Lineshape Theory and Photon Counting Statistics for Spectral Fluctuations in Quantum Dots: a L\'evy Walk Process

TL;DR

This paper develops a stochastic lineshape theory and analyzes photon counting statistics for quantum dots exhibiting power-law spectral and intensity fluctuations, revealing new resonances, narrowing effects, and large photon count fluctuations.

Contribution

It introduces a novel lineshape model for frequency modulation with power-law statistics and maps photon counting fluctuations to a Lévy walk process, uncovering unprecedented behaviors.

Findings

Discovery of new resonances and narrowing in lineshape due to power-law modulation.

Identification of large photon count fluctuations and increasing Q factor over time.

Mapping photon counting statistics to Lévy walk processes with unique fluctuation characteristics.

Abstract

Recent experimental observations have found two different kinds of ``strange kinetic behaviors" in individual semiconductor nanocrystals (or quantum dots). Fluorescence intermittency observed in the quantum dots shows power--law statistics in both {\it on} and {\it off} times. Spectral diffusion of the quantum dots is also described by power--law statistics in the sojourn times. Motivated by these experimental observations we consider two different but related problems: (a) a stochastic lineshape theory for the Kubo-Anderson oscillator whose frequency modulation follows power-law statistics and (b) photon counting statistics of quantum dots whose intensity fluctuation is characterized by power-law kinetics. In the first problem, we derive an analytical expression for the lineshape formula and find rich type of behaviors when compared with the standard theory. For example, new type of resonances and narrowing behavior have been found. We show that the lineshape is extremely sensitive to the way the system is prepared at time $t=0$ and discuss the problem of stationarity. In the second problem, we use semiclassical photon counting statistics to characterize the fluctuation of the photon counts emitted from quantum dots. We show that the photon counting statistics problem can be mapped onto a L\'evy walk process. We find unusually large fluctuations in the photon counts that have not been encountered previously. In particular, we show that $Q$ may increase in time even in the long time limit.