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Condensed Matter

Nonlinear Excitations in Ultracold Atoms Trapped in Triple Optical Lattices

Pradosh Basu, Barun Halder, Sriganapathy Raghav, Utpal Roy

Published Sep 9, 2022• 3 citations
Publisher

Abstract

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.

DOI
10.3390/condmat7030052

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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.
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.
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.
Bose–Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years—particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes—gap solitons and soliton clusters—are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.
The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.
Compacton matter waves are considered in Bose-Einstein condensates (BEC) and in binary BEC mixtures, trapped in deep optical lattices in the presence of strong and rapid periodic time modulations of the atomic scattering length, are considered.For this, we derive vector averaged discrete nonlinear Schrödinger equations (DNLSE) and show that compacton solutions of different types can exist as stable excitations.Stability properties are studied by linear analysis and by direct numerical integrations of the DNLSE system.
The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in nonmetallic solids and develop "experimental" techniques for studying nonlinear problems, continues to yield a wealth of results in the theory and applications of nonlinear Hamiltonian systems with many degrees of freedom. Inspired by the studies of this seminal model, solitary-wave dynamics in lattice dynamical systems have proven vitally important in a diverse range of physical problems-including energy relaxation in solids, denaturation of the DNA double strand, self-trapping of light in arrays of optical waveguides, and Bose-Einstein condensates (BECs) in optical lattices. BECs, in particular, due to their widely ranging and easily manipulated dynamical apparatuses-with one to three spatial dimensions, positive-to-negative tuning of the nonlinearity, one to multiple components, and numerous experimentally accessible external trapping potentials-provide one of the most fertile grounds for the analysis of solitary waves and their interactions. In this paper, we review recent research on BECs in the presence of deep periodic potentials, which can be reduced to nonlinear chains in appropriate circumstances. These reductions, in turn, exhibit many of the remarkable nonlinear structures (including solitons, intrinsic localized modes, and vortices) that lie at the heart of the nonlinear science research seeded by the FPU paradigm.