Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA.
J Chem Phys. 2010 Apr 14;132(14):144105. doi: 10.1063/1.3327760.
Time-resolved spectroscopy that uses more than one incoherent excitation, and thus has multiple periods of time evolution, is becoming more common. A recent example is multiple population-period transient spectroscopy (MUPPETS), which is implemented as a high-order transient grating. In this paper, a formalism is developed to treat these types of incoherent spectroscopy in a manner that parallels the Liouville-pathway formalism used to treat multidimensional coherent spectroscopy. A Hilbert space of incoherent (population) states is defined and general expressions for transition and time-evolution operators acting on these states are derived from the corresponding quantum operators. This formalism describes incoherent experiments that involve an arbitrary number of temporal dimensions in terms of pathways through the Hilbert space. Each pathway is associated with a multiple-time rate-correlation function. Previous work has shown that these multiple-time correlation functions can measure heterogeneity in electronic-relaxation rates. Thus, they are an analog of coherent "echo" experiments, which measure heterogeneity in frequencies. We show that similar "MUPPETS echo" experiments can be done on any incoherent variable. For a dilute molecular solute, the Hilbert-space method leads to a systematic treatment of multidimensional transient gratings. The extension of irreducible-tensor methods to the incoherent Hilbert space results in a classification of orientational gratings of arbitrary order. The general methods developed in this paper are applied more specifically to single-photon, dipole transitions in the following paper.
使用不止一种非相干激发且因此具有多个时间演化周期的时间分辨光谱学越来越常见。最近的一个例子是多群体-瞬态光谱学（MUPPETS），它被实现为高阶瞬态光栅。在本文中，我们开发了一种形式主义方法，以类似于用于处理多维相干光谱学的刘维尔途径形式主义的方式来处理这些类型的非相干光谱学。定义了一个非相干（群体）态的希尔伯特空间，并从相应的量子算符推导出作用于这些态的跃迁和时间演化算符的一般表达式。该形式主义以通过希尔伯特空间的途径来描述涉及任意数量的时间维度的非相干实验。每条途径都与一个多时间相关函数相关联。以前的工作表明，这些多时间相关函数可以测量电子弛豫率的非均匀性。因此，它们是相干“回波”实验的模拟，该实验测量频率的非均匀性。我们表明，可以在任何非相干变量上进行类似的“MUPPETS 回波”实验。对于稀分子溶质，希尔伯特空间方法导致对多维瞬态光栅的系统处理。将不可约张量方法扩展到非相干希尔伯特空间导致任意阶取向光栅的分类。本文中开发的一般方法更具体地应用于以下论文中的单光子、偶极跃迁。
