Analysing Non-Markovian Open Quantum Systems to Understand the Role of the External Environment in Cryptochrome-Based Magnetoreception

磁感，一些动物感知地磁场的能力，一直是科学界的一个相当有趣的话题。四十年的广泛研究明确表明，候鸟非凡的导航能力得到了视觉“磁罗盘”的支持。现在人们普遍认为，隐色素是候鸟视网膜中的一种黄素蛋白，负责促进这种“第六感”。在隐色素中，自由基对被认为是由光激活产生的，量子相干自旋动力学使得自由基对随后的重组对地球磁场的倾斜很敏感。目前大多数鸟类磁罗盘模型孤立地处理隐花色素的自旋动力学。然而，最近对这种蛋白质的体外磁敏感性的理论研究和实验研究表明，孤立的隐花色素对地磁场的响应太小，无法切实支持导航。我们假设这种“相互作用强度差距”可以通过隐花色素与其环境（即其开放系统性质）的相互作用来理解和解决。传统上，人们可能会预测嘈杂的生物环境只会导致隐花色素的相干性丧失，从而破坏其对外部场的敏感性。然而，我们的初步研究表明，与直觉相反，似乎环境本身可以加强微妙的自旋相干。具体来说，系统池相互作用可以是非马尔可夫行为的一个来源，在某些条件下，可以作为自旋动力学的驱动因素，增强系统的相干性和灵敏度。这与在大多数量子技术应用中观察到的情况相反，在这些应用中，与外部环境的相互作用会导致相干性损失和量子效应的抑制。本项目旨在从理论上研究由于嵌入生物环境而受到非马尔可夫噪声和驱动的自由基系统的自旋动力学。为此，我们将开发工具来处理非马尔可夫耦合和驱动条件下实际复杂的自由基对系统的开系统自旋动力学。然后，我们将这些方法应用于隐花色素中的自由基对过程，以及隐花色素领域之外的生物自由基过程，如脂质过氧化。最初的方法将基于由Tanimura和Kubo开发的层次运动方程（HEOM）框架，而随后将基于基于波函数的HEOM扩展实现更大，更现实的模型。非马尔可夫效应以前还没有在自由基自旋动力学中研究过，但初步分析表明，它们是破译磁感受的关键。该项目将提供相应的答案，具有深远的应用，例如发展仿生量子技术，以及对我们理解支撑生物功能的量子效应的影响。

Magnetoreception, the ability of some animals to sense the geomagnetic field, has been a topic of considerable intrigue within the scientific community. Four decades of extensive research have demonstrate unequivocally that the extraordinary ability of migratory birds to navigate is supported by a visual 'magnetic compass'. It is now widely accepted that cryptochromes, a type of flavoprotein within the retinae of migratory birds, are responsible for facilitating this 'sixth sense'. Within cryptochromes, a radical pair is thought to be generated by photoactivation, the quantum coherent spin dynamics of which render the radical pair's subsequent recombination sensitive to the inclination of the Earth's magnetic field.The majority of current models of the avian magnetic compass treat the spin dynamics of the cryptochrome in isolation. However, recent theoretical investigations and experimental studies of the protein's magnetosensitivity in vitro show that the response of an isolated cryptochrome to the geomagnetic fields is far too small to feasibly support navigation. We hypothesize that this 'interaction strength gap' could be understood, and resolved, in terms of interactions of the cryptochrome with its environment, i.e. its open-system nature. Conventionally, one might predict that the noisy biological environment would solely lead to coherence loss in the cryptochrome, thus destroy its sensitivity to the external field. However, our preliminary studies suggest that, counterintuitively, it seems as though the environment itself can reinforce the delicate spin coherences. Specifically, the system-bath interaction can be a source of non-Markovian behaviour, which, under certain conditions, can act as driver of the spin dynamics and enhance the coherence and sensitivity of the system. This is contrary to what is observed in most instances quantum-technological applications for which interactions with an external environment lead to coherence loss and suppression of quantum effects.This project aims to theoretically study the spin dynamics of radical systems subject to non-Markovian noise and driving as a result of their embedding in a biological environment. To this end, we will develop the tools to treat the open-system spin dynamics of realistically complex radical pair systems under conditions of non-Markovian coupling and driving. We will then apply these approaches to radical pair processes in cryptochrome and, in addition, biological radical processes outside of the cryptochrome realm, such as lipid peroxidation. Initial approaches will be based on the framework of the hierarchical equations of motion (HEOM), developed by Tanimura and Kubo, while large, more realistic models will later be realized based on wave function-based extensions to HEOM. Non-Markovian effects have not been previously studied in radical spin dynamics, but preliminary analysis suggests that they hold the key to deciphering magnetoreception. This project will provide the corresponding answer, with far-reaching applications, e.g. for the development biomimetic quantum technology, and implications as to our understanding of quantum effects underpinning biological function.