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

Abstract: 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 dynamic 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 to 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.