Solitons in Bose–Einstein condensates trapped in a double-well potential

Abstract

We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrödinger/Gross-Pitaevskii equations, describing two Bose-Einstein condensates trapped in an asymmetric double-well potential, in particular, when the scattering lengths in the condensates have arbitrary magnitudes and opposite signs. The solitons are found to exist everywhere where they are permitted by the dispersion law. Using the Vakhitov-Kolokolov criterion and numerical methods, we show that, except for small regions in the parameter space, the solitons are stable to small perturbations. Some of them feature self-trapping of almost all the atoms in the condensate with no atomic interaction or weak repulsion coupled to the self-attractive condensate. An unusual bifurcation is found, when the soliton bifurcates from the zero solution without a visible jump in the shape, but with a jump in the number of trapped atoms. By means of numerical simulations, it is found that, depending on values of the parameters and the initial perturbation, unstable solitons either give rise to breathers or completely break down into incoherent waves ("radiation"). A version of the model with the self-attraction in both components, which applies to the description of dual-core fibers in nonlinear optics, is considered too, and new results are obtained for this much studied system.

A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity

“…One numerical technique that can be used in this case is the Newton's method or any of its modifications (see e.g. [5]). While this method is known to be very fast and also to be able to converge to both fundamental and excited-state solitary waves, it also has drawbacks.…”

Energy barrier for collapse in a pair of tunnel-coupled condensates with scattering lengths of opposite signs

“…To apply the VK criterion for stability of the stationary points in the 2D case (as compared to the 1D case [20]) one has to rely on numerics to establish the number of negative eigenvalues of the operator Λ 1 . The following simple strategy was used.…”

“…Here we focus on the analysis of the ground state in the system and its energy, whereas the detailed derivation of the coupled-mode system and some of the auxiliary analytical results can be found in our previous publications Refs. [18,19,20].…”

Stable circulation modes in a dual-core matter-wave soliton laser

“…[5]), with weakly repulsive and attractive interactions between atoms in the reservoir and cavity, respectively (the sign and size of the respective scattering lengths can be controlled by external magnetic field through the Feshbach-resonance effect [7]; note that static soliton states in dual-core traps, with opposite signs of the scattering lengths in them, were studied in Ref. [8]). In the model, both edges of the reservoir, and the left edge of the cavity are impenetrable, while an outlet (valve) at the right edge of the cavity releases pulses into an outcoupling MW guide.…”