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ACTA PHOTONICA SINICA

Correlation Functions Investigation of Single Quantum Tow-Levels and Tow-States Systems

Jia Suo-Tang

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The three-level dye molecule single quantum system interacting with a cw laser field is investigated.The dynamic process of a single-molecule emitted photon is described by rate equations with absorbing boundary condition.It is demonstrated that the dynamics of the single-molecule processes and the statistics of time-resolved photon detection can be conveniently described in terms of renewal stochastic processes.The approach of calculating the correlation function by calculating the delay function that is an important physics quantity reflecting single quantum system dynamic process is given,and explicit expressions of correlation functions for two-levels and two-states systems are derived.This approach can be used for calculate dynamics parameter of molecular transition based on the fluorescence intensity correlation function.

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Journal of Suzhou University•Jan 1, 2009•0 citations

A Stochastic Theory of Single Molecule Spectroscopy

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arXiv:cond-mat/0311428•Nov 19, 2003•0 citations

Theory for Wavelength-Resolved Photon Emission Statistics in Single-Molecule Fluorescence Spectroscopy

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

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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.

The Journal of Chemical Physics•Feb 10, 2009•22 citations

Quantum jumps and photon statistics in fluorescent systems coupled to classically fluctuating reservoirs

Adrián A. Budini

In this paper, we develop a quantum-jump approach for describing the photon emission process of single fluorophore systems coupled to complex classically fluctuating reservoirs. The formalism relies on an open quantum system approach where the dynamics of the system and the reservoir fluctuations are described through a density matrix whose evolution is defined by a Lindblad rate equation. For each realization of the photon-measurement processes it is possible to define a conditional system state (stochastic density matrix) whose evolution depends on both the photon detection events and the fluctuations between the configurational states of the reservoir. In contrast to standard fluorescent systems the photon-to-photon emission process is not a renewal one, being defined by a (stochastic) waiting time distribution that in each recording event parametrically depends on the conditional state. The formalism allows calculating experimental observables such as the full hierarchy of joint probabilities associated with the time intervals between consecutive photon recording events. These results provide a powerful basis for characterizing different situations arising in single-molecule spectroscopy, such as spectral fluctuations, lifetime fluctuations and light-assisted processes.

arXiv:1005.3595•Journal of Physics B Atomic Molecular and Optical Physics•May 19, 2010•22 citations
The three-level dye molecule single quantum system interacting with a cw laser field is investigated.The dynamic process of a single-molecule emitted photon is described by rate equations with absorbing boundary condition.It is demonstrated that the dynamics of the single-molecule processes and the statistics of time-resolved photon detection can be conveniently described in terms of renewal stochastic processes.The approach of calculating the correlation function by calculating the delay function that is an important physics quantity reflecting single quantum system dynamic process is given,and explicit expressions of correlation functions for two-levels and two-states systems are derived.This approach can be used for calculate dynamics parameter of molecular transition based on the fluorescence intensity correlation function.
A theory is formulated for time dependent fluctuations of the spectrum of a single molecule in a dynamic environment. In particular, we investigate the photon counting statistics of a single molecule undergoing a spectral diffusion process. Based on the stochastic optical Bloch equation, fluctuations are characterized by Mandel's QQQ parameter yielding the variance of number of emitted photons and the second order intensity correlation function, g(2)(t)g^{(2)}(t)g(2)(t). Using a semi-classical approach and linear response theory, we show that the QQQ parameter can be described by a three-time dipole correlation function. This approach gene ralizes the Wiener-Khintchine formula that gives the average number of fluorescent photons in terms of a one-time dipole correlation function. We classify the time ordering properties of the three-time dipole correlation function, and show that it can be represented by three different pulse shape functions similar to those used in the context of nonlinear spectroscopy. An exact solution is found for a single molecule whose absorption frequency undergoes a two state random telegraph process (i.e., the Kubo-Anderson sudden jump process.) Simple expressions are obtained from the exact solution in the slow and fast modulation regimes based on appropriate approximations for each case. In the slow modulation regime QQQ can be large even in the long time limit, while in the fast modulation regime it becomes small.
We derive the moment generating function for photon emissions from a single molecule driven by laser excitation. The frequencies of the fluoresced photons are explicitly considered. Calculations are performed for the case of a two-level dye molecule, showing that measured photon statistics will display a strong and nonintuitive dependence on detector bandwidth. Moreover, it is demonstrated that the antibunching phenomenon, associated with negative values of Mandel's Q parameter, results from correlations between photons with well separated frequencies.
The stream of photons emitted by a single quantum system such as a molecule or a nanocrystal is often statistically characterized by the distribution of delays between consecutive photons, or by the autocorrelation function of the intensity, or by the distributions of on- and off-times. We derive and discuss general relations between their Laplace transforms, addressing the influence of detection yield and background. Our analytical treatment applies to any distribution of delays and to random telegraph signals, including nonexponential distributions. We examine the special case of systems switching between two states characterized by different distributions of delays, where the switching can obey various statistics. We show that the second-order autocorrelation function keeps track of long-time fluctuations which are obviously lost in averaging the distributions of delays. We apply our formalism to random telegraphs, in particular to those with power-law distributions of on- and/or of off-times, which are encountered in the blinking of single semiconductor nanocrystals.
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.
In this paper, we develop a quantum-jump approach for describing the photon emission process of single fluorophore systems coupled to complex classically fluctuating reservoirs. The formalism relies on an open quantum system approach where the dynamics of the system and the reservoir fluctuations are described through a density matrix whose evolution is defined by a Lindblad rate equation. For each realization of the photon-measurement processes it is possible to define a conditional system state (stochastic density matrix) whose evolution depends on both the photon detection events and the fluctuations between the configurational states of the reservoir. In contrast to standard fluorescent systems the photon-to-photon emission process is not a renewal one, being defined by a (stochastic) waiting time distribution that in each recording event parametrically depends on the conditional state. The formalism allows calculating experimental observables such as the full hierarchy of joint probabilities associated with the time intervals between consecutive photon recording events. These results provide a powerful basis for characterizing different situations arising in single-molecule spectroscopy, such as spectral fluctuations, lifetime fluctuations and light-assisted processes.