任意镜面位移的量子光力学：含非马尔可夫反作用噪声的非线性朗之万方程
Quantum optomechanics with arbitrary mirror displacement: nonlinear Langevin equation with non-Markovian back-action noises
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中文总结 AI 辅助
本研究采用泛函微扰方法推导含非马尔可夫反作用噪声的非线性朗之万方程，可处理任意镜面位移，为高精度量子光力学实验提供理论支持。
中文摘要 AI 辅助
量子光力学（QOM）研究通常被限制在腔中的量子场与镜子、膜或材料介质的量子运动之间的相互作用，这类介质通常被假设运动足够缓慢且粒子产生可忽略，这是动态卡西米尔效应的核心关注点，还包含用于有效控制的驱动激光场。这个快速发展的领域有广泛应用，从量子传感到引力波探测。由于光机械耦合是非线性的，大多数理论研究假设镜面运动幅度x保持很小，近年有几篇论文处理镜面位移的x²、x³阶项。本研究采用[1]提出并经[2]完善的泛函微扰方法，适用于足够弱的光机械耦合，可处理镜面的任意位移，而非仅x的幂级数展开高阶项。我们首先自洽推导量子场的影响泛函及其作用在运动镜面上的非马尔可夫反作用噪声，由此得到由这些量子场反作用噪声驱动的非线性朗之万方程。接着展示我们的通用建模与处理结果如何与文献中的模型及朗之万方程关联，从流行的辐射压力Nx耦合（N为光子数）到近期的x³阶结果。我们希望该新方法及结果能为未来高精度QOM实验提供有用的理论支持。
英文摘要
Quantum optomechanics (QOM) explores the interaction between a quantum field, often confined in a cavity, and the quantum motion of mirrors, membranes or material media, usually assumed slow enough with negligible particle production, which is the central concern of dynamical Casimir effects, and a drive laser field for effective control. This rapidly developing field has a wide range of applications, from quantum sensing to the detection of gravitational waves. Because the opto-mechanical coupling is nonlinear, most theoretical investigations assume that the amplitude of mirror motion $x$ remains small. Recent years saw several papers treating $x^2, x^3$ orders in the mirror displacement. In our work we take a different route, deploying the functional perturbative method presented in [1] and enriched in [2], applicable for sufficiently weak opto-mechanical couplings. With this we can treat arbitrary displacement of the mirror, not just at a higher order in a power series expansion in $x$. We first derive the influence action of the quantum field and its non-Markovian noises back-reacting on the moving mirror with self-consistency. From it we derive a nonlinear Langevin equation driven by these back-action noises from the quantum field. We then show how results from our general modeling and treatment can be linked with the models and the Langevin equations presented in the literature, starting with the popular radiation pressure $Nx$ coupling, with $N$ the photon number, up to the recent $x^3$ order results. We hope this new approach and the results presented here can provide useful theoretical support for high precision QOM experimentation in the future.
发表机构
- Universidad de Santiago de Chile（圣地亚哥智利大学）
- Millennium Institute for Research in Optics（光学研究千年研究所）
- Tamkang University（淡江大学）
- University of Maryland, College Park（马里兰大学帕克分校）
机构由 AI 辅助整理，请以论文原文为准。
