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Laser Physics Letters

Bose–Einstein condensate in a bichromatic optical lattice: an exact analytical model

Ajay Nath, Utpal Roy

Published Oct 13, 2014• 25 citations
Publisher

Abstract

We provide an exact analytical model for the dynamics of a 1D Bose–Einstein condensate loaded in a bichromatic optical lattice. Although a host of exact solutions result from this novel method, we mainly concentrate on the solitonic excitations. The trapping potential and its depth of lattice frustration can be varied by tuning the power and the wavelengths of the two overlaying laser beams. Both attractive and repulsive regimes are thoroughly investigated. In the attractive domain, we obtain bright soliton, which reveals interesting variations with the depth of lattice frustration. Localization of the matter wave density is demonstrated as one of the applications in this regime. In the repulsive domain, dark soliton is obtained when the potential resembles an optical lattice. With appropriate tuning of the potential parameter, the dark soliton becomes modulated with an oscillatory background and gradually transforms to bright solitary trains.

DOI
10.1088/1612-2011/11/11/115501

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Abstract We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose–Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to a 1D OL trap can have both repulsive and attractive contact interactions. Dark-in-bright solitons are the excited states of bright solitons. The solitons, when subjected to a small perturbation, exhibit sustained breathing oscillation. Dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium velocities the collision between two solitons is found to be quasi-elastic. Results are demonstrated by a numerical simulation of the three-dimensional mean-field Gross–Pitaevskii equation in three spatial dimensions employing realistic interaction parameters for a dipolar 164 Dy BEC.
We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bichromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of schemes for quantum simulations and processing quantum information.
As a coherent matter wave,the Bose-Einstein condensate(BEC) provides a playground for the investigation of the macroscopic quantum phenomenon.The nonlinear optical lattice,which is consisted of two counter-propagating laser beams,is a powerful and widely used tool for the controlling of the dynamics of the coherent matter wave.In view of the potential applications of BEC,two or more independently grown condensates provide extra controllable degrees of freedom and can be used in many areas,such as quantum metrology and quantum computation.In this paper,a multi-mode description is introduced to characterize the multi-component coherent matter wave.To determine the evolution property of the multi-mode matter wave in a nonlinear optical lattice,we solve the multi-mode coupled nonlinear equations.A set of analytical bright soliton solutions are constructed with a similarity transformation.
By developing a multiple-scale method, we study analytically the dynamics of the soliton inside the semi-infinite band gap (SIBG) of quasi-one-dimensional Bose–Einstein condensates trapped in an optical lattice. In the linear case, a stable condition of soliton formation is obtained. For a weak nonlinearity, whether there occurs a spatially propagating or localized gap soliton is determined by the lattice depth. Meanwhile, we predict the existence of the dark (bright) gap solitons for the repulsive (attractive) interactions in the SIBG, different from that of the gap solitons in other energy gaps. And the collision of two dark (or bright) solitons is nearly elastic under a safe range of atomic numbers. An experimental protocol is further designed for observing these phenomena.
In the present contribution, we explore a host of different stationary states, namely dark-bright solitons and their lattices, that arise in the context of multicomponent atomic Bose-Einstein condensates. The latter are modeled by systems of coupled Gross-Pitaevskii equations with general interaction (nonlinearity) coefficients gij{g}_{ij}gij​. It is found that in some particular parameter ranges such solutions can be obtained in analytical form, however, numerically they are computed as existing in a far wider parametric range. Many features of the solutions under study, such as their analytical form without the trap or the stability and dynamical properties of one dark-bright soliton even in the presence of the trap are obtained analytically and corroborated numerically. Additional features, such as the stability of soliton lattice homogeneous states or their existence and stability in the presence of the trap, are examined numerically.
Various solitary wave excitations are found for a Bose-Einstein condensate in presence of two hybrid potentials in the form of triple mixtures of optical lattices. One of these potentials comprises of a combination of two important lattice profiles, such as frustrated optical lattice and double-well super-lattice, within one. Another represents a composite lattice combination, resulting in a wider and deeper frustrated optical lattice. The dynamical equation for such a system is solved by the exact analytical method to obtain a bright solitary wave, periodic wave and cnoidal wave excitations. We also report Anderson localization, bifurcation of condensate at the center and a competition between two different types of localizations upon trap engineering. Dynamical and structural stability analyses are also carried out, which reveal the obtained solutions as extremely stable for structural noise incorporation and sufficiently stable for dynamical stability. These triple mixtures of optical lattices impart better tunability on the condensate profile, which has made this system a true quantum simulator.