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Journal of Physics B Atomic Molecular and Optical Physics

Dynamic generation of matter solitons from linear states via time-dependent scattering lengths

P. G. Kevrekidis, V. V. Konotop, Augusto S. Rodrigues, D. J. Frantzeskakis

Published Mar 29, 2005• 34 citations
Publisher

Abstract

In this paper, we examine the possibility of generating bright and dark solitons, as well as multi-pulse solitary waves in Bose–Einstein condensates. Starting from the linear limit of the problem, where such solutions are known explicitly , we use 'dynamic continuation' through the temporal variation of the scattering length, which can be realized in experiments upon using external time-dependent magnetic fields. We examine the stability of the resulting solutions both through direct numerical simulations and through numerical continuation of the relevant steady states and linear stability analysis. Analytical results, illustrating the nature of the bifurcation of the nonlinear solutions, are found to be in good agreement with the numerical findings.

DOI
10.1088/0953-4075/38/8/008

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In this paper, we examine the possibility of generating bright and dark solitons, as well as multi-pulse solitary waves in Bose–Einstein condensates. Starting from the linear limit of the problem, where such solutions are known explicitly , we use 'dynamic continuation' through the temporal variation of the scattering length, which can be realized in experiments upon using external time-dependent magnetic fields. We examine the stability of the resulting solutions both through direct numerical simulations and through numerical continuation of the relevant steady states and linear stability analysis. Analytical results, illustrating the nature of the bifurcation of the nonlinear solutions, are found to be in good agreement with the numerical findings.
In this paper, we consider a Gross-Pitaevskii (GP) equation with a time-dependent nonlinearity and a spatiotemporal complex linear term which describes the dynamics of matter-wave solitons in Bose-Einstein condensates (BECs) with time-dependent interatomic interactions in a parabolic potential in the presence of feeding or loss of atoms. We establish the integrability conditions under which analytical solutions describing the modulational instability and the propagation of both bright and dark solitary waves on a continuous wave background are obtained. The obtained integrability conditions also appear as the conditions under which the solitary waves of the BECs can be managed by controlling the functional gain or loss parameter. For specific BECs, the dynamics of bright and dark solitons are investigated analytically through the found exact solutions of the GP equation. Our results show that under the integrability conditions, the gain or loss parameter of the GP equation can be used to manage the motion of both bright and dark solitons. We show that for BECs with loss (gain) of atoms, the bright and dark solitons during their propagation have a compression (broadening) in their width. Furthermore, under a safe range of parameters and under the integrability conditions, it is possible to squeeze a bright soliton of BECs with loss of atoms into the assumed peak matter density, which can provide an experimental tool for investigating the range of validity of the 1D GP equation. Our results also reveal that under the conditions of the solitary wave management, neither the injection or the ejection of atoms from the condensate affects the soliton peak during its propagation.
We present an analytical study on the dynamics of bright and dark solitons in Bose–Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross–Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton's parameters (amplitude, width, and period) can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.
We investigate dynamical effects of a bright soliton in Bose–Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross–Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.
We study the dynamics of non-autonomous bright-dark matter-wave solitons in two- and three- component Bose-Einstein condensates. Our setting includes a time-dependent parabolic potential and scattering length, as well as Rabi coupling of the separate hyperfine states. By means of a similarity transformation, we transform the non-autonomous coupled Gross-Pitaevskii equations into the completely integrable Manakov model with defocusing nonlinearity, and construct the explicit form of the non-autonomous soliton solutions. The propagation characteristics for the one-soliton state, and collision scenarios for multiple soliton states are discussed in detail for two types of time-dependent nonlinearities: a kink-like one and a periodically modulated one, with appropriate time-dependence of the trapping potential. We find that in the two-component condensates the nature of soliton propagation is determined predominantly by the nature of the nonlinearity, as well as the temporal modulation of the harmonic potential; switching in this setting is essentially due to Rabi coupling. We also perform direct numerical simulation of the non-autonomous two-component coupled Gross-Pitaevskii equations to corroborate our analytical predictions. More interestingly, in the case of the three-component condensates, we find that the solitons can lead to collision-induced energy switching (energy-sharing collision), that can be profitably used to control Rabi switching or vice-versa. An interesting possibility of reversal of the nature of the constituent soliton, i.e., bright (dark) into dark (bright) due to Rabi coupling is demonstrated in the three-component setting.
Motivated by recent proposals of ``collisionally inhomogeneous'' Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons of a BEC characterized by a periodic, piecewise-constant scattering length. We use a ``stitching'' approach to analytically approximate the pertinent solutions of the underlying nonlinear Schr\"odinger equation by matching the wave function and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that stationary solitons must be centered in one of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations.