Bulk fluorescence measurements cannot probe the survival-time distribution of single molecules

Using a straightforward theoretical approach, we show that an ensemble of dyes with a simple first-order photobleaching kinetics yields a power-law decaying emission intensity in a heterogeneous excitation field in bulk fluorescence experiments. Our theoretical considerations are experimentally confirmed for two distinct classes of small organic fluorophores represented by the classical laser dye rhodamine-6G on glass in air and the cyanine dye DiI(C18) in a thin polymethylmethacrylate film. Our results provide evidence that the time course of bleaching in a bulk sample in general does not allow derivation of the properties of survival times of individual quantum systems.

Figure 1

Simplified Jablonski diagram for the bleaching of a fluorophore. Excitation from the ground state $\left(G\right)$ occurs with rate $\omega$ which depends on the illumination intensity. From the excited state $\left(E\right)$ relaxation to the ground state via spontanous emission of a photon is possible with rate $\Gamma$. Alternatively, a transition to the bleached state $\left(B\right)$ may occur with rate $\gamma$ which, in general, also depends on the illumination intensity.

Figure 2

Equation (5) yields a power-law decay $F\left(t\right)\sim 1∕t^{\alpha }$ for the fluorescence. The exponent $\alpha$ is near to unity for $\mu =0$ (highlighted by the dashed line) and decreases for increasing values of $\mu$. Inset: the exponent $\alpha$ is approximately given by $\alpha =1∕(1+\mu )$ (full line).

Figure 3

(a) Representative power-law decay $F\left(t\right)\sim 1∕t^{\alpha }$ $(\alpha \approx 0.83)$ of the bulk fluorescence for immobilized DiI. Inset: The exponent $\alpha$ increases logarithmically with the applied laser intensity $I_0$ (highlighted by the full line). (b) Representative power-law decay $F\left(t\right)\sim 1∕t^{\alpha }$ $(\alpha \approx 1)$ of the bulk fluorescence for immobilized Rh6G.