Engineering bright solitons to enhance the stability of two-component Bose–Einstein condensates

Abstract

We consider a system of coupled Gross-Pitaevskii (GP) equations describing a binary quasi-one-dimensional Bose-Einstein condensate (BEC) with intrinsic timedependent attractive interactions, placed in a time-dependent expulsive parabolic potential, in a special case when the system is integrable (a deformed Manakov's system). Since the nonlinearity in the integrable system which represents binary attractive interactions exponentially decays with time, solitons are also subject to decay. Nevertheless, it is shown that the robustness of bright solitons can be enhanced in this system, making their respective lifetime longer, by matching the time dependence of the interaction strength (adjusted with the help of the Feshbachresonance management) to the time modulation of the strength of the parabolic potential. The analytical results, and their stability, are corroborated by numerical simulations. In particular, we demonstrate that the addition of random noise does not impact the stability of the solitons.

Spatiotemporal engineering of matter-wave solitons in Bose–Einstein condensates

“…It is also seen that the frequency and amplitude of the ac component need to be large enough to maintain the stability. Note that, for frequencies larger than 10 6 π, the width of the condensate a(t) assumes very small values in the course of the evolution (as predicted by VA), suggesting that the collapse may occur in the solution of the full 3D equation (72). The stability is predicted by VA only for Λ < 9, i.e., for the repulsive dc component of the nonlinearity coefficient.…”

“…We start the consideration with the 2D case, presenting, consecutively, results produced by VA, application of the averaging method to the GP equation, and results produced by numerical simulations. In particular, in the case of the high-frequency modulation, it is possible to apply the averaging method to the 2D equation (72), without using VA [6,55,132]. The averaging method may also be applied to the 2D NLS equation with a potential rapidly varying in space, rather than in time, the main result being renormalization of parameters of the equation and a shift of the collapse threshold [140].…”

“…Here, it is assumed that the ac frequency ω is large, and the 2D GP equation (72) is rewritten in the following form,…”

“…A typical example of the formation of a self-confined condensate in simulations of the 2D equation(72). Panel (a) shows the collapsing state in the absence of the ac modulation at t ≈ 0.3.…”

An atomic bright vector soliton as an active particle

“…External force can accelerate the small cloud as a whole, and its motion is well described with a single collective coordinate that can carry both kinetic and potential energy. If the soliton is created in a multicomponent Bose-Einstein condensate [14][15][16][17][18], it can also have internal energy. If for example the bright vector soliton is placed in a constant magnetic field, and is composed of atoms of one atomic species with atoms in spin states |− = |F (1) , m…”