• Advanced Photonics
  • Vol. 1, Issue 4, 046004 (2019)
Liangwei Zeng1、2 and Jianhua Zeng1、2、*
Author Affiliations
  • 1Chinese Academy of Sciences, Xi’an Institute of Optics and Precision Mechanics, State Key Laboratory of Transient Optics and Photonics, Xi’an, China
  • 2University of Chinese Academy of Sciences, Beijing, China
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    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.

    1 Introduction

    Bose–Einstein condensate (BEC) consists of interacting and ideal dilute Bose gases cooled down to a very low temperature (i.e., around absolute zero) and is one of the most famous examples of the macroscopic quantum phenomena that have attracted increasing interest in past decades. Because of being equipped with intrinsic nonlinear effect arising from atom–atom collisions, the BEC (and more broadly, ultracold atoms) is an innately nonlinear medium in which there are many emergent nonlinear phenomena, such as matter–wave four-wave mixing, bright and dark solitons, vortices and vortex lattices, and dynamic instabilities.1 In addition to basic research interests, BEC also provides useful applications in cold atom interferometry, atom lasers, and optical atomic clocks, with unprecedented precision and stability, and, more excitingly, quantum information processing.17 Recently, the study of BEC has maintained a good momentum of development and expansion, attracting increasing attention in various fields, which has manifested its emergence in solid-state matter and its BEC-like phenomenon caused by elementary excitations in solids (bosonic quasiparticles) in conditions of thermodynamic equilibrium;8,9 the latter can also occur under nonequilibrium conditions, and thus has been dubbed nonequilibrium Bose–Einstein-like condensation.8,9

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    Liangwei Zeng, Jianhua Zeng. Gap-type dark localized modes in a Bose–Einstein condensate with optical lattices[J]. Advanced Photonics, 2019, 1(4): 046004
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    Category: Research Articles
    Received: Mar. 21, 2019
    Accepted: May. 20, 2019
    Published Online: Aug. 28, 2019
    The Author Email: Zeng Jianhua (zengjh@opt.ac.cn)