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arXiv 1712.09142quant-ph
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量子光学力学的高阶算符方法

Method of Higher-Order Operators for Quantum Optomechanics

Sina Khorasani

摘要:

我们演示了高阶算子方法在非线性标准光力学中的应用。结果表明,在频移中存在对称性破缺,对应于红色和蓝色边带的不等价性。这是由于非线性高阶过程导致不相等的失谐。类似地,高阶共振位移存在,表现为光学和机械共振两者的变化。我们提供了第一个已知的方法来明确估计人口的相干声子。我们还计算了高阶相互作用和相干声子对弹簧效应的修正,并表明这些修正在测量单光子光-机相互作用率时是非常重要的。结果表明,高阶算子在求解具有不同乘性噪声项的光机相互作用时存在非唯一性和多样性选择,其中最小基可提供精确的线性朗之万方程,而解耦一个朗之万方程,从而使整个标准光机问题可由显式表达式精确求解.最后,我们提出了一个详细的治疗乘性噪声以及非线性动态稳定阶段的高阶算子的方法。类似的方法可以在标准光学力学领域之外用于量子物理中的二次和所有其他类型的非线性相互作用。

英文摘要:

We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises from nonlinear higher-order processes leading to inequal detunings. Similarly, a higher-order resonance shift exists appearing as changes in both of the optical and mechanical resonances. We provide the first known method to explicitly estimate the population of coherent phonons. We also calculate corrections to spring effect due to higher-order interactions and coherent phonons, and show that these corrections can be quite significant in measurement of single-photon optomechanical interaction rate. It is shown that there exists non-unique and various choices for the higher-order operators to solve the optomechanical interaction with different multiplicative noise terms, among which a minimal basis offers exactly linear Langevin equations, while decoupling one Langevin equation and thus leaving the whole standard optomechanical problem exactly solvable by explicit expressions. We finally present a detailed treatment of multiplicative noise as well as nonlinear dynamic stability phases by the method of higher-order operators. Similar approach can be used outside the domain of standard optomechanics to quadratic and all other types of nonlinear interactions in quantum physics.

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