Collaborative Research: From Quantum Droplets & Spinor Solitons to Vortex Knots & Topological States: Beyond the Standard Mean-Field in Atomic BECs

合作研究：来自量子液滴

• 批准号: 2110038
• 负责人: Ricardo Carretero
• 金额: $ 20.18万
• 依托单位: San Diego State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2110038&HistoricalAwards=false
• 关键词: Collaborative; Research; Quantum; Droplets; Spinor

The realm of Bose-Einstein condensates (BECs) was originally proposed as a curious feature of the statistical properties of atomic particles with integer spin by Bose and Einstein in the 1920's. This consisted of the condensation of the excited states particles into the ground state of the system and the formation of a macroscopic, coherent “super-wave” therein, allowing the study and observation of quantum mechanical properties beyond microscopic scales. However, the temperatures needed for its experimental realization were so low that it took about 70 years for E.A. Cornell, W. Ketterle, and C.E. Wieman to realize BECs in the lab. The importance of this feat was recognized only a few years later via the 2001 Nobel Prize in Physics. This has, in turn, enabled a pristine platform where numerous exciting features of nonlinear dynamics of waves and coherent structures can be studied and experimentally observed. Importantly, these coherent structures are also of wide applicability in numerous other areas of physics including, most notably, nonlinear optics, plasma physics, and water waves. Within atomic physics, BECs have also been fundamental toward the study of remarkable quantum features such as superconductivity and superfluidity and, in that capacity, they have been front and center toward the experimental discoveries connected to the vortices and their lattices cited in the 2003 Nobel Prize in Physics and the topological phases and their transitions associated with the 2016 Nobel Prize in Physics. The aim of this project is to advance the state-of-the-art at this exciting nexus of atomic physics theory, physical BEC experiments, applied mathematical analysis, and the forefront of scientific computing, while at the same time training a new generation of scientists and mathematicians at this scientific interface and transcending disciplinary boundaries. In line with the past trajectory of the PIs, an emphasis on the diversity, equity and inclusion of under-represented groups will be sought within this research effort.More concretely, the principal thrust of the present project consists of the study of non-trivial extensions of standard BEC settings. In particular, the main axes of the proposal consider the following themes. (1) Two-component mutually attractive BECs that allow, through quantum corrections and the famous Lee-Huang-Yang (LHY) contribution, for the highly timely formation of so-called quantum droplets. The key realization for such droplets is that their emergence stems from the interplay between repulsive mean-field and attractive beyond-mean-field contributions. (2) Three (F =1) and five (F=2) spin component settings supporting symbiotic (dark-antidark and dark-bright) solitary wave structures with unprecedented integrable or weakly non-integrable properties. (3) 3D vortex knot structures in one and multi-component/spinor settings. Vortex knots constitute one of the most elusive types of vortical structures for which limited experimental and theoretical analysis exists. The PIs will also explore in the spinor settings complex non-trivial topological patterns such as Alice rings and Dirac monopoles. (4) Topologically nontrivial toroidal trapping settings, where the interplay of the intrinsic metric and curvature of the system with the effective nonlinearity can yield unprecedented coherent structures and dynamics thereof. More broadly within this theme, the PIs will study nonlinear waves such as solitons and vortices confined on different types of curved surfaces. This ambitious program should push the boundaries of the state-of-the-art mean-field-theoretic understanding, offering numerous beyond-mean-field insights and elucidating their range of validity as well as the interplay of nonlinearity with quantum, as well as thermodynamic effects.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

玻色-爱因斯坦凝聚体（BEC）最初是由玻色和爱因斯坦在20世纪20年代提出的，作为具有整数自旋的原子粒子的统计特性的一个奇怪特征。这包括将激发态粒子凝聚成系统的基态，并在其中形成宏观的、相干的“超波”，从而允许研究和观察超越微观尺度的量子力学性质。然而，实验实现所需的温度非常低，E.A.花了大约70年的时间。Cornell，W. Ketterle和C.E. Wieman在实验室实现BEC。这一壮举的重要性仅在几年后通过2001年诺贝尔物理学奖得到了认可。这反过来又实现了一个原始平台，可以在其中研究和实验观察波和相干结构的非线性动力学的许多令人兴奋的特征。重要的是，这些相干结构在物理学的许多其他领域也具有广泛的适用性，包括最显着的非线性光学，等离子体物理学和水波。在原子物理学中，BEC也是研究超导性和超流性等显着量子特征的基础，并且在这方面，它们一直是2003年诺贝尔物理学奖中引用的与涡旋及其晶格有关的实验发现的前沿和中心，以及与2016年诺贝尔物理学奖相关的拓扑相及其转变。该项目的目的是推进原子物理理论，物理BEC实验，应用数学分析和科学计算前沿这一令人兴奋的联系的最新技术，同时培养新一代科学家和数学家在这个科学界面和超越学科界限。根据以往的研究轨迹，本研究将着重关注代表性不足群体的多样性、公平性和包容性。更具体地说，本项目的主要重点是研究标准BEC设置的非平凡扩展。特别是，该提案的主要重点考虑了以下主题。(1)双组分相互吸引的BEC，通过量子校正和著名的李-黄-杨（LHY）贡献，允许高度及时地形成所谓的量子液滴。这种液滴的关键实现是，它们的出现源于排斥性平均场和吸引性超出平均场贡献之间的相互作用。(2)三个（F =1）和五个（F=2）自旋组件设置支持共生（暗-反暗和暗-亮）孤立波结构与前所未有的可积或弱不可积属性。(3)一个和多个组件/旋量设置中的3D涡流结结构。涡结是一种最难以捉摸的涡结构类型，其实验和理论分析都很有限。PI还将在旋量设置中探索复杂的非平凡拓扑模式，如Alice环和Dirac单极。(4)拓扑非平凡的环形捕获设置，其中系统的内在度量和曲率与有效非线性的相互作用可以产生前所未有的相干结构和动力学。更广泛地说，在这个主题内，PI将研究非线性波，如孤子和涡旋限制在不同类型的曲面上。这个雄心勃勃的计划应该推动最先进的平均场理论的理解的界限，提供了许多超越平均场的见解，并阐明其有效性范围以及非线性与量子的相互作用，以及热力学效应。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

项目成果

Superfluid vortex multipoles and soliton stripes on a torus

• DOI: 10.1103/physreva.105.063325
• 发表时间: 2022-01
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: J. D’Ambroise;R. Carretero-Gonz'alez;P. Schmelcher;P. Kevrekidis

Solitary waves in a quantum droplet-bearing system

• DOI: 10.1103/physreva.107.063308
• 发表时间: 2023-02
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: G. Katsimiga;S. Mistakidis;G. N. Koutsokostas;D. Frantzeskakis;R. Carretero-González;P. Kevrekidis

Dragging a defect in a droplet Bose-Einstein condensate

• DOI: 10.1103/physreva.107.033310
• 发表时间: 2022-09
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: S. Saqlain;T. Mithun;R. Carretero-Gonz'alez;P. Kevrekidis

Interactions and Dynamics of One-Dimensional Droplets, Bubbles and Kinks

一维液滴、气泡和扭结的相互作用和动力学

• DOI: 10.3390/condmat8030067
• 发表时间: 2023
• 期刊: Condensed Matter
• 影响因子: 1.7
• 作者: Katsimiga, Garyfallia C.;Mistakidis, Simeon I.;Malomed, Boris A.;Frantzeskakis, Dimitris J.;Carretero-Gonzalez, Ricardo;Kevrekidis, Panayotis G.
• 通讯作者: Kevrekidis, Panayotis G.

Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation

二维正弦 - 戈登方程中的扭结 - 反扭结条纹相互作用

• DOI: 10.1016/j.cnsns.2021.106123
• 发表时间: 2022
• 期刊: Communications in Nonlinear Science and Numerical Simulation
• 影响因子: 3.9
• 作者: Carretero-González, R.;Cisneros-Ake, L.A.;Decker, R.;Koutsokostas, G.N.;Frantzeskakis, D.J.;Kevrekidis, P.G.;Ratliff, D.J.
• 通讯作者: Ratliff, D.J.