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arXiv:2208.09972 · Physical Review A

Soliton collisions in Bose-Einstein condensates with current-dependent interactions

Qian Jia, Haibo Qiu, Antonio Muñoz Mateo

Published Dec 19, 2022• 9 citations
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Abstract

We study general collisions between chiral solitons in Bose-Einstein condensates subject to combined attractive and current-dependent interatomic interactions. A simple analysis based on the linear superposition of the solitons allows us to determine the relevant time and space scales of the dynamics, which is illustrated by extensive numerical simulations. By varying the differential amplitude, the relative phase, the average velocity, and the relative velocity of the solitons, we characterize the different dynamical regimes that give rise to oscillatory and interference phenomena. Apart from the known inelastic character of the collisions, we show that the chiral dynamics involves an amplitude reduction with respect to the case of regular solitons. To compare these results with feasible ultracold-gas experiments, the influence of harmonic confinement is analyzed in both the emergence and the interaction of chiral solitons.

DOI
10.1103/physreva.106.063314

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We study general collisions between chiral solitons in Bose-Einstein condensates subject to combined attractive and current-dependent interatomic interactions. A simple analysis based on the linear superposition of the solitons allows us to determine the relevant time and space scales of the dynamics, which is illustrated by extensive numerical simulations. By varying the differential amplitude, the relative phase, the average velocity, and the relative velocity of the solitons, we characterize the different dynamical regimes that give rise to oscillatory and interference phenomena. Apart from the known inelastic character of the collisions, we show that the chiral dynamics involves an amplitude reduction with respect to the case of regular solitons. To compare these results with feasible ultracold-gas experiments, the influence of harmonic confinement is analyzed in both the emergence and the interaction of chiral solitons.
Abstract The collision between two chiral solitons in a Bose-Einstein Condensate (BEC) under density-dependent gauge potential is studied. By means of Poincaré-Lighthill-Kuo (PLK) perturbation method, the different kinds of colliding chiral soliton pairs self-consistently excited upon the background of the system are obtained analytically. The coupling of the current nonlinearity induced by the gauge potential and mean-field atomic interaction results in rich collision dynamics of chiral soliton pairs. When the atomic interaction is repulsive, head-on collisions of dark-dark and dark-bright solitons are observed. However, when the atomic interaction is attractive, unidirectional chiral dark soliton pairs are excited, and overtaking collision between two chiral dark solitons takes place. The phase shifts following the collision of soliton pairs are derived analytically and confirmed numerically. Interestingly, due to the contribution of the density-dependent gauge potential, the phase shifts of the two interacting chiral solitons are different from each other. This is distinct from the case without the density-dependent gauge potential, where the phase shifts of the two colliding ordinary solitons are the same. Thus, phase shifts of interacting chiral soliton pairs can be used to identify the chiral properties of solitons in BEC under density-dependent gauge potential. Furthermore, both elastic and inelastic collisions of chiral solitons in the system are presented numerically. The phase diagram for occurrence of elastic and inelastic collisions of chiral soliton is obtained, which strongly depends on the strength of density-dependent gauge potential.
We investigate two vector-soliton–like matter waves collisions in two-component Bose-Einstein condensates with attractive interactions and Gaussian barrier. We present a detailed numerical analysis of the roles of atomic interactions, barrier, relative velocity, and relative phase in collisional dynamics. We show that the interspecies interactions are crucial to make the wave packet propagate as a “breather”. We find that the collision-induced trajectory shifts of waves are mainly determined by the intraspecies interactions and proportional to them in the weak nonlinearity regime. Moreover, we explore the meeting time of colliding waves and find it depends on the competition between barrier potential and atomic interactions. Particularly, we study the collisions of two waves with a slight velocity asymmetry (or with different relative phases) and the waves merging and split are demonstrated. The underlying inelastic mechanism closely related to energy exchange is briefly discussed as well.
During the last decade the physics of ultracold quantum gases has matured into a highly active and versatile field of research. Experiments dedicated to the physics of Bose-Einstein condensates have been performed and diverse phenomena, which are distinguished by fundamentally different regimes of interaction, can be investigated. Particularly solitons, characterized as non-spreading wavepackets, are stabilized against dispersion by a suitable non-linear interaction and can propagate in a condensate[1,2]. In the present work the dynamical evolution of long-lived dark solitons has been studied as a paradigm of non-linear physics for the first time. We have been able to observe oscillations of dark solitons in elongated Bose-Einstein condensates and good agreement with the theoretically predicted oscillation frequency of ω/√2 has been obtained [1]. Moreover the results of detailed studies of the collision of two dark solitons distinguished by different depths are presented. This particular feature enables the identification of the individual solitons beyond the actual collision process and as a central result we show shown that these peculiar entities interpenetrate without significantly influencing each other [3]. The theoretical description of solitons as weakly interacting quasi particles is in good agreement with these findings. Continuative studies on vectorial “dark-bright” solitons and their dynamical properties complement the investigations on dark solitons.
Bright solitary-waves may be created in dilute Bose-Einstein condensates of at tractively interacting atoms in one dimensional regimes. In integrable systems, such solitary waves are particle-like objects called solitons. We investigate the consequences of non-integrability on the solitary waves in trapped Bose-Einstein condensates caused by an axial harmonic trap, and non-integrability caused by three dimensional effects. To analyse the soliton-like nature of the solitary-waves in an axial harmonic trap, a particle analogy for the solitary-waves is formulated. Exact Soliton solutions exist in the absence of an external trapping potential, which behave in a particle-like manner, and we find the particle analogy we employ to be a good model also when a harmonic trapping potential is present up to a gradual shift in the trajectories when the harmonic trap period is short compared with the, collision time of the solitons. We find that the collision time of the solions is dependent on the relative phase of the solitons as they collide. In the case of two solitons, the particle model is integrable, and the dynamics are completely regular. In the case of a system of two solitary waves of equal norm, the solitons are shown to retain their phase difference for repeated collisions. The extension to three particles supports both regular and chaotic regimes. The trajectory shift observed for two solitons carrier over to the case of three solitons. This shift aside, the agreement between the particle model and the wave dynamics remains good, even in chaotic regimes. We predict that these chaotic regimes will be an indicator of rapid depletion of the condensate due to quantum transitions of the condensate particles into non-condensate modes. To analyse the residual effects of the three dimensional nature of the solitary waves, we use a nonlinear Schrödinger equation with an additional quintic term. We perform variational calculations, and confirm the collapse of a soliton when the number of particles contained therein is increased past a critical number. We investigate the effects of varying the axial trap frequency and scattering length on the critical number. We propose a method to model particle exchange between solitons by extending the variational treatment to two solitons.
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Abstract: In this thesis we experimentally observe the dynamics of dark solitons in elongated Bose-Einstein condensates (BEC) in the crossover regime between 1D and 3D. Dark solitons are dynamically stable in this regime. This allows the observation of the collisional and oscillational dynamics of two dark solitons in a harmonically confined BEC over several oscillation periods. We can detect the repulsive intersolitonic interaction as an increase of the oscillation frequency of the two solitons strongly depending on their mean distance. Thereby we give the first experimental evidence of the theoretically predicted repulsive interaction between the solitons. We compare our experimental findings to numerical simulations of the Gross-Pitaevskii equation and effective 1D equations. Additionally we develop a model in which the solitons are approximated by repulsively interacting classical particles. This model is based on a soliton interaction potential suggested by [Kiv1995] and can describe the essentials of the soliton dynamics. We observe well agreement between the soliton oscillation frequencies measured in the experiment, the numerical simulations and the results of the particle model. Besides we verify the theoretical prediction that the oscillation frequency of dark solitons in a harmonically confined BEC should be slower than the trap frequency.