Collisions of matter-wave solitons

Abstract

Solitons are localised wave disturbances that propagate without changing shape, a result of a nonlinear interaction which compensates for wave packet dispersion. Individual solitons may collide, but a defining feature is that they pass through one another and emerge from the collision unaltered in shape, amplitude, or velocity, but with a new trajectory reflecting a discontinuous jump. This remarkable property is mathematically a consequence of the underlying integrability of the one-dimensional (1D) equations, such as the nonlinear Schrödinger equation, that describe solitons in a variety of wave contexts, including matter-waves 1, 2 . Here we explore the nature of soliton collisions using Bose-Einstein condensates of atoms with attractive interactions confined to a quasi-one-dimensional waveguide. We show by real-time imaging that a collision between solitons is a complex event that differs markedly depending on the relative phase between the solitons. By controlling the strength of the nonlinearity we shed new light on these fundamental features of soliton collisional dynamics, and explore the implications of collisions in the proximity of the crossover between one and three dimensions 1 arXiv:1407.5087v2 [cond-mat.quant-gas]

Roles of Interfering Radiation Emitted from Decaying Pulses Obeying Soliton Equations Belonging to the Ablowitz–Kaup–Newell–Segur Systems

“…In fact, Nguyen et al confirmed that their bright BEC soliton did not diffuse and stayed still in an almost flat axial geometry. 29) The experimental realization of a BEC bright soliton means that, from Eq. (27), the key parameter A = LV 0 satisfies π/2 < A < 3π/2.…”

“…According to Ref. 29, we can calculate the value of a r and obtain a r ∼ 6µm. In the observation of the first bright soliton trains of the same 7 Li atoms, their radial trap size was reported to be about 47µm.…”

“…[23][24][25][26][27][28] Recently, collisions between such BEC solitons have been experimentally examined and reported. [29][30][31] Similar experiments are also promising possible in the field of nonlinear optics. [32][33][34][35][36] In real experiments, however, one cannot generate pure solitons that are the exact solutions of the NLSE, and the word "solitons" is often used to mean multiple pulses of condensates or photons.…”

An Approximation Method for the Scattering Data of One-Dimensional Soliton Equations under Arbitrary Rapidly Decreasing Initial Pulses

“…29) In the experiment, a confinement trap in the xdirection was applied and was not completely removed during the collision process. Owing to the existence of this trap, the geometry was not completely flat.…”

“…In sec.4, we show some illustrative applications and present a brief model of a collision experiment with attractively interacting BEC solitons. [29][30][31] We compare the results obtained by the presented method with those from direct numerical integration to check the consistency between them. The final section is devoted to a discussions and concluding remarks.…”