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Controllable nonlocal interactions between dark solitons in dipolar condensates

T Bland, M. E. Edmonds, Nick P. Proukakis, AM Martin, DHJ O'Dell, Nicholas G. Parker

Published Dec 1, 2015• 0 citations
Publisher

Abstract

We study the family of static and moving dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates, exploring their modified form and interactions. The density dip of the soliton acts as a giant antidipole which adds a nonlocal contribution to the conventional local soliton-soliton interaction. We map out the stability diagram as a function of the strength and polarization direction of the atomic dipoles, identifying both roton and phonon instabilities. Away from these instabilities, the solitons collide elastically. Varying the polarization direction relative to the condensate axis enables tuning of this nonlocal interaction between repulsive and attractive; the latter case supports unusual dark-soliton bound states. Remarkably, these bound states are themselves shown to behave like solitons, emerging unscathed from collisions with each other.

DOI
10.25405/ncl.34258164

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We study the family of static and moving dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates, exploring their modified form and interactions. The density dip of the soliton acts as a giant antidipole which adds a nonlocal contribution to the conventional local soliton-soliton interaction. We map out the stability diagram as a function of the strength and polarization direction of the atomic dipoles, identifying both roton and phonon instabilities. Away from these instabilities, the solitons collide elastically. Varying the polarization direction relative to the condensate axis enables tuning of this nonlocal interaction between repulsive and attractive; the latter case supports unusual dark-soliton bound states. Remarkably, these bound states are themselves shown to behave like solitons, emerging unscathed from collisions with each other.
We study the family of static and moving dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates, exploring their modified form and interactions. The density dip of the soliton acts as a giant antidipole which adds a nonlocal contribution to the conventional local soliton-soliton interaction. We map out the stability diagram as a function of the strength and polarization direction of the atomic dipoles, identifying both roton and phonon instabilities. Away from these instabilities, the solitons collide elastically. Varying the polarization direction relative to the condensate axis enables tuning of this nonlocal interaction between repulsive and attractive; the latter case supports unusual dark-soliton bound states. Remarkably, these bound states are themselves shown to behave like solitons, emerging unscathed from collisions with each other.
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 nonlocal 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.
Thanks to their immense purity and controllability, dipolar Bose-Einstein condensates are an exemplar for studying fundamental nonlocal nonlinear physics. Here we show that a family of fundamental nonlinear waves---the dark solitons---are supported in trapped quasi-one-dimensional dipolar condensates and within reach of current experiments. Remarkably, the oscillation frequency of the soliton is strongly dependent on the atomic interactions, in stark contrast to the nondipolar case. Established analytical techniques are shown to not capture the simulated dynamics. These sensitive waves may act as mesoscopic probes of the underlying quantum matter field.
We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free space and in the presence of an optical lattice (OL). Free-space solitons may exist with an arbitrarily weak local attraction if the strength of the DD repulsion is fixed. In the case of the DD attraction, solitons do not exist beyond a maximum value of the local-repulsion strength. In the system which includes the OL, a stability region for subfundamental solitons is found in the second finite band gap. For the existence of gap solitons (GSs) under the attractive DD interaction, the contact repulsion must be strong enough. In the opposite case of the DD repulsion, GSs exist if the contact attraction is not too strong. Collisions between solitons in the free space are studied too. In the case of the local attraction, they merge or pass through each other at small and large velocities, respectively. In the presence of the local repulsion, slowly moving solitons bounce from each other.
Abstract We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose–Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to a 1D OL trap can have both repulsive and attractive contact interactions. Dark-in-bright solitons are the excited states of bright solitons. The solitons, when subjected to a small perturbation, exhibit sustained breathing oscillation. Dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium velocities the collision between two solitons is found to be quasi-elastic. Results are demonstrated by a numerical simulation of the three-dimensional mean-field Gross–Pitaevskii equation in three spatial dimensions employing realistic interaction parameters for a dipolar 164 Dy BEC.
Abstract. A model of the Bose-Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE) with additional terms describing long-range dipoledipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially as concerns their collapseinduced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions. Collapse instability of solitons in the nonpolynomial Schrödinger equation with dipole-dipole interactions2 1