Abstract
We study the stability, form and interaction of single and multiple dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates. The solitons are found numerically as stationary solutions in the moving frame of a non-local Gross Pitaevskii equation, and characterized as a function of the key experimental parameters, namely the ratio of the dipolar atomic interactions to the van der Waals interactions, the polarization angle and the condensate width. The solutions and their integrals of motion are strongly affected by the phonon and roton instabilities of the system. Dipolar matter-wave dark solitons propagate without dispersion, and collide elastically away from these instabilities, with the dipolar interactions contributing an additional repulsion or attraction to the soliton-soliton interaction. However, close to the instabilities, the collisions are weakly dissipative.
Highlights
Solitary waves, or solitons, are excitations of nonlinear systems that possess both wavelike and particle-like qualities
This has striking consequences, as observed experimentally in the form of magnetostriction of the condensate [38] and shape-dependent stability [39], anisotropic collapse and explosion [40], and droplet formation analogous to the Rosensweig instability in classical ferrofluids [41,42]. This modulational instability is a direct result of the roton dip the dipolar interactions introduce into the excitation spectrum [43,44]. Another prominent physical system that supports dark solitons with nonlocal interactions are nonlinear optical media, where the interaction of the electric field of light with the material gives rise to a defocussing local nonlinearity [45], and a nonlocal nonlinearity can arise due to thermal conduction
In particular we seek to establish their soliton-like nature. We will approach this by reference to the general definition of a soliton given by Johnson and Drazin [19], which is of three key properties: (i) permanent form, (ii) localized within a region of space, and (iii) emergence from collisions unchanged, barring a phase shift
Summary
Solitons, are excitations of nonlinear systems that possess both wavelike and particle-like qualities. Dipoles introduce long-range anisotropic interactions falling off as 1/r3, in contrast to the usual short-range isotropic interactions, and give rise to an additional nonlocal nonlinearity [37] This has striking consequences, as observed experimentally in the form of magnetostriction of the condensate [38] and shape-dependent stability [39], anisotropic collapse and explosion [40], and droplet formation analogous to the Rosensweig instability in classical ferrofluids [41,42]. This modulational instability is a direct result of the roton dip the dipolar interactions introduce into the excitation spectrum [43,44] Another prominent physical system that supports dark solitons with nonlocal interactions are nonlinear optical media, where the interaction of the electric field of light with the material gives rise to a defocussing local nonlinearity [45], and a nonlocal nonlinearity can arise due to thermal conduction. The body of the paper is supported by a technical appendix explaining the numerical method used to obtain the dark soliton solutions
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