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In this paper, we develop a quantum-jump approach for describing thephoton-emission process of single fluorophore systems coupled to complexclassically fluctuating reservoirs. The formalism relies on an open quantumsystem approach where the dynamic of the system and the reservoir fluctuationsare described through a density matrix whose evolution is defined by a Lindbladrate equation. For each realization of the photon measurement processes it ispossible to define a conditional system state (stochastic density matrix) whoseevolution depends on both the photon detection events and the fluctuationsbetween the configurational states of the reservoir. In contrast to standardfluorescent systems the photon-to-photon emission process is not a renewal one,being defined by a (stochastic) waiting time distribution that in eachrecording event parametrically depends on the conditional state. The formalismallows calculating experimental observables such as the full hierarchy of jointprobabilities associated to the time intervals between consecutive photonrecording events. These results provide a powerful basis for characterizingdifferent situations arising in single-molecule spectroscopy, such as spectralfluctuations, lifetime fluctuations, and light assisted processes.

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