We use path integrals to calculate perturbative corrections to the correlation function of a particle under the action of nonlinear optical tweezers, both in the overdamped and underdamped regimes. In both cases, it is found that to leading order, nonlinearities manifest as shifts in the characteristic frequency of the system. The results are compared to numerical simulations. The present calculations enable a direct experimental method to access the nonlinear optical trap parameters by analyzing position data, similarly to standard harmonic tweezers.

中文翻译：

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路径积分和非线性光镊

我们使用路径积分来计算在过阻尼和欠阻尼状态下，在非线性光镊作用下对粒子相关函数的微扰校正。在这两种情况下，都发现非线性领先表现为系统特征频率的变化。将结果与数值模拟进行比较。与标准谐波镊子类似，本计算使通过分析位置数据来访问非线性光学陷阱参数的直接实验方法成为可能。