Motivated by the spin self-rephasing recently observed in an atomic clock, we introduce a simple dynamical model to study the competition between dephasing and synchronization. Two spins $S$ are taken to be initially parallel and in the plane perpendicular to an inhomogeneous magnetic field $Δ$ that tends to dephase them. In addition, the spins are coupled by exchange interaction $J$ that tries to keep them locked. The analytical solution of the classical dynamics shows that, there is a phase transition to a synchronized regime for sufficiently large exchange interaction $J>Δ$ compared to the inhomogeneity. The quantum dynamics is solved analytically in four limits -- large/small $J/Δ$ and large/small $S$ -- and numerically in between. In sharp contrast to the classical case, the quantum solution features very rich $S$-dependent multiscale dynamics. For any finite $S$, there is no synchronization but a crossover around $J=Δ$ between two regimes. The synchronization transition is only recovered when $S\to \infty$, approaching the classical solution in a non-trivial way. Quantum effects therefore suppress the synchronization transition.
Quantum synchronization of spin-1 system: Enhanced synchronization due to additive Lindblad operators
The University of Oklahoma（俄克拉荷马大学）；Center for Quantum Research and Technology, The University of Oklahoma（俄克拉荷马大学量子研究与技术中心）；Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma（俄克拉荷马大学霍默·L·多德物理与天文系）；Oak Ridge National Laboratory（橡树岭国家实验室）
Exceptional point induced quantum phase synchronization and entanglement dynamics in mechanically coupled gain-loss oscillators
School of Nanoscience and Technology, IIT Kharagpur（IIT 哈格普尔理工学院纳米科学与技术学院）；Electronics and Electrical Communication Engineering Department, IIT Kharagpur（IIT 哈格普尔理工学院电子与电气通信工程系）；School of Natural and Computing Sciences, University of Aberdeen（阿伯丁大学自然与计算科学学院）
Universal Manipulation of Quantum Synchronization in Spin Oscillator Networks
Renmin University of China（中国人民大学）；Shenzhen Technology University（深圳理工大学）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心）；Quantum Science Center of Guangdong-Hongkong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心）
Auxiliary-state facilitated phase synchronization phenomena in isolated spin systems
The University of Oklahoma（俄克拉荷马大学）；Center for Quantum Research and Technology, The University of Oklahoma（俄克拉荷马大学量子研究与技术中心）；Department of Physics, The Chinese University of Hong Kong（香港中文大学物理系）；Quantum Information Science Section, Computational Sciences and Engineering Division, Oak Ridge National Laboratory（橡树岭国家实验室计算科学与工程处量子信息科学科）
Field-Trial Quantum Key Distribution with Qubit-Based Frame Synchronization
Guangxi University（广西大学）；The 34th Research Institute of China Electronics Technology Group Corporation（中国电子科技集团公司第三十四研究所）；Ji Hua Laboratory（季华实验室）；Guangxi Zhuang Autonomous Region Information Center（广西壮族自治区信息中心）
Mediated Transmission of Quantum Synchronization in Star Networks
Renmin University of China（中国人民大学）；School of Physics, Renmin University of China（中国人民大学物理学院）；Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学量子态构建与操控教育部重点实验室）
Quantum synchronization in atom-cavity coupled systems
Indian Association for the Cultivation of Science（印度科学培养印度协会）；Indian Institute of Technology, Kanpur（坎普尔印度理工学院）；TCG Centres of Research and Education in Science and Technology（TCG科学技术研究与教育中心）
Krylov space perturbation theory for quantum synchronization in closed systems
Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Université Paris-Saclay, CNRS, LPTMS（巴黎萨克雷大学法国国家科学研究中心理论物理与数学实验室）；Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室）
Enhanced Quantum Synchronization via Quantum Machine Learning
Universidad de Santiago de Chile (USACH)（智利圣地亚哥大学）；Center for the Development of Nanoscience and Nanotechnology（纳米科学与纳米技术发展中心）；University of the Basque Country UPV/EHU（巴斯克地区大学）；IKERBASQUE, Basque Foundation for Science（巴斯克科学基金会）；Shanghai University（上海大学）
