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arXiv:1307.4314 · Physical Review A

Dynamical generation of interwoven soliton trains by nonlinear emission in binary Bose-Einstein condensates

Valeriy A. Brazhnyi, David Novoa, Chandroth P. Jisha

Published Jul 23, 2013• 4 citations
arXivHTMLPDF

Abstract

We propose a method for the generation of trains of alternating bright solitons in two-component Bose-Einstein condensates, using controlled emission of nonlinear matter waves in the uncoupled regime with spatially varying intraspecies interaction and out-of-phase oscillations of the ground states in the trap. Under this scheme, solitons are sequentially launched from the different components and interact with each other through phase-independent cross coupling. We obtain an analytical estimation of the critical condition for soliton emission using a geometric guiding model, in analogy with integrated optical systems. In addition, we show how strong initial perturbations in the system can trigger the spontaneous generation of supersolitons, i.e., localized phononlike excitations of the soliton trains. Finally, we demonstrate the controllable generation of slow and fast supersolitons by adding external localized potentials in the nonlinear region.

DOI
10.1103/physreva.88.013629

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We propose a method for the generation of trains of alternating bright solitons in two-component Bose-Einstein condensates, using controlled emission of nonlinear matter waves in the uncoupled regime with spatially varying intraspecies interaction and out-of-phase oscillations of the ground states in the trap. Under this scheme, solitons are sequentially launched from the different components and interact with each other through phase-independent cross coupling. We obtain an analytical estimation of the critical condition for soliton emission using a geometric guiding model, in analogy with integrated optical systems. In addition, we show how strong initial perturbations in the system can trigger the spontaneous generation of supersolitons, i.e., localized phononlike excitations of the soliton trains. Finally, we demonstrate the controllable generation of slow and fast supersolitons by adding external localized potentials in the nonlinear region.
We propose a simple way to generate nonlinear excitations in a controllable way by managing interactions in Bose-Einstein condensates. Under the action of a quantum analog of a classical piston, the condensed atoms are pushed through the trap, generating vortex rings infully three-dimensional condensates or soliton trains in quasi-one-dimensional scenarios. The vortex rings form due to transverse instability of the shock-wave train, enhanced and supported by the energy transfer between waves. We elucidate in what sense the self-interactions within the atom cloud define the properties of the generated vortex rings and soliton trains. Based on the quantum-piston scheme we study the behavior of two-component Bose-Einstein condensates and analyze how the presence of an additional superfluid influences the generation of vortex rings or solitons in the other component, and vice versa. Finally, we show the dynamical emergence of skyrmions within two-component systems in the immiscible regime.
We investigate the combined soliton solutions of two-component Bose–Einstein condensates with external potential. The "phase diagram" is obtained for the formation regions of different combined solitons. Our results show that the intraspecies (interspecies) interaction strengths and the external trapped potential clearly affect the formation of dark-dark, bright-bright, and dark–bright soliton solutions in different regions. Especially, we find that the bright–bright (dark–dark) soliton can exist in the case of both repulsive (attractive) intraspecies interaction strengths in the presence of external potential. This novel phenomenon is completely different from the formation of soliton solution of one-component Bose–Einstein condensates without external potential, and it will be useful for the study of two-component Bose–Einstein condensates.
Solitons are localized wave packets whose dispersion is compensated by a nonlinearity. Solitons are observed in many wave settings including optics, fluids, plasmas, and matter-waves. Bright matter-wave solitons were first created by quenching the interactions in a quasi-one dimensional atomic Bose-Einstein condensate (BEC) from repulsive to attractive. Under some conditions a train of up to 10 solitons was formed. Neighboring solitons were observed to repel one another, an effect that was attributed to an alternating π-0-π phase distribution. There has been a theoretical debate whether this phase structure is inherent to the formation of the train, or if it evolves through a series of mergers and annihilations between neighboring solitons that are in-phase, and hence attractive. This paper shows that the interaction quench initiates a modulation instability (MI) in which weak perturbations undergo a nonlinear amplification, resulting in their exponential growth. Results show that the number of solitons is consistent with the initial size of the condensate divided by 2πξ. Furthermore, once formed, there are few solitons lost to merger or annihilation collisions. From this, we conclude that the soliton train is created with an alternating phase structure, rather than evolving into one.
We present a systematic study of the generation of the array of optical or matter-wave kinks (dark solitons) in the ground state (GS) of binary systems. We consider quasi-one-dimensional systems described by a pair of nonlinear Schr\"odinger (NLSE's) or Gross-Pitaevskii equations (GPE's), which are coupled by the linear mixing, with local strength $\ensuremath{\Omega}$, and by nonlinear interactions. We assume the self-repulsive nonlinearity in both components, and include the effects of a harmonic trapping potential, while the nonlinear interaction between the components may be both repulsive and attractive. The model may be realized in terms of periodically modulated slab waveguides in nonlinear optics and also in Bose-Einstein condensates. Depending on the sign and strengths of the linear and nonlinear couplings between the components, the ground states in such binary systems may be symmetric, antisymmetric, or asymmetric. In this work, we introduce a periodic spatial modulation of the linear coupling, making $\ensuremath{\Omega}$ an odd or even function of the coordinate (xxx). The sign flips of $\ensuremath{\Omega}(x)$ strongly modify the structure of the GS in the binary system, as the relative sign of its components tends to lock to the local sign of $\ensuremath{\Omega}$. Using a systematic numerical analysis and an analytic approximation, we demonstrate that the GS of the trapped system contains one or several kinks (dark solitons) in one component, while the other component does not change its sign. The final results are presented in the form of maps showing the number of kinks in the GS as a function of the system's parameters, with the odd (even) modulation function giving rise to the odd (even) number of the kinks. The modulation of $\ensuremath{\Omega}(x)$ also produces a strong effect on the transition between states with nearly equal and strongly unequal amplitudes of the two components.
We report on the controlled creation of multiple soliton complexes of the dark-bright type in one-dimensional two-component, three-component, and spinor Bose-Einstein condensates. The formation of solitonic entities of the dark-bright type is based on the so-called matter-wave interference of spatially separated condensates. In all three cases, a systematic numerical study is carried out upon considering different variations of each system's parameters both in the absence and in the presence of a harmonic trap. It is found that manipulating the initial separation or the chemical potential of the participating components allows us to tailor the number of nucleated dark-bright states. Particularly, the number of solitons generated increases upon increasing either the initial separation or the chemical potential of the participating components. Similarities and differences of the distinct models considered herein are showcased, while the robustness of the emerging states is illustrated via direct numerical integration, demonstrating their long time propagation. Importantly, for the spinorial system, we unravel the existence of beating dark soliton arrays that are formed due to the spin-mixing dynamics. These states persist in the presence of a parabolic trap, often relevant for associated experimental realizations.
The controlled creation of dark-bright (DB) soliton trains in multicomponent Bose-Einstein condensates (BECs) is a topic of ongoing interest. In this work we generalize earlier findings on the creation of dark soliton trains in single-component BECs [A. Romero-Ros et al., Phys. Rev. A 103, 023329 (2021)] to two-component BECs. By choosing suitable filled box-type initial configurations (FBTCs) and solving the direct scattering problem for the defocusing vector nonlinear Schr\"odinger equation with nonzero boundary conditions we obtain analytical expressions for the DB soliton solutions produced by a general FBTC. It is found that the size of the initial box and the amount of filling directly affect the number, size, and velocity of the solitons, while the initial phase determines the parity (even or odd) of the solutions. Our analytical results are compared to direct numerical integration of the coupled Gross-Pitaevskii equations, both in the absence and in the presence of a harmonic trap, and an excellent agreement between the two is demonstrated.