人工磁场下两腿Bose-Hubbard梯中的束缚态及其量子相变动力学

Dynamics of quantum phase transition is an important interdisciplinary problem among quantum physics and condensed matter physics. The study of this problem will not only broaden our understanding of quantum physics, but also will promote the development of quantum technology. Attribute to their robust quantum coherence and hight controllability, ultracold bosons in two-leg ladder with artificial magnetic field are excellent systems for exploring dynamics of quantum phase transition. By applying both analytical and numerical methods, this project will investigate bound state and dynamics in two-leg Bose-Hubbard ladder under an artificial magnetic field. Through concentrating on the problems of bound state, ground-state phase diagram, dynamics of quantum phase transition and many-body quantum dynamics, the project will aim to explore:(i) how to produce bound state in the continuum and to manipulate the localization degree of these bound states in a periodically modulated two-leg Bose-Hubbard ladder by adjusting the modulation parameter; (ii) how to capture universal scalings of quantum phase transitions from the dynamical excitation across the quantum critical points in a two-leg Bose-Hubbard ladder under an artificial magnetic field; (iii) how the long-range dipole-dipole interaction affects ground-state phase diagram, dynamics of quantum phase transition and many-body quantum dynamics in a two-leg Bose-Hubbard ladder under an artificial magnetic field.

量子相变动力学是量子物理和凝聚态物理中一个有待深入研究的关键课题，这方面的研究不仅将增进我们对量子物理的理解，而且将推动现代量子技术的发展。由于具有稳固的量子相干性和高度的可控性，人工磁场下两腿梯子光晶格中的超冷玻色凝聚原子体系为量子相变动力学的研究提供了新的挑战与机遇。解析分析结合数值模拟，本项目将研究人工磁场下两腿Bose-Hubbard梯中超冷玻色原子的束缚态及其动力学。围绕束缚态、基态相图、量子相变动力学和多体量子动力学等关键科学问题，项目将深入探究：（1）周期调制外场下两腿Bose-Hubbard梯中的束缚态及其调控;（2）人工磁场下两腿Bose-Hubbard梯中超冷原子跨越量子相变临界点的普适动力学行为;（3）长程各向异性的偶极相互作用对人工磁场下Bose-Hubbard梯子体系量子相、量子相变动力学以及多体量子动力学的影响。

我们主要研究了外场下梯子光晶格中玻色凝聚原子的束缚态、PT对称性、拓扑特性及其动力学，发展了处理时间周期调制梯子光晶格中玻色凝聚原子体系的理论和数值方法，揭示了体系某些量子动力学所服从的基本规律,探索了调控体系量子态的新手段。代表性的工作有：(1)利用共振调制的梯子光晶格去实现量子连续带中的束缚态；(2) 利用二维倾斜Harper-Hofstadter格子中布洛赫振荡的量子漂移去测量带拓扑。在本项目的支持下，共完成项目SCI论文11篇，其中Phys. Rev. A/B/R论文4篇。