Dynamical decoupling (DD) technique is one of the most successful methods to suppress decoherence in qubit systems. In this paper, we studied a solvable pure dephasing model and investigated how DD sequences and initial correlations affect this system. We gave the analytical expressions of decoherence functions and compared the decoherence suppression effects of DD pulses in Ohmic, sub-Ohmic and super-Ohmic environments. Our results show that (1) The initial system-environment correlation will cause additional decoherence. In order to control the dynamic process of open quantum system more accurately and effectively, the initial correlation between the system and reservoir must be considered. (2) High frequency DD pulses can significantly reduce the amplitude of the decoherence function even in the presence of initial system-environment correlations.

中文翻译：

---

具有初始系统-环境相关性的动态解耦

动态去耦（DD）技术是抑制量子位系统退相干的最成功的方法之一。在本文中，我们研究了一个可解的纯移相模型，并研究了 DD 序列和初始相关性如何影响该系统。我们给出了退相干函数的解析表达式，并比较了DD脉冲在欧姆、亚欧姆和超欧姆环境中的去相干抑制效果。我们的结果表明（1）初始系统-环境相关性会导致额外的退相干。为了更准确有效地控制开放量子系统的动态过程，必须考虑系统与储层的初始相关性。