Many-body dynamics of non-Markovian open quantum systems

在过去的几年里，原子和固体物理中的许多实验平台已经开发出对强相互作用的多粒子系统的特殊控制。这些平台对于探索量子物理的基本元素和一系列量子技术的潜在应用都很有趣。随着这种控制的改进，一个关键的开放问题成为如何描述和控制开放多体量子系统，即多体量子系统与其环境耦合。这可能会产生不必要的影响（例如，退相干），也会产生新的工具（例如，冷却和制备量子态的新方法）。来自量子光学和其他领域的许多技术已经被用来描述马尔可夫开放量子系统（其中环境有效地没有系统过去进化的记忆），非马尔可夫系统，其中环境具有非平凡的记忆效应，直到最近才开始探索。这些都很重要，因为它们在许多固态系统中自然发生（例如，基于超导量子比特的量子计算机中的退相干），也因为它们可以为在多体系统中设计新现象提供新的机会，或者为未来的量子技术产生新的控制水平。在这个项目中，我们的目标是进一步发展和应用最先进的数值技术，包括时间演化矩阵乘积算子（TEMPO）和基于纯态层次（HOPS）的量子态扩散技术。我们将扩展这些技术，以探索非马尔可夫耗散如何与多体系统的量子相干动力学相互作用。这些效应既出现在固态量子技术中，也出现在光学腔中高度受控的冷原子系统中。主要目标将是：1)了解强相互作用多粒子系统中相干过程和非马尔可夫耗散之间相互作用的基本物理学；2)扩展最近发展的数值方法，为研究广泛系统中的非马尔可夫耗散提供新的工具；3)确定非马尔可夫耗散动力学可以为未来量子技术中多体系统的应用提供工具的领域。

Over the past years, many experimental platforms in atomic and solid state physics have developed exceptional control over strongly interacting many-particle systems. These platforms are interesting both for exploring fundamental elements of quantum physics, and for potential applications across a range of quantum technologies. As this control has improved, one key open question has become how to describe and control open many-body quantum systems, i.e., many-body quantum systems coupled to their environment. This can give rise both to unwanted effects (e.g., decoherence), and to new tools (e.g., new ways to cool and prepare quantum states). Many techniques from quantum optics and other fields have been employed to describe Markovian open quantum systems (where the environment effectively has no memory of the past evolution of the system), non-Markovian systems where an environment has non-trivial memory effects have only recently started to be explored. These are important both because they occur naturally in many solid-state systems (e.g., decoherence in quantum computers based on superconducting qubits), and also because they can give rise to new opportunities to engineer novel phenomena in many-body systems, or generate new levels of control for future quantum technologies. In this project we aim to further develop and apply state of the art numerical techniques, including Time-Evolving Matrix Product Operators (TEMPO) and quantum state diffusion techniques based on a Hierarchy of Pure States (HOPS). We will extend these techniques in order to explore how non-Markovian dissipation interacts with the quantum coherent dynamics of many-body systems. These effects appear both in solid-state quantum technologies and in highly controlled systems of cold atoms in optical cavities. The primary objectives will be: 1) to gain an understanding of the fundamental physics which results from the interplay between coherent processes and non-Markovian dissipation in strongly interacting many-particle systems, 2) to extend recently developed numerical methods to provide new tools for studying non-Markovian dissipation in a broad range of systems, and 3) to identify areas where non-Markovian dissipative dynamics can provide tools for applications of many-body systems in future quantum technologies.