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Optics & Optoelectronic Technology

Evolution of a Dark Soliton in a Trapped Bose-Einstein Condensate with Three-Body Interactions

Hong Li

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The evolution characteristics of a Bose-Einstein condensate dark soliton with three-body interactions are investigated by the variational approach.The effects of a harmonic trapping potential on the motion of the dark soliton are discussed. It is shown that the dark soliton will oscillate in the harmonic potential. The trapping strength and the sign of three-body interactions affect the evolution of the dark soliton and change the oscillation characteristics of the Bose-Einstein condensate system.

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The evolution characteristics of a Bose-Einstein condensate dark soliton with three-body interactions are investigated by the variational approach.The effects of a harmonic trapping potential on the motion of the dark soliton are discussed. It is shown that the dark soliton will oscillate in the harmonic potential. The trapping strength and the sign of three-body interactions affect the evolution of the dark soliton and change the oscillation characteristics of the Bose-Einstein condensate system.
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.
Generation of dark solitons from large initial excitations and their evolution in a quasi-one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a single deep soliton main characteristics of its motion such as a frequency and amplitude of oscillations are calculated by means of the perturbation theory which in the leading order results in a Newtonian dynamics, corrections to which are computed as well. It is shown that long-time dynamics of a dark soliton in a generic situation deviates substantially from outcomes of the naive application of the Ehrenfest theorem. We also consider three different techniques of controllable creation of multi-soliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multi-soliton effects are discussed.
The stability of three coupled Bose-Einstein condensate (BEC) solitons is investigated by the variational approach in two conventional time-independent trapping potentials. The effects of parameters of the potentials and the initial conditions of the BEC soliton system on the stationary state and self-trapping are discussed. It is found that the trapping potentials play an important role in the stability of the system and change the characteristics of the system, and there are different critical potential amplitude values corresponding to different trapping potentials and initial conditions of the BEC soliton system.
The stability properties of dark solitons in quasi-one-dimensional Bose-Einstein condensate (BEC) loaded in a Jacobian elliptic sine potential with three-body interactions are investigated theoretically. The solitons are obtained by the Newton-Conjugate Gradient method. A stationary cubic-quintic nonlinear Schrödinger equation is derived to describe the profiles of solitons via the multi-scale technique. It is found that the three-body interaction has distinct effect on the stability properties of solitons. Especially, such a nonlinear system supports the so-called dark solitons (kink or bubble), which can be excited not only in the gap, but also in the band. The bubbles are always linearly and dynamically unstable, and they cannot be excited if the three-body interaction is absent. Both stable and unstable kinks, depending on the physical parameters, can be excited in the BEC system.