An Intermittent Poisson Process Generating 1/f Noise with Possible Application to Fluorescence Intermittency

Abstract

Quantum dots (QD) and other nanoparticles exhibit fluorescence intermittency switching irregularly between bright ("on") and dark ("off") states. On- and off-times follow a power-law statistics with exponents ranging from -1 to -2. The empirical power spectral density of this two-state process shows a 1/fx shape with an exponent x reverting from ≈1 at low frequencies to ≈2 at high frequency. Based on theoretical considerations, the low frequency region can be attributed to the on-state; however, there are some discrepancies in attributing the off-states to the high frequency region. This difficulty can be overcome by introducing a Poisson process which is gated by the two-state process giving rise to an intermittent Poisson process (IPP); in this way, the statistical features of the two-state process are transferred to the IPP. The power spectral density of the IPP can be derived in closed form for arbitrarily distributed on/off-states. Besides shot noise the power spectrum of the IPP exhibits excess noise with two scaling regions which can be attributed to the respective on/off-states. The results are applied to interpret the power spectrum of fluorescence intermittency in QDs.