Chen Hong-Bin, Chen Yueh-Nan
Department of Engineering Science, National Cheng Kung University, Tainan, 70101, Taiwan.
Center for Quantum Frontiers of Research and Technology, NCKU, Tainan, 70101, Taiwan.
Sci Rep. 2021 May 11;11(1):10046. doi: 10.1038/s41598-021-89400-3.
An important mathematical tool for studying open quantum system theory, which studies the dynamics of a reduced system, is the completely positive and trace-preserving dynamical linear map parameterized by a special parameter-time. Counter-intuitively, akin to the Fourier transform of a signal in time-sequence to its frequency distribution, the time evolution of a reduced system can also be studied in the frequency domain. A recent proposed idea which studies the representation of dynamical processes in the frequency domain, referred to as canonical Hamiltonian ensemble representation (CHER), proved its capability of characterizing the noncalssical traits of the dynamics. Here we elaborate in detail the theoretical foundation within a unified framework and demonstrate several examples for further studies of its properties. In particular, we find that the thermal fluctuations are clearly manifested in the manner of broadening CHER, and consequently rendering the CHER less nonclassical. We also point out the discrepancy between the notions of nonclassicality and non-Markovianity, show multiple CHERs beyond pure dephasing, and, finally, to support the practical viability, propose an experimental realization based upon the free induction decay measurement of nitrogen-vacancy center in diamond.
研究开放量子系统理论（该理论研究约化系统的动力学）的一个重要数学工具是由特殊参数时间参数化的完全正定且迹保持的动力学线性映射。与直觉相反，类似于将时间序列中的信号进行傅里叶变换以得到其频率分布，约化系统的时间演化也可以在频域中进行研究。最近提出的一种在频域中研究动力学过程表示的想法，称为正则哈密顿系综表示（CHER），证明了其表征动力学非经典特性的能力。在此，我们在一个统一框架内详细阐述其理论基础，并展示几个示例以进一步研究其性质。特别地，我们发现热涨落以拓宽CHER的方式清晰地表现出来，从而使CHER的非经典性降低。我们还指出了非经典性和非马尔可夫性概念之间的差异，展示了除纯退相之外的多个CHER，最后，为支持其实际可行性，提出了一种基于金刚石中氮空位中心自由感应衰减测量的实验实现方案。
