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Physical Review A

Non-Poissonian intermittent fluorescence from complex structured environments

Adrián A. Budini

Published Jun 14, 2006• 23 citations
Publisher

Abstract

We characterize the photon-counting statistics of single-chromophore systems submitted to continuous laser radiation and embedded in a complex structured environment able to induce strong non-Markovian effects in the decay dynamics. In the weak-laser-excitation regime, the photon-emission process can be described through a delay function. We demonstrate that the dynamics, by itself, is able to develop a non-Poissonian intermittent fluorescence phenomenon where the bright and dark intervals are characterized by probability distributions that may depart from an exponential one.

DOI
10.1103/physreva.73.061802

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We characterize the photon-counting statistics of single-chromophore systems submitted to continuous laser radiation and embedded in a complex structured environment able to induce strong non-Markovian effects in the decay dynamics. In the weak-laser-excitation regime, the photon-emission process can be described through a delay function. We demonstrate that the dynamics, by itself, is able to develop a non-Poissonian intermittent fluorescence phenomenon where the bright and dark intervals are characterized by probability distributions that may depart from an exponential one.
In this paper, we formulate a quantum jump approach associated with single fluorescent systems whose radiative decay is defined by a Lindblad-like equation with a memory kernel. We base our results in a generalized Born–Markov approximation, which allows us to get our results from a full microscopic description. In the weak-laser-excitation regime, the photon-emission process can be described through a delay function, which in a natural way provides the basis for unravelling the dynamics in terms of a stochastic density matrix. As in the Markovian case, the stochastic dynamics consists in periods where the evolution is smooth and non-unitary, interrupted at random times where the photon-detection events produce a sudden change in the system state. The phenomenon of non-Poissonian intermittent fluorescence induced by complex environments (Budini 2006 Phys. Rev. A 73 061802) is analysed in the context of this approach.
An analysis of intermittent fluorescence is presented for a single molecule driven by a continuous-wave laser field. The interruptions of fluorescence are caused by transition of the molecule to a triplet state. A method previously developed to calculate photon distribution for continuous-wave fluorescence is applied to analyze photon statistics of fluorescence blinking. The probability w N (T) of counting N photons over a time interval T is derived for intermittent fluorescence. The photons counted over relatively short intervals are found to have a sub-Poissonian (narrower than Poisson) distribution. The photon distribution over intervals longer than the mean off time has a complicated form with two maxima; i.e., a super-Poissonian (wider than Poisson) distribution is obtained.
By considering single chromophore systems whose radiative decay can be written in terms of a nonlocal Lindblad-type evolution, the authors extend the formalism of generalized optical Bloch equations [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett. 90, 238305 (2003)] to non-Markovian dynamics. They demonstrate that photon statistical properties such as bunching and antibunching, as well as sub- and super-Poissonian photon statistics can be fitted in the context of non-Markovian dynamics. The nonlocal effects may arise due to the interaction with a complex structured environment. In this case, the photon statistics can be related with the parameters that define the microscopic system-environment interaction. Alternatively, the authors demonstrate that effective dynamics such as triplet blinking, where the system is coupled via incoherent transitions to an extra dark state, can also be worked out in terms of generalized non-Markovian optical Bloch equations. The corresponding memory contributions are mapped with those that arise from the microscopic approach.
Single fluorophore systems attached to complex hosting molecules may exhibit a light-assisted fluorescence blinking phenomenon between two or more different intensity states whose sojourn statistic depends on the pumping laser intensity and also may depart from an exponential law. In contrast with standard phenomenological models, here we demonstrate that such kind of radiation patterns can be microscopically derived and characterized by describing the fluorophore decay through a composite reservoir where quantum degrees of freedom associated to the host molecule mediate the interaction between the fluorophore and a bosonic bath associated to its natural decay.
Distribution function w(N)(T) for photons created by three-level nanoparticle in time interval T under cw laser excitation is calculated for various methods of photon counting. It is found that each exponential process exp(-lambda(i)t) in quantum dynamics of three-level nanoparticle manifests itself via Poissonian function P(N)(lambda(i)t)=(lambda(i)t)(N) exp(-lambda(i)t)/N! in the photon distribution function w(N)(T). The distribution function w(N)(T) is expressed via two or three integrals of two or three Poissonian functions P(N)(lambda(i)t). The simple mathematical expression for w(N)(T) enables one to calculate photon distribution in blinking fluorescence with on and off intervals. A scaling between photon distribution function w(N)(T) and photoelectric pulse distribution function w(n)(T) is found. Comparison of the theoretical distribution w(n)(T) and the distribution measured in blinking fluorescence of single polymer molecule dPPV-PPyV and complex organic molecule 1,1(')-didodecyl-3,3,3('),3(')-tetramethylindocarbocyanine perchlorate (DiI) is carried out. The theoretical distributions are able to describe those found in an experiment.
Statistics of fluorescence photons emitted by a single two-level atom interacting with a continuous wave laser field are analyzed. The photon-counting distribution is calculated for the so-called intermediate fluorescence photons, i.e., those counted during the time interval between instants at which photons are emitted. The result is a sub-Poissonian (narrower than Poisson) distribution, which agrees with experimental observations. This intermediate-photon distribution is used to calculate the average number of fluorescence photons, the second factorial moment of the photon-counting distribution, and Mandel’s Q parameter commonly used to evaluate the deviation of photon statistics from the Poisson distribution. The theoretical expressions obtained for moments of the intermediate-photon distribution are different from well-known Mandel’s formulas.