Photon counting statistics in the presence of spectral diffusion induced by nonequilibrium environmental fluctuations

We theoretically investigate the statistical properties of photon emission of a driven two-level single-molecule system undergoing spectral diffusion induced by nonequilibrium environmental fluctuations. Within the framework of the generating function method and the stochastic Liouville equation, we analyze the influence of the nonequilibrium characteristics of environmental fluctuations respectively governed by nonstationary Ornstein-Uhlenbeck noise and random telegraph noise on the photon counting statistics of the driven single-molecule system. In the slow modulation limit of spectral diffusion, the intensity and statistical fluctuations of photon emission depend on the environmental nonequilibrium characteristics at short time scales, whereas they become independent of the nonequilibrium characteristics of environmental fluctuations in the steady state. In the fast modulation limit of spectral diffusion, neither the line shape nor the Mandel's parameter depends on the environmental nonequilibrium characteristics owing to the rapid relaxation of environmental fluctuations. These findings not only shed light on the role of nonequilibrium environmental fluctuations in shaping the photon emission properties of single-molecule systems but also provide a basis for distinguishing between equilibrium and nonequilibrium characteristics of environmental fluctuations in experimental measurements.