利用多维耦合相干态研究开放系统中量子相干与环境的相互作用

A quantum system is almost impossible to be isolated form the external environment. Though the latter was traditionally considered to be the detriment of the system's internal coherence, which is the essence behind the emergence of intriguing features and promising applications of quantum theory. However, recent advances in experiments, for example in light-harvesting systems, suggest the environment could play a constructive role for long-lasting coherence, as well as fast and highly efficient energy transfer. This has attracted vast theoretical interest to treat the interplay between the intra-system and environment dynamics in challenging regimes, where the traditional perturbation and Markovian approximations no longer hold. This calls for considerable efforts to develop numerical methodologies to treat the noisy quantum dynamics in a fully non-perturbative and non-markovian way, such as: hierarchical equation of motion methods; path integral methods or various transform techniques. This project is based on a very different method: (i) to adopt a grid of coupled coherent states as a truncated basis for the bosonic field, and then use a simplified variational principle (Ehrenfest trajectories) to determine their evolution; (ii) to use a full-variational principle to determine the amplitudes of the wave functions. The main advantage of this technique is to avoid the exponential scaling of the Hilbert space with the number of degrees of freedom and thus to save computational costs. Our aim is to combine the merits of other methods to develop an approach able to treat the system-environment interaction faithfully under less restrictive conditions, in order to: (i) understand to what extent the quantum effects may play a role in open systems, when the system-environment interaction is neither weak or too strong to become classical (as is the case in some biological composite systems); (ii) investigate whether such mechanisms could provide inspiration for engineering artificial applications, e.g. vastly improved man-made compounds for solar energy technology.

量子系统总是与外界环境相互作用的。以往人们认为外界会破坏量子系统的相干性(相干性是量子理论显示其优越性与具有应用前景的起源与根本)。但是，最近的实验，如在光合作用系统中，表明外界环境或许扮演着积极的角色：使相干过程持续变长；优化能量传输的速度和效率。这引起了很大的兴趣，人们试图用纯量子理论来解释这个具有挑战性的区域，因为传统的微扰理论和马科夫近似已不再适用。目前，处理系统与环境的作用的方法有：层级法，路径积分法，多种不同的转换法等。而本课题是基于另一种方法：以多维耦合相干态作为玻色模的基矢, 利用变分原理让基矢随时间动态演化；来避免基矢随自由度的增加呈指数增长，从而减低对计算的要求，结合其他数值的方法，发展出可适用不同物理系统的数值方法：(1）解释开放系统中，系统与环境是如何相互作用的（如生物系统中）；（2）是否可以利用他们之间相互作用的机制来开发新型的器件，如人造太阳能采集器件。

揭示我们所感兴趣的量子子系统与它周围宏观的热库之间的相互作用，对理解物理，化学，与生物领域中的耗散量子现象非常重要。但是，由于热库中存在庞大不可控制的自由度，使得真实模拟这种作用具有挑战性，特别是当两者间的耦合处于中间区域，因为此时传统的微扰与马科夫近似不再适用。本项目中，我们主要讨论了Super-Ohmic 单个自旋-玻色系统：热库的谱密度截止频率与自旋中的贯穿频率相当，即此时热库的记忆效应变得重要。采用相对有限数目的多维耦合相干态作为玻色场的基矢，运用简化的变分原理（Ehrenfest trajectories) 来引导其演化，用全变分方法决定波函数的幅度，我们得到了收敛的数值结果。这些结果与MCTDH（Multi-configurational time dependent Hartree)方法的结论吻合，和QUAPI方法在一定时间范围内基本一致。我们发现通过选择有效的热库模分立化方案，来覆盖与量子子系统相互作用的重要热库模，可降低对计算资源的要求。我们分析了由于数值近似带来的计算误差，给出了几何误差上限的推导，或许这可运用于其他数值模拟方法。为了设计有机的三重态-三重态上转换光电材料，我们正着手研究此过程中的耦合和动力学演化，例如重点考虑分子（感光剂）几何结构的影响。