Margolin G, Protasenko V, Kuno M, Barkai E
Department of Chemistry and Biochemistry, Notre Dame University, Notre Dame, Indiana 46556, USA.
J Phys Chem B. 2006 Sep 28;110(38):19053-60. doi: 10.1021/jp061487m.
We analyze photon statistics of blinking CdSe-ZnS nanocrystals interacting with a continuous wave laser field, showing that the process is described by a ballistic Lévy walk. In particular, we show that Mandel's Q parameter, describing the fluctuations of the photon counts, is increasing with time even in the limit of long time. This behavior is in agreement with the theory of Silbey and co-workers (Jung et al. Chem. Phys. 2002, 284, 181), and in contrast to all existing examples where Q approaches a constant, independent of time in the long time limit. We then analyze the distribution of the time averaged intensities, showing that they exhibit a nonergodic behavior, namely, the time averages remain random even in the limit of a long measurement time. In particular, the distribution of occupation times in the on-state compares favorably to a theory of weak ergodicity breaking of blinking nanocrystals. We show how our data analysis yields information on the amplitudes of power-law decaying on and off time distributions, information not available using standard data analysis of on and off time histograms. Photon statistics reveals fluctuations in the intensity of the bright state indicating that it is composed of several states. Photon statistics exhibits a Lévy walk behavior also when an ensemble of 100 dots is investigated, indicating that the strange kinetics can be observed already at the level of small ensembles.
我们分析了与连续波激光场相互作用的闪烁CdSe-ZnS纳米晶体的光子统计特性，结果表明该过程可用弹道式列维游走描述。具体而言，我们发现描述光子计数涨落的曼德尔Q参数即使在长时间极限下也随时间增加。这种行为与西尔贝及其同事的理论（荣格等人，《化学物理杂志》，2002年，第284卷，第181页）一致，与所有现有例子相反，在那些例子中，Q在长时间极限下趋近于一个与时间无关的常数。然后我们分析了时间平均强度的分布，结果表明它们呈现出非遍历性行为，即即使在长时间测量极限下，时间平均值仍保持随机。特别是，处于亮态的占据时间分布与闪烁纳米晶体弱遍历性破坏理论相当吻合。我们展示了我们的数据分析如何得出关于幂律衰减开和关时间分布幅度的信息，而这是使用开和关时间直方图的标准数据分析无法获得的信息。光子统计揭示了亮态强度的涨落，表明它由几个状态组成。当研究100个点的集合时，光子统计也呈现出列维游走行为，这表明在小集合水平上就能观察到这种奇特的动力学。
