Gap-type dark localized modes in a Bose-Einstein condensate with optical lattices

Abstract

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.

10 pages, 6 figures

References in corpus (11)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Experimental observation of oscillating and interacting matter wave dark solitons
• Collisions of matter-wave solitons
• A purely Kerr nonlinear model admitting flat-top solitons
• Bright solitons in ultracold atoms
• Resonant scattering of matter wave gap-solitons by optical lattice defects
• Suppression of the critical collapse for one-dimensional solitons by saturable quintic nonlinear lattices
• Matter-wave dark solitons in box-like traps
• Asymmetric localized states in periodic potentials with a domain wall-like Kerr nonlinearity

Cited by in corpus (16)

• One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential
• Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension
• Quadratic fractional solitons
• Stable and oscillating solitons of $\mathcal{P}\mathcal{T}$-symmetric couplers with gain and loss in fractional dimension
• Localized modes and dark solitons sustained by nonlinear defects
• Electromagnetically induced moiré optical lattices in a coherent atomic gas
• Hinge solitons in three-dimensional second-order topological insulators
• Phase engineering of chirped rogue waves in Bose-Einstein condensates with a variable scattering length in an expulsive potential
• Bubbles and W-shaped solitons in Kerr media with fractional diffraction
• Flat-floor bubbles, dark solitons, and vortices stabilized by inhomogeneous nonlinear media
• Localized modes in nonlinear fractional systems with deep lattices
• Arbitrary synthetic dimensions via multi-boson dynamics on a one-dimensional lattice
• Supersolid Gap Soliton in a Bose-Einstein Condensate and Optical Ring Cavity coupling system
• Light gap bullets in defocusing media with optical lattices
• One-dimensional purely Lee-Huang-Yang fluids dominated by quantum fluctuations in two-component Bose-Einstein condensates
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging