【作者】 杨波；

【导师】 张波；

【作者基本信息】 武汉理工大学 ， 力学， 2022， 博士

【摘要】 里德堡原子系统是一种重要的量子模拟平台。因其高度可控性和可拓展性,使得该平台可以研究传统固体材料中难以研究的强关联系统中的动力学问题,例如,Ising模型中非平衡动力学问题。由于激光线宽和激发态原子的自发辐射等耗散因素的存在,使得此系统本质上是一种驱动-耗散的量子系统,该系统动力学演化遵循林德布拉德(Lindblad)方程。对于N个原子且每个原子有d能级里德堡原子系统,其动力学方程所需变量个数为d~N,相应的理论模拟有极大的挑战,因此需要尽可能地减少变量个数。本文结合绝热近似和投影算符方法首先推导出里德堡三能级原子系统的二阶等效动力学方程,再通过迭代方法和矩阵运算可将该方程递推到四阶,并具有Lindblad方程的形式。应用该方程研究了两个相互作用的三能级里德堡原子,结果表明在长时间的动力学演化中,相较于二阶等效方程,四阶方程能更精确地描述该系统的性质。对于N个里德堡原子系统,其变量个数与原子个数呈指数关系。将其密度算符表示为矩阵乘积态的形式,则所需变量个数只与原子个数的多项式呈正比,从而极大地减少了变量个数。矩阵乘积态方法已广泛用于一维封闭量子系统,而对于二维开放量子系统,其计算十分复杂。本文通过二维晶格到一维链的映射和密度算符的向量化,将矩阵乘积态的时间依赖变分原理方法扩展到二维开放量子系统中,并研究了该系统中空间关联函数的淬火动力学。由于里德堡原子间的排斥相互作用,系统中会建立反铁磁关联。与此同时耗散作用会极大地影响反铁磁关联的建立过程。系统中有两种耗散因素:消除中间态能级所引起的里德堡态等效自发辐射和激光线宽所导致的失相。前者抑制了在长时间的淬火过程中关联函数的增长;后者则会导致反铁磁关联在较短的弛豫时间内达到一个稳定值。本文还研究了晶格中关联函数的传播与格点路径的关系。在方型晶格中,两个格点间最短路径数量越多,失相速率对关联函数的传播影响越大。而在三角形晶格中,两个格点间的最短路径数量远小于次最短路径的数量,在较短时间演化过程中,关联函数的传播由最短路径所主导,而在长时间演化过程中,次最短路径对关联函数的传播有显著的影响。更多还原

【Abstract】 Rydberg atomic system is an important quantum simulation platform.Due to the high controllability and scalability,this platform can be used to investigate the dynamics property of strong correlated systems,which is extremely difficult to study in a conventional solid-state material,for example,the nonequilibrium dynamics in Ising model.Owing to the finite linewidth of laser and spontaneous decay of excited states,Rydberg atomic system is regarded as a driven-dissipative many-body interacting quantum system.The dynamical evolution of density operator of the system fulfills Lindblad equation.For a Rydberg atomic system with d-level and N atoms,the total number of the variables is d~N.The corresponding numerical simulation is extremely challenging,therefore,we need to reduce the number of variables.This thesis firstly combines adiabatic elimination and projection operator method to derive a second-order effective two-level dynamical equation for a three-level Rydberg atomic system.Through iteration and matrix operations,this equation is then generalized to a fourth-order effective form.And both equations conserve the form of a Lindblad equation.This effective equation is applied to two interacting three-level Rydberg atoms.Compared to the second-order effective equation,the results show that the fourth-order equation can better describe the property of the system in the long-time dynamical evolution.For a N-body Rydberg atomic system,the total number of variables is proportional to the exponential of the number of atoms.If the density operator is expressed as matrix product states(MPS),then the number of variables is only proportional to the polynomials of the number of atoms.Conventionally,MPS is only applied to one-dimensional closed quantum systems.And the application to two-dimensional open quantum system is extremely complex.But the application of MPS can be expanded to two-dimensional open quantum systems by the mapping of a two-dimensional lattice to a one-dimensional chain and the vectorization of density operator.Based on this method,we study the quench dynamics of spatial correlation in a two-dimensional driven-dissipative Rydberg system using time-dependent variational principle based on the generalized MPS.Due to the repulsive interaction between Rydberg atoms,antiferromagnetic correlation can be built in the square lattice system.Meanwhile,decoherence in the system can also significantly affect the dynamical evolution of correlations.In the system,there are two dissipative factors:the effective spontaneous decay of Rydberg state induced by the intermediate state and dephasing caused by the laser linewidth.The former suppresses significantly the growth of correlation in the long-time quench process and the results are consistent with experimental results.The latter leads to a short relaxation time for the antiferromagnetic correlation to reach a stable value.This thesis also studies the relation between the propagation of correlations and the path between lattices.In the square lattice,the larger the number of shortest path between lattices is,the more significant the effect of dephasing on the propagation of correlations is.In the triangular lattice,the number of nearest paths is much smaller than the next-nearest paths.Consequently,the propagation of correlation is determined by the nearest paths in the short time evolution.And the next-nearest paths are dominant in the long-time of correlation propagation.更多还原