具有色散和耗散光机械耦合的光机械学的朗之万方程描述
The Langevin-equation description of optomechanics with the dispersive and dissipative optomechanical coupling
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中文总结 AI 辅助
研究光机械系统，用基于经典波动方程的方法推导相关方程，与朗之万方程形式比较，评估其有效性及适用范围，发现涉及耗散光机械耦合时该形式存在问题，如腔衰减率与耦合关系不符、输入场相位因子缺失等。
中文摘要 AI 辅助
光机械系统的描述通常基于量子朗之万方程形式。该框架是从现象学引入或基于模型哈密顿量。然而，处理光机械法布里 - 珀罗腔或内部有半透明机械活性膜的改进迈克尔逊 - 萨尼亚克干涉仪时，可通过替代方法进行无模型考虑。此方法基于系统中的经典波动方程，在引力波领域很流行，称为输入 - 输出关系方法。本文用此方法推导了腔内场阶梯算符、随机反作用力及输入镜处场之间关系的方程，简化结果并与朗之万方程形式的相应预测比较，评估其有效性并修正适用范围。发现涉及耗散光机械耦合时，该形式存在明显问题，如法布里 - 珀罗腔衰减率与长度有关却未产生耗散光机械耦合，输入镜处场关系可能不正确，且朗之万方程形式在输入场处缺少一个相位因子，此因子在涉及耗散光机械耦合时很重要。
英文摘要
The description of the optomechanical systems is commonly based on the quantum Langevin equation formalism. This framework is introduced phenomenologically or based on a model Hamiltonian. However, once dealing with the optomechanical Fabry-Perot cavity or the modified Michelson-Sagnac interferometer with a semitransparent mechanically active membrane inside, a model-free consideration is also possible by using an alternative approach. Such an approach, which is based on the classical wave equations, is popular in the gravitational-wave community where it is termed as input-output relations approach. In this work, using the aforementioned approach, we derived the equations for the ladder operator of the intracavity field, stochastic back-action force, and the relation between the fields at the input mirror. Then we simplified the obtained results down to the range of applicability of the Langevin equation formalism and compared these with the corresponding predictions of the latter formalism. This enabled us to critically assess the validity of the Langevin equation formalism and rectify its range of applicability to find that the latter is more stringent than that intuitively expected. In the case where the dissipative optomechanical coupling is involved we identified appreciable problems with this formalism. It was found that, disregarding the fact that decay rate of the optomechanical Fabry-Perot cavity depends on its length, no dissipative optomechanical coupling is generated. This is in contrast with the prediction of the standard Langevin-equation based treatment. It was found that the Langevin equation formalism misses a phase factor at the input field; this factor turns out to be important for the situation involving the dissipative optomechanical coupling.
