Nonlinearity-induced localization in a periodically driven semidiscrete system

Driben, Rodislav; Malomed, Boris A.; Meier, Torsten; Yulin, A. V.

doi:10.1103/physreve.97.062210

Cited by 5 publications

(3 citation statements)

References 47 publications

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“…The objective of this article is to produce a relatively brief summary of results for multidimensional (chiefly, two-dimensional) discrete and semi-discrete solitons, which were considered in less detail in previous reviews and, on the other hand, draw growing interest in the context of the current work with 2D and 3D solitons in diverse physical contexts [27,28]. Furthermore, the presence of the two or three coordinates makes it also possible to define semi-discrete states as ones that are discrete in one direction and continuous in the perpendicular one [81][82][83][84].…”

Section: The Subject and Structure Of The Present Articlementioning

confidence: 99%

Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings

Malomed

2024

Entropy

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This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross–Pitaevskii (GP) equations with the Lee–Huang–Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole–dipole and quadrupole–quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ(2)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin–orbit-coupled (SOC) binary Bose–Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

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Section: The Subject and Structure Of The Present Articlementioning

confidence: 99%

Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings

Malomed

2024

Entropy

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“…This framework captures a broad range of nonlinear physical settings, including two-mode optical cavities [59][60][61], optical waveguide couplers [37,46] and coupled superconducting microwave cavities [11], but also quantum gases trapped in doublewell potentials [62,63] and two-component Bose-Einstein condensates [64]. In fact, the periodically-driven nonlinear Schrödinger equation (or Gross-Pitaevskii equation [65]) was previously investigated in the context of driven quantum gases [66][67][68][69][70][71], and more recently, in the realm of topological photonics [41,42,[72][73][74]; see also Refs. [46,75,76].…”

Section: Introductionmentioning

confidence: 99%

Floquet engineering of optical nonlinearities: a quantum many-body approach

Goldman¹

2022

Preprint

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Subjecting a physical system to a time-periodic drive can substantially modify its properties and applications. This Floquet-engineering approach has been extensively applied to a wide range of classical and quantum settings in view of designing synthetic systems with exotic properties. Considering a general class of two-mode nonlinear optical devices, we show that effective optical nonlinearities can be created by subjecting the light field to a repeated pulse sequence, which couples the two modes in a fast and time-periodic manner. The strength of these drive-induced optical nonlinearities, which include an emerging four-wave mixing, can be varied by simply adjusting the pulse sequence. This leads to topological changes in the system's phase space, which can be detected through light intensity and phase measurements. Our proposal builds on an effective-Hamiltonian approach, which derives from a parent quantum many-body Hamiltonian describing driven interacting bosons. As a corollary, our results equally apply to Bose-Einstein condensates in driven double-well potentials, where pair tunneling effectively arises from the periodic pulse sequence. Our scheme offers a practical route to engineer and finely tune exotic nonlinearities and interactions in photonics and ultracold quantum gases.

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“…The study and understanding of localization is essential for the coherent transport of BEC in an optical lattice and helps to well control the dynamics of Bose gases in an optical lattice. Since the Anderson localization has been proposed, localized phenomena have been studied in different types of optical lattices [2][3][4][5][6][7][8]. Soliton, breather and self-trapping are remarkable localized phenomena in the lattice system, and they possess some key hallmark, respectively.…”

mentioning

confidence: 99%

Localization of a Bose-Einstein condensate in a two-leg ladder subject to an artificial magnetic field

Zhang¹,

Cai²,

He³

et al. 2019

EPL

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We investigate the localization of a Bose-Einstein condensate trapped in a two-leg ladder in the presence of an artificial magnetic field via Bose-Hubbard model and discuss its abundant localized phenomena using variational approximation and direct numerical simulation. A two-leg bosonic ladder provides an ideal platform to study the complex dynamics of Bose-Einstein condensates in an optical lattice subject to an artificial magnetic field. As a main result, the system displays rich interesting localized states including self-trapping, soliton and breather. The coupling of the repulsive atomic interaction, artificial magnetic field, the rung-to-leg coupling ratio of the ladder, and the initial population difference of atoms between the two legs of the ladder results in the transitions between the localized states. The critical conditions for the transitions between the localized states are given analytically and are intuitively demonstrated in the phase diagram. Particularly, when the rung-to-leg coupling radio of the ladder satisfies a critical condition, we have the localized states with no local atomic currents between the two legs, otherwise, we observe the localized states with local atomic currents between the two legs. Finally, the results obtained via variational method are confirmed by the numerical simulations of the full discrete nonlinear Schrödinger equation describing the system.

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Nonlinearity-induced localization in a periodically driven semidiscrete system

Cited by 5 publications

References 47 publications

Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings

Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings

Floquet engineering of optical nonlinearities: a quantum many-body approach

Localization of a Bose-Einstein condensate in a two-leg ladder subject to an artificial magnetic field

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