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Physical Review A

Light-assisted non-Poissonian fluorescence blinking from bosonic composite reservoirs

Adrián A. Budini

Published Aug 29, 2007• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.76.023825

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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.
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.
In this paper, single-molecule spectroscopy experiments based on continuous laser excitation are characterized through an open quantum system approach. The evolution of the fluorophore system follows from an effective Hamiltonian microscopic dynamic where its characteristic parameters, i.e., its electric dipole, transition frequency, and Rabi frequency, as well as the quantization of the background electromagnetic field and their mutual interaction, are defined in an extended Hilbert space associated to the different configurational states of the local nanoenvironment. After tracing out the electromagnetic field and the configurational states, the fluorophore density matrix is written in terms of a Lindblad rate equation. Observables associated to the scattered laser field, such as optical spectrum, intensity-intensity correlation, and photon-counting statistics, are obtained from a quantum-electrodynamic calculation also based on the effective microscopic dynamic. In contrast with stochastic models, this approach allows one to describe in a unified way both the full quantum nature of the scattered laser field as well as the classical nature of the environment fluctuations. By analyzing different processes such as spectral diffusion, lifetime fluctuations, and light assisted processes, we exemplify the power of the present approach.
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.
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.
Fluorescence from an ensemble of noninteracting molecules excited by continuous laser radiation is considered as a glow of M individual molecules. The expression that governs the autocorrelation function (ACF) of fluorescence from M molecules is derived based on the theoretical expression that governs the ACF of fluorescence from a single-molecule. Fluctuations of blinking fluorescence and its statistical properties are analyzed using a computer simulation. The results of statistical analysis of the computer experiment are in good agreement with the derived formula that governs the ACF of fluorescence from several molecules.
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.