arXiv 1801.018002018-01quant-ph

超越标准二次光学力学的动量场相互作用

Momentum-Field Interactions Beyond Standard Quadratic Optomechanics

Sina Khorasani

发表信息：: Chapter 1, pp. 1-17 in Quantum Mechanics: Theory, Analysis, and Applications, edited by A. I. Arbab, Nova Science Publishers, New York City (2018); ISBN 978-1-53614-208-2

摘要：

这一章总结了最近的进展，在理论和分析工具的二次光机相互作用，作为当代非线性量子光学的突出领域之一。在这里，我们首先要强调的是，存在哪些类型的非线性相互作用，以及每种非线性相互作用的物理解释。光与机械运动之间的标准二次相互作用表示为腔光强度与镜位置平方的乘积。然而，也存在非标准的二次光机相互作用，它在数学上呈现不同的形式，表现为场动量和镜动量的平方积。这种非标准的二次相互作用来源于两种修正：镜场之间的动量交换和动量守恒，以及不同机制引起的相对论修正。当机械频率与光学频率之比不再可以忽略时，这两种类型的非标准相互作用就变得相关了。接下来，我们转向这种相互作用的解决方案技术，并引入一个正式的高阶算子方法来处理量子系统的非线性演化。这使得人们能够使用线性代数的分析工具准确地研究任何类型的量子非线性相互作用。为了利用高阶算子方法的分析能力，首先需要确定一个闭李代数，它应该在交换下精确或近似地满足闭性，并被称为基。在已知高阶算子的基础上，可以着手构造相应的朗之万方程，现在可以使用现有的线性代数数学工具箱方便地分析该方程，以产生谱密度、矩和期望值。

英文摘要：

This chapter summarizes the recent progress in the theory and analytical tools of quadratic optomechanical interactions, as one of the prominent domains of contemporary nonlinear quantum optics. Emphasis has been put here first to show what types of nonlinear interactions do exist, and what physical interpretations follow each. The standard quadratic interactions between light and mechanical motion is expressed as the product of cavity light intensity and squared mirror position. However, there exists a non-standard quadratic optomechanical interaction as well, which assumes a mathematically different form and appears as the squared product of field and mirror momenta. This non-standard type of quadratic interaction originates from two corrections: the momentum exchange and conservation among mirror and field, as well as relativistic corrections due to different mechanisms. Both these types of non-standard interactions become relevant when the ratio of mechanical to optical frequency is no longer negligible. Next, we turn to the solution technique of such interactions, and introduce a formal higher-order operator method to tackle the nonlinear evolution of quantum systems. This enables one to accurately study any type of quantum nonlinear interaction using the analysis tools of linear algebra. In order to employ the analytical power of higher-order operator method, one first needs to identify a closed Lie algebra, which should satisfy closedness property under commutation either exactly or approximately, and is referred to as the basis. Having the basis of higher-order operators known, one may proceed to construct the corresponding Langevin equations, which can be now conveniently analyzed using the existing mathematical toolbox of linear algebra to yield the spectral densities, moments, and expectation values.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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