Manifestation of single macromolecule quantum dynamics in photon distribution function of blinking fluorescence

Looking at a blinking quantum emitter through time slots: the effect of blind times

Most experimental observations of physical processes are naturally accompanied by "blind" ("dead") times, which in principle can distort the result of measurements. Here we analyze how the presence of blind times in measurements changes the measured statistics of blinking fluorescence of single quantum dots. We show that information can be extracted even for blinking processes with characteristic times longer than both blind times and time slots between them.

Blinking fluorescence of single donor-acceptor pairs: important role of "dark'' states in resonance energy transfer via singlet levels

The influence of triplet levels on Förster resonance energy transfer via singlet levels in donor-acceptor (D-A) pairs is studied. Four types of D-A pair are considered: (i) two-level donor and two-level acceptor, (ii) three-level donor and two-level acceptor, (iii) two-level donor and three-level acceptor, and (iv) three-level donor and three-level acceptor. If singlet-triplet transitions in a three-level acceptor molecule are ineffective, the energy transfer efficiency E=I_{A}/(I_{A}+I_{D}), where I_{D} and I_{A} are the average intensities of donor and acceptor fluorescence, can be described by the simple theoretical equation E(F)=FT_{D}/(1+FT_{D}). Here F is the rate of energy transfer, and T_{D} is the donor fluorescence lifetime. In accordance with the last equation, 100% of the donor electronic energy can be transferred to an acceptor molecule at FT_{D}≫1. However, if singlet-triplet transitions in a three-level acceptor molecule are effective, the energy transfer efficiency is described by another theoretical equation, E(F)=F[over ¯](F)T_{D}/[1+F[over ¯](F)T_{D}]. Here F[over ¯](F) is a function of F depending on singlet-triplet transitions in both donor and acceptor molecules. Expressions for the functions F[over ¯](F) are derived. In this case the energy transfer efficiency will be far from 100% even at FT_{D}≫1. The character of the intensity fluctuations of donor and acceptor fluorescence indicates which of the two equations for E(F) should be used to find the value of the rate F. Therefore, random time instants of photon emission in both donor and acceptor fluorescence are calculated by the Monte Carlo method for all four types of D-A pair. Theoretical expressions for start-stop correlators (waiting time distributions) in donor and acceptor fluorescence are derived. The probabilities w_{N}^{D}(t) and w_{N}^{A}(t) of finding N photons of donor and acceptor fluorescence in the time interval t are calculated for various values of the energy transfer rate F and for all four types of D-A pair. Comparison of the calculated D and A fluorescence trajectories with those measured by Weiss and co-workers proves the important role of triplet levels in energy transfer via singlet levels.

Photon statistics in blinking fluorescence of single PPV-PPyV molecule

A theoretical six-level model for blinking fluorescence of single PPV-PPyV copolymer molecule excited by CW-laser light is proposed. The model has been chosen in accordance with the following facts found in the Paul Barbara group experiment: (i) alternation of two types of fluorescence with moderate and strong levels of emission, (ii) existence of "dark" states with no fluorescence, (iii) linear dependence of inverse on-interval duration on laser intensity, and (iv) existence of laser intensity independent off-intervals. Relations between the distribution function w''(N, T) for photons emitted by a single molecule, the distribution function w'(N, T) for photons arriving at photomultiplier tube (PMT) and photo-electric pulse distribution w(N, T) created in a PMT are discussed. The theory is able to describe pulse distribution function w(N, T) measured experimentally at signal acquisition time T = 0.1 s. Values of all rate constants of the model have been found from comparison of the theory with the experiment. Distributions w(on, off)(t) of on- and off-times and distribution w(N, T) of pulses have been calculated for infrequent and frequent inter-conformational jumps in single copolymer molecule.

Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations

The large-deviation method can be used to study the measurement trajectories of open quantum systems. For optical arrangements this formalism allows to describe the long time properties of the (nonequilibrium) photon counting statistics in the context of a (equilibrium) thermodynamic approach defined in terms of dynamical phases and transitions between them in the trajectory space [J. P. Garrahan and I. Lesanovsky, Phys. Rev. Lett. 104, 160601 (2010)]. In this paper, we study the thermodynamic approach for fluorescent systems coupled to complex reservoirs that induce stochastic fluctuations in their dynamical parameters. In a fast modulation limit the thermodynamics corresponds to that of a Markovian two-level system. In a slow modulation limit, the thermodynamic properties are equivalent to those of a finite system that in an infinite-size limit is characterized by a first-order transition. The dynamical phases correspond to different intensity regimes, while the size of the system is measured by the transition rate of the bath fluctuations. As a function of a dimensionless intensive variable, the first and second derivatives of the thermodynamic potential develop an abrupt change and a narrow peak, respectively. Their scaling properties are consistent with a double-Gaussian probability distribution of the associated extensive variable.

Super-Poissonian statistics of on-off jumps in blinking fluorescence of single molecules

Blinking fluorescence of a single guest molecule embedded in a polymer matrix and excited by cw laser light is considered. Such fluorescence exhibits quantum jumps from bright on-intervals to dark off-intervals, i.e., so-called on-->off jumps. A system with one type of on-intervals and with two types of off-intervals is studied. A distribution function w(N)(T) for the number N of on-->off jumps in a time interval T is derived. The distribution function is expressed via a threefold integral of three Poissonian functions, each of which relates to the corresponding exponential process in the quantum dynamics of a fluorescent impurity center. Numerical calculations of the distribution function w(N)(T) for four time intervals T of various durations are carried out. The distribution function w(N)(T) is broader as compared with the Poissonian one and has two maxima, one of which relates to observed time intervals without on-->off jumps.