Photon Statistics and Dynamics of Fluorescence Resonance Energy Transfer

We report high time-resolution measurements of photon statistics from pairs of dye molecules coupled by fluorescence resonance energy transfer (FRET). In addition to quantum-optical photon antibunching, we observe photon bunching on a time scale of several nanoseconds. We show by numerical simulation that configuration fluctuations in the coupled fluorophore system could account for minor deviations of our data from predictions of basic Förster theory. With further characterization we believe that FRET photon statistics could provide a unique tool for studying DNA mechanics on time scales from ${10}^{-9}–{10}^{-3}\mathrm{}\mathrm{s}$.

Figure 1

Energy-level diagram of molecular states relevant to the basic Förster model. Donor states on the left are coupled by FRET to acceptor states on the right.

Figure 2

Schematic diagram of the apparatus. When making cross-correlation measurements, the $50/50$ beam splitters are removed to improve collection efficiency. Spectral filters and focusing optics at the APDs are not shown.

Figure 3

Measured correlation functions for high FRET-efficiency donor-acceptor pair fluorescence. Top: donor intensity autocorrelation (partially contaminated by inactive Cy5). Middle: acceptor intensity autocorrelation. Bottom: donor-acceptor cross correlation, the average intensity in the acceptor channel, given a photon arrival in the donor channel at $\tau =0$. See text for a discussion of the bunching at $\sim \pm 5\mathrm{n}\mathrm{s}$ in the acceptor autocorrelation.

Figure 4

Monte Carlo calculation of correlation functions for a jump-process Förster transfer rate with correlation time ${\tau }_F=7$. Top: donor intensity autocorrelation. Middle: acceptor intensity autocorrelation. Bottom: donor-acceptor cross correlation. The smooth curves are deterministic simulations with fixed ${\Gamma }_F(t)=⟨{\Gamma }_F⟩$. The parameters used were ${\Gamma }_1={\Gamma }_2=1$, ${\Gamma }_F^H=10$, ${\Gamma }_F^L=0$, $f=0.1$. All rates (times) are in units of the laser excitation rate ${\Gamma }_L$ ($1/{\Gamma }_L$).