Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system–bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system–bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

中文翻译：

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非线性光谱的半经典路径积分计算

非线性光学响应函数的计算允许理论和实验之间的深入联系。实验记录的光谱提供了高密度的信息，但是要客观地解开重叠的信号并获得对系统动力学的详细和可靠的了解，必须将测量与理论方法结合起来。在这里，我们提出了一种新的，高度准确和高效的基于轨迹的半经典路径积分方法，用于计算非马尔可夫开放量子系统的高阶非线性光学响应函数。原则上，该方法适用于一般的哈密顿量，并且对系统内部或系统-浴耦合的形式没有任何限制。该方法在系统上是可改进的，并且在基于扰动理论的方法定性分解的参数范围内被证明是有效的。作为此处介绍的方法的测试，我们研究了耦合二聚体的系统浴模型，将其与数值精确结果和基于标准近似扰动理论的计算进行了比较。此外，我们研究了具有离散电子振动态的单体，该单体可用作将来在非线性电子光谱学中研究电子振动特征的起点。