Extended Data Fig. 3: Determination of saturation parameter, transition coherence time, and excited-state lifetime for a single molecule.
a, Fluorescence excitation spectra at a series of excitation powers. The corresponding saturation parameters S are marked on the colour bar along with the power values. Solid lines represent fits to Lorentzian functions. The background, determined via Lorentzian fitting, has been subtracted from each spectrum. b, Extracted fluorescence intensity at a series of excitation powers (S parameters). The fluorescence intensity for each excitation power (S parameter) is extracted by fitting the excitation spectrum in a to a Lorentzian function, with the error bar representing the fitting uncertainty (1σ). The red curve is a fitting of the experimental data to the saturation curve \(I={I}_{{\rm{sat}}}/\left(1+{P}_{{\rm{sat}}}/P\right)\). c, Extracted linewidth Δν at a series of excitation powers (saturation parameters). The linewidth\(\Delta {\rm{\nu }}\) for each S is extracted by fitting the excitation spectrum to a Lorentzian function, with the error bar representing the fitting uncertainty (1σ). The red curve is a fitting of the experimental data to the theoretical expression \(\Delta {\rm{\nu }}=\sqrt{1+S}/\left(\pi {\tau }_{2}\right)\). From the fitting, the transition coherence time \({\tau }_{2}\) is determined to be 9.37 ± 0.43 ns, where the uncertainty is the fitting uncertainty (1σ). d, Photoluminescence decay curve. The red curve is a fitting of the experimental curve to an exponential decay function. From the fitting, the excited-state lifetime \({\tau }_{1}\) is determined to be 4.69 ± 0.03 ns, where the uncertainty is the fitting uncertainty (1σ).
