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Register a new userSpatiotemporal engineering of matter-wave solitons in Bose-Einstein condensates
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Emmanuel Kengne Professor
Publication date
2020
fields
Physics
and research's language is
English
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Since the realization of Bose-Einstein condensates (BECs) in optical potentials, intensive experimental and theoretical investigations have been carried out for matter-wave solitons, coherent structures, modulational instability (MI), and nonlinear excitation of BEC matter waves, making them objects of fundamental interest in the vast realm of nonlinear physics and soft condensed-matter physics. Ubiquitous models, which are relevant to the description of diverse nonlinear media are provided by the nonlinear Schrodinger (NLS), alias Gross-Pitaevskii (GP) equations. In many settings, nontrivial solitons and coherent structures, which do not exist or are unstable in free space, can be created or stabilized by means of various management techniques, which are represented by NLS and GP equations with spatiotemporal coefficients in front of linear or nonlinear terms. Developing this direction of research in various settings, efficient schemes of the spatiotemporal modulation of coefficients in the NLS/GP equations have been designed to engineer desirable robust nonlinear modes. This direction and related ones are the main topic of the present review. A broad and important theme is the creation and control of 1D solitons in BEC by means of combination of the temporal or spatial modulation of the nonlinearity strength and a time-varying trapping potential. An essential ramification of this topic is analytical and numerical analysis of MI of continuous-wave states, and control of the nonlinear development of MI. In addition to that, the review also includes some topics that do not directly include spatiotemporal modulation but address physically important phenomena which demonstrate similar soliton dynamics. These are soliton motion in binary BEC, three-component solitons in spinor BEC, and dynamics of two-component solitons under the action of spin-orbit coupling.
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We examine the spectral properties of single and multiple matter-wave dark solitons in Bose-Einstein condensates confined in parabolic traps, where the scattering length is periodically modulated. In addition to the large-density limit picture previously established for homogeneous nonlinearities, we explore a perturbative analysis in the vicinity of the linear limit, which provides good agreement with the observed spectral modes. Between these two analytically tractable limits, we use numerical computations to fill in the relevant intermediate regime. We find that the scattering length modulation can cause a variety of features absent for homogeneous nonlinearities. Among them, we note the potential oscillatory instability even of the single dark soliton, the potential absence of instabilities in the immediate vicinity of the linear limit for two dark solitons, and the existence of an exponential instability associated with the in-phase motion of three dark solitons.
We numerically study the breathing dynamics induced by collision between bright solitons in the one-dimensional Bose-Einstein condensates with strong dipole-dipole interaction. This breathing phenomenon is closely related to the after-collision short-lived attraction of solitons induced by the dipolar effect. The initial phase difference of solitons leads to the asymmetric dynamics after collision, which is manifested on their different breathing amplitude, breathing frequency, and atom number. We clarify that the asymmetry of breathing frequency is directly induced by the asymmetric atom number, rather than initial phase difference. Moreover, the collision between breathing solitons can produce new after-two-collision breathing solitons, whose breathing amplitude can be adjusted and reach the maximum (or minimum) when the peak-peak (or dip-dip) collision happens.
Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schroedinger or Gross-Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.
We present a comprehensive analysis of the form and interaction of dipolar bright solitons across the full parameter space afforded by dipolar Bose-Einstein condensates, revealing the rich behaviour introduced by the non-local nonlinearity. Working within an effective one-dimensional description, we map out the existence of the soliton solutions and show three collisional regimes: free collisions, bound state formation and soliton fusion. Finally, we examine the solitons in their full three-dimensional form through a variational approach; along with regimes of instability to collapse and runaway expansion, we identify regimes of stability which are accessible to current experiments.
We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameter and external trap potential through similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schr{o}dinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures, namely rogue waves, dark-and bright soliton-rogue wave, and rogue wave-breather-like wave for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Further we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single, two and three composite rogue waves for three component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials.
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