The spectra of even and odd internal modes are found for one-and two-dimensional solitons, and the rate constant characterizing nonlinear internal-mode damping is determined. The possibility of experimental verification of the results is discussed.
We investigate the interactions between components of various vector solitons in Bose—Einstein condensates by means of the least action principle, and derive the effective potentials for different vector solitons, which indicate that the interactions are of short range, and may be repulsive or attractive decided by the different intra- and inter-species interactions in such a system. In the case of attraction, the two solitons will oscillate about and pass through each other around the equilibrium state. The comparison of analytical results with mumertical simulation is presented.
Excited states of Bose–Einstein condensates are considered in the large density limit of the Gross–Pitaevskii equation with repulsive inter-atomic interactions and a harmonic potential. The relative dynamics of dark solitons (density dips on the localized condensate) with respect to the harmonic potential and to each other is approximated using the averaged Lagrangian method. This permits a complete characterization of the equilibrium positions of the dark solitons as a function of the chemical potential. It also yields an analytical handle on the oscillation frequencies of dark solitons around such equilibria. The asymptotic predictions are generalized for an arbitrary number of dark solitons and are corroborated by numerical computations for 2- and 3-soliton configurations.
The evolution characteristics of the Bose-Einstein Condensate(BEC) soliton with three-body interactions are investigated with a variational approach and direct numerical simulations of the Gross-Pitaevskii-Ginzburg equation.It is found that the effects of the three-body interactions on the evolution characteristics of the BEC soliton are larger than the effecs of the two-body interactions.Its effect depends on the sign of the interactions,the number of atoms in the trap,the coefficient of the trap and the initial pulse width of the BECs soliton.