Continuous Coherent Quantum Feedback with Time Delays: Tensor Network Solution,Physical Review X

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Continuous Coherent Quantum Feedback with Time Delays: Tensor Network Solution
Physical Review X ( IF 11.6 ) Pub Date : 2024-09-09 , DOI: 10.1103/physrevx.14.031043
Kseniia Vodenkova _{1,

2} , Hannes Pichler _{1,

2}

Affiliation

In this paper, we develop a novel method to solve problems involving quantum optical systems coupled to coherent quantum feedback loops featuring time delays. Our method is based on exact mappings of such non-Markovian problems to equivalent Markovian driven dissipative quantum many-body problems. In this work, we show that the resulting Markovian quantum many-body problems can be solved (numerically) exactly and efficiently using tensor network methods for a series of paradigmatic examples, consisting of driven quantum systems coupled to waveguides at several distant points. In particular, we show that our method allows solving problems in so far inaccessible regimes, including problems with arbitrary long time delays and arbitrary numbers of excitations in the delay lines. We obtain solutions for the full real-time dynamics as well as the steady state in all these regimes. Finally, motivated by our results, we develop a novel mean-field approach, which allows us to find the solution semianalytically, and we identify parameter regimes where this approximation is in excellent agreement with our tensor network results.

Published by the American Physical Society

2024

中文翻译：

具有时间延迟的连续相干量子反馈：张量网络解

在本文中，我们开发了一种新方法来解决涉及量子光学系统与具有时间延迟的相干量子反馈回路耦合的问题。我们的方法基于此类非马尔可夫问题与等效马尔可夫驱动的耗散量子多体问题的精确映射。在这项工作中，我们表明，对于一系列范式示例，可以使用张量网络方法精确有效地解决所产生的马尔可夫量子多体问题，这些示例由耦合到几个遥远点的波导的驱动量子系统组成。特别是，我们表明，我们的方法可以解决迄今为止无法访问的范围内的问题，包括延迟线中具有任意长时间延迟和任意激发次数的问题。我们获得了所有这些状态下的全实时动态和稳态的解决方案。最后，在我们的结果的激励下，我们开发了一种新的平均场方法，它使我们能够以半分析方式找到解决方案，并且我们确定了这种近似与我们的张量网络结果非常一致的参数范围。美国物理学会 2024 年出版

更新日期：2024-09-09

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