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Ab InitioFew-Mode Theory for Quantum Potential Scattering Problems
Physical Review X ( IF 12.5 ) Pub Date : 2020-01-13 , DOI: 10.1103/physrevx.10.011008
Dominik Lentrodt , Jörg Evers

Few-mode models are a cornerstone of the theoretical work in quantum optics, with the famous single-mode Jaynes-Cummings model being only the most prominent example. In this work, we develop an ab initio few-mode theory, a framework connecting few-mode system-bath models to ab initio methods. We first present a method to derive exact few-mode Hamiltonians for noninteracting quantum potential scattering problems and demonstrate how to rigorously reconstruct the scattering matrix from such few-mode Hamiltonians. We show that, upon inclusion of a background scattering contribution, an ab initio version of the well-known input-output formalism is equivalent to standard scattering theory. On the basis of these exact results for noninteracting systems, we construct an effective few-mode expansion scheme for interacting theories, which allows us to extract the relevant degrees of freedom from a continuum in an open quantum system. As a whole, our results demonstrate that few-mode as well as input-output models can be extended to a general class of problems and open up the associated toolbox to be applied to various platforms and extreme regimes. We outline differences of the ab initio results to standard model assumptions, which may lead to qualitatively different effects in certain regimes. The formalism is exemplified in various simple physical scenarios. In the process, we provide a proof of concept of the method, demonstrate important properties of the expansion scheme, and exemplify new features in extreme regimes.

中文翻译:

用于量子势散射问题的从头算数模式理论

很少有模型是量子光学理论工作的基石,著名的单模Jaynes-Cummings模型只是最突出的例子。在这项工作中,我们开发了一个从头开始的少模式理论,这是一个将少模式系统浴模型与从头开始的方法相连接的框架。我们首先提出一种用于推导非相互作用量子势散射问题的精确多模哈密顿量的方法,并演示如何从此类多模哈密顿量严格重建散射矩阵。我们表明,在包括背景散射贡献后,从头算众所周知的输入输出形式主义的版本等同于标准散射理论。基于这些非相互作用系统的精确结果,我们为相互作用的理论构造了有效的少模扩展方案,这使我们能够从开放量子系统的连续体中提取相关的自由度。总体而言,我们的结果表明,少数模式以及输入输出模型可以扩展到一般问题类别,并打开关联的工具箱以应用于各种平台和极端状况。我们概述了从头算起的差异结果符合标准模型假设,可能会导致某些方案在质量上产生不同的影响。形式主义在各种简单的物理场景中得到了体现。在此过程中,我们提供了该方法的概念证明,展示了扩展方案的重要属性,并举例说明了极端情况下的新功能。
更新日期:2020-01-13
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