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International Conference on Transparent Optical Networks

Dynamics of matter solitons in weakly modulated optical lattices

Vladimír Kuzmiak, Valeriy A. Brazhnyi, V. V. Konotop

Published Jan 20, 2005• 1 citation
Publisher

Abstract

It was shown that matter solitons can be effectively managed by smooth variation of parameters of optical lattices in which the atomic condensate is embedded. The phenomenon is based on the effect of the lattice modulation of the carrier wave that transports the soliton and thus can be well described in terms of the effective mass approach, where a specific form of the band structure is of primary importance. We considered linear and parabolic modulation to demonstrate the possibilities of management of matter solitons.

DOI
10.1109/icton.2004.1360268

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It was shown that matter solitons can be effectively managed by smooth variation of parameters of optical lattices in which the atomic condensate is embedded. The phenomenon is based on the effect of the lattice modulation of the carrier wave that transports the soliton and thus can be well described in terms of the effective mass approach, where a specific form of the band structure is of primary importance. We considered linear and parabolic modulation to demonstrate the possibilities of management of matter solitons.
It is shown that matter solitons can be effectively managed by means of smooth variations of parameters of optical lattices in which the condensate is loaded. The phenomenon is based on the effect of lattice modulations on the carrier wave transporting the soliton and that is why it is well understood in terms of the effective mass approach, where a particular spatial configuration of the band structure is of primary importance. Linear, parabolic, and spatially localized modulations are considered as case examples. It is shown that these defects can originate an accelerating and oscillating motion of matter solitons as well as they can simulate soliton interactions with attractive and repulsive defects.
In the present work this situation is studied analytically and numerically. In particular, we show that this is a way of managing the dynamics of matter waves - making them accelerating, oscillating, etc. In a general case, to describe the effect of the modulation, we compute dependence of the gap structure, of the group velocity of the Bloch wave, and of the effective mass of the soliton on spatial variable. The effective mass approach appears to be a useful analytical tool in this case, as well. The main physical interest of this situation consists of the fact that now the defect affects a matter soliton by interacting with its carrier wave and gives origin to various resonant effects
We consider several effects of the matter wave dynamics which can be observed in Bose–Einstein condensates embedded into optical lattices. For low-density condensates, we derive approximate evolution equations, the form of which depends on relation among the main spatial scales of the system. Reduction of the Gross–Pitaevskii equation to a lattice model (the tight-binding approximation) is also presented. Within the framework of the obtained models, we consider modulational instability of the condensate, solitary and periodic matter waves, paying special attention to different limits of the solutions, i.e. to smooth movable gap solitons and to strongly localized discrete modes. We also discuss how the Feshbach resonance, a linear force and lattice defects affect the nonlinear matter waves.
We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.
We report some investigations on the existence of matter-wave solitons when considering cross-combined optical lattices (OL) in three dimensions (3D), where we have a nonlinear OL in one of the directions, which is perpendicular to a two-dimensional (2D) plane with linear OLs in either one or both directions. This study can be useful to manage 3D solitons through spatial modulations of the scattering length in one of the OL directions. Another independent study is reported, by considering bright solitons manifested in a bosonic condensate gas carrying collinear dipole moments, which induces an external polarizing field with strength periodically modulated along one of the coordinates. This leads to an effective nonlocal nonlinear lattice, with solitonic solutions. Their dynamics and mobility can be investigated by an effective one-dimensional (1D) model. Interactions between solitons are also reported within this 1D model. In all the cases, we consider full numerical and variational approaches.
Abstract We consider matter–wave solitons in spin–orbit coupled Bose–Einstein condensates embedded in an optical lattice and study the dynamics of the soliton within the framework of Gross–Pitaevskii equations. We express spin components of the soliton pair in terms of nonlinear Bloch equations and investigate the effective spin dynamics. It is seen that the effective magnetic field that appears in the Bloch equation is affected by optical lattices, and thus the optical lattice influences the precessional frequency of the spin components. We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in the presence of the optical lattice. It is shown that the spin density is periodically varying due to flipping of spinors between the two states. The amplitude of spin-flipping oscillation increases with lattice strength. We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters. We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components. It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.