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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Dynamics of matter solitons in modulated optical lattices

Valeriy A. Brazhnyi, V. V. Konotop, V. Kuzimiak

Published Jan 25, 2006• 0 citations
Publisher

Abstract

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

DOI
10.1109/cleoe.2005.1568473

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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
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.
The dynamics of matter waves in linear and nonlinear optical lattices subject to a spatially uniform linear force is studied both analytically and numerically. It is shown that by properly designing the spatial dependence of the scattering length it is possible to induce long-living Bloch oscillations of gap-soliton matter waves in optical lattices. This occurs when the effective nonlinearity and the effective mass of the soliton have opposite signs for all values of the crystal momentum in the Brillouin zone. The results apply to all systems modeled by the periodic nonlinear Schrödinger equation, including propagation of light in photonic and photorefractive crystals with tilted band structures.
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.
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.
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.
The physical mechanism underlying scattering properties of matter-wave gap solitons (GSs) by linear-optical-lattice defects is investigated. The occurrence of repeated reflection, transmission, and trapping regions for increasing strengths of an optical-lattice defect are shown to be due to resonances with impurity modes inside the defect potential with chemical potentials and numbers of atoms matching corresponding quantities of the incoming GSs. For small amplitude GSs the number of these resonances coincides with the number of bound states existing in the defect potential for the given defect strength. The dependence of the positions and widths of the transmission resonant peaks on incoming velocities is investigated by means of defect-mode analysis and effective-mass theory. The comparisons with direct integrations of the Gross-Pitaevskii equation provide good agreement confirming the correctness of our approach. Multiple resonant transmissions through arrays of optical lattice defects are also investigated and the possibility of using them for very precise GS dynamical filters is also suggested.