给定环境下稳定开放量子系统的哈密顿量方法

摘要

For open quantum systems described by the Lindblad master equation under given dissipations, this paper achieves the stabilization of the target equilibrium state by designing the system Hamiltonians. Via the coherence vector framework, the original matrix system model is transformed into a vector linear system and their stability equivalence is proved. By guaranteeing the stability of the vectorized linear model and letting its unique equilibrium state equal the desired target state, a frame for the design of the system Hamiltonian is obtained. In particular, this paper discusses the value range of the elements of the system Hamiltonian under these two conditions and points out that the system Hamiltonian can be obtained from their intersection set. Numerical simulation experiments on a two level system verify the effectiveness of the proposed Hamiltonian stabilization scheme.%针对耗散已知情况下Lindblad主方程描述的开放量子系统,本文通过哈密顿量的设计实现了系统对于目标平衡态的稳定化.借助相干矢量体系,将矩阵形式下的原始系统模型转换为了一个矢量形式的线性系统,并证明了变换前后系统稳定属性的等价性.通过保证矢量化线性系统模型的稳定性,并使系统的唯一平衡态等于期望的目标态,得到了系统哈密顿量的设计框架.特别地,本文讨论了这两类条件下系统哈密顿量各元素的范围,并指出根据它们的交集即可构成所设计的系统哈密顿量.最后,在一个两能级系统上进行了数值仿真实验,验证了本文哈密顿量稳定化方案的有效性.