Quantum jumps and photon statistics 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.

Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction

“…Our derivations follow the theory originally developed in quantum optics to study single photon counting statistics 31,39,40 and extended to quantum transport by Brandes.…”

Non-Markovianity through multipartite correlation measures

“…(16) and (17) define the unitary and dissipative dynamics for the two-qubit system, given that the bath is in configurational state 1 and configurational state 2, respectively. The constants {γ [40,42]. On the other hand, the second line of Eqs.…”

Counting quantum jumps: A summary and comparison of fixed-time and fluctuating-time statistics in electron transport

“…As we will observe, nonrenewal dynamics can emerge even under the Markovian assumption, indicating that correlations between successive waiting times arise from the internal dynamics of the quantum system. Although in mesoscopic electron transport, non-renewal statistics are a relatively new research premise [35,36,38,40,42,45,83], they have a long history in chemical physics, where they were used to describe single-molecule processes in spectroscopy [105][106][107]127] and kinetics [104,128].…”

“…For equilibrated phonons, the definition in Eq. (105) indicates that the FPTD behavior will be determined by two poles at z = −(T 10 + T 01 ) ± (T 10 + T 01 ) 2 − 4T 10 T D 01 ; (184) however, for the parameters chosen, T 01 ≈ T D 01 and the transport is dominated by one pole at approximately −(T 10 + T 01 ). This is the behavior observed in Fig.(2a).…”