Efficient numerical method for predicting nonlinear optical spectroscopies of open systems.
Efficient numerical method for predicting nonlinear optical spectroscopies of open systems.
复制标题
用于预测开放系统非线性光学光谱的有效数值方法。
作者：
P. A. Rose;J. Krich
非线性光学光谱是探测分子和纳米级系统中量子动力学的强大工具。虽然关于超快光谱的直觉通常是通过考虑脉冲光脉冲来建立的，但实际实验具有有限持续时间的脉冲，这对于解释和预测实验结果非常重要。我们提出了一种新的免费开源光谱建模方法，称为超快超快（UF2）光谱，它能够在计算上高效且方便地预测非线性光谱，例如处理任意有限持续时间脉冲形状。 UF2 是一种基于傅立叶的方法，需要对系统密度矩阵的刘维尔传播子进行对角化。我们还提出了龙格-库塔-欧拉（RKE）直接传播方法。我们将开放系统动力学纳入世俗雷德菲尔德、完整雷德菲尔德和带有马尔可夫浴的 Lindblad 形式主义中。对于非马尔可夫系统，将与记忆效应相对应的自由度带入系统并进行非扰动处理。我们分析了算法的计算复杂度，并通过数值证明，包括对角化传播器的成本，对于具有任意希尔伯特空间维度的世俗 Redfield 模型，UF2 比直接传播方法快 20-200 倍；对于完整的 Redfield 模型，至少在传播器需要超过 20 GB 来存储的系统尺寸上，它同样更快；对于 Lindblad 模型，它的速度更快，可达接近 100 的希尔伯特空间维度，小型系统的加速速度超过 500 倍。UF2 和 RKE 是更大的开源超快软件套件的一部分，其中包括用于自动生成和计算费曼图的工具。
Nonlinear optical spectroscopies are powerful tools for probing quantum dynamics in molecular and nanoscale systems. While intuition about ultrafast spectroscopies is often built by considering impulsive optical pulses, actual experiments have finite-duration pulses, which can be important for interpreting and predicting experimental results. We present a new freely available open source method for spectroscopic modeling, called Ultrafast Ultrafast (UF2) spectroscopy, which enables computationally efficient and convenient prediction of nonlinear spectra, such as treatment of arbitrary finite duration pulse shapes. UF2 is a Fourier-based method that requires diagonalization of the Liouvillian propagator of the system density matrix. We also present a Runge-Kutta-Euler (RKE) direct propagation method. We include open system dynamics in the secular Redfield, full Redfield, and Lindblad formalisms with Markovian baths. For non-Markovian systems, the degrees of freedom corresponding to memory effects are brought into the system and treated nonperturbatively. We analyze the computational complexity of the algorithms and demonstrate numerically that, including the cost of diagonalizing the propagator, UF2 is 20-200 times faster than the direct propagation method for secular Redfield models with arbitrary Hilbert space dimension; it is similarly faster for full Redfield models at least up to system dimensions where the propagator requires more than 20 GB to store; and for Lindblad models, it is faster up to Hilbert space dimension near 100 with speedups for small systems by factors of over 500. UF2 and RKE are part of a larger open source Ultrafast Software Suite, which includes tools for automatic generation and calculation of Feynman diagrams.