Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems.We show that the time average of the observation function which is not the $L^1(m)$ function, whose average with respect to the invariant measure $m$ is finite, converges to the generalized arcsine distribution. This result leads to the novel view that the correlation function is intrinsically random and does not decay. Moreover, it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean.Comment: 8 pages, 8 figure

Statistical Aging and Non Ergodicity in the Fluorescence of Single Nanocrystals

The relation between single particle and ensemble measurements is adressed for semiconductor CdSe nanocrystals. We record their fluorescence at the single molecule level and analyse their emission intermittency, which is governed by unusual random processes known as Levy statistics. We report the observation of statistical aging and ergodicity breaking, both related to the occurrence of Levy statistics. Our results show that the behaviour of ensemble quantities, such as the total fluorescence of an ensemble of nanocrystals, can differ from the time averaged individual quantities, and must be interpreted with care.Comment: 4 pages, 3 figure

Energy Transfer from Individual Semiconductor Nanocrystals to Graphene

Energy transfer from photoexcited zero-dimensional systems to metallic systems plays a prominent role in modern day materials science. A situation of particular interest concerns the interaction between a photoexcited dipole and an atomically thin metal. The recent discovery of graphene layers permits investigation of this phenomenon. Here we report a study of fluorescence from individual CdSe/ZnS nanocrystals in contact with single- and few-layer graphene sheets. The rate of energy transfer is determined from the strong quenching of the nanocrystal fluorescence. For single-layer graphene, we find a rate of ~ 4ns-1, in agreement with a model based on the dipole approximation and a tight-binding description of graphene. This rate increases significantly with the number of graphene layers, before approaching the bulk limit. Our study quantifies energy transfer to and fluorescence quenching by graphene, critical properties for novel applications in photovoltaic devices and as a molecular ruler

Sample-Averaged Biexciton Quantum Yield Measured by Solution-Phase Photon Correlation

The brightness of nanoscale optical materials such as semiconductor nanocrystals is currently limited in high excitation flux applications by inefficient multiexciton fluorescence. We have devised a solution-phase photon correlation measurement that can conveniently and reliably measure the average biexciton-to-exciton quantum yield ratio of an entire sample without user selection bias. This technique can be used to investigate the multiexciton recombination dynamics of a broad scope of synthetically underdeveloped materials, including those with low exciton quantum yields and poor fluorescence stability. Here, we have applied this method to measure weak biexciton fluorescence in samples of visible-emitting InP/ZnS and InAs/ZnS core/shell nanocrystals, and to demonstrate that a rapid CdS shell growth procedure can markedly increase the biexciton fluorescence of CdSe nanocrystals.United States. Dept. of Energy. Office of Basic Energy Sciences (DE-FG02-07ER46454)United States. Dept. of Energy. Office of Basic Energy Sciences (DE-SC0001088)National Institutes of Health (U.S.) (9P41EB015871-26A1

Weakly non-ergodic Statistical Physics

We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum dots and the sub-diffusive continuous time random walk model. When the fluctuations become normal we recover usual ergodic statistical mechanics. Examples of a particle undergoing fractional dynamics in a binding force field are worked out in detail. We briefly discuss possible physical applications in single particle experiments

Ultrafast single photon emitting quantum photonic structures based on a nano-obelisk

A key issue in a single photon source is fast and efficient generation of a single photon flux with high light extraction efficiency. Significant progress toward high-efficiency single photon sources has been demonstrated by semiconductor quantum dots, especially using narrow bandgap materials. Meanwhile, there are many obstacles, which restrict the use of wide bandgap semiconductor quantum dots as practical single photon sources in ultraviolet-visible region, despite offering free space communication and miniaturized quantum information circuits. Here we demonstrate a single InGaN quantum dot embedded in an obelisk-shaped GaN nanostructure. The nano-obelisk plays an important role in eliminating dislocations, increasing light extraction, and minimizing a built-in electric field. Based on the nano-obelisks, we observed nonconventional narrow quantum dot emission and positive biexciton binding energy, which are signatures of negligible built-in field in single InGaN quantum dots. This results in efficient and ultrafast single photon generation in the violet color region