Nonexponential statistics of fluorescence photobleaching

In this paper, I consider theoretical models of the decay via photobleaching of a sample of surface-immobilized fluorescent molecules excited by a spatially varying laser intensity profile. I show that, with mild restrictions on the photobleaching mechanism, the fluorescence decay measured in a nonuniform excitation profile is always nonexponential. Under the same conditions, the fluorescence decay can always be approximated by a discrete sum of exponentials. A particular example is given in which a homogeneous population of fluorophores with a single (intensity-dependent) photobleaching lifetime, when illuminated by a Gaussian laser, exhibits power law fluorescence decay at long times. These results indicate that the observation of multiple exponentials in single molecule or ensemble photobleaching lifetime measurements can arise solely as an artifact of a spatially varying laser profile and is not necessarily indicative of heterogeneity in molecular internal states, conformation, or local environment

Tracking-FCS: Fluorescence correlation spectroscopy of individual particles

We exploit recent advances in single-particle tracking to perform fluorescence correlation spectroscopy on individual fluorescent particles, in contrast to traditional methods that build up statistics over a sequence of many measurements. By rapidly scanning the focus of an excitation laser in a circular pattern, demodulating the measured fluorescence, and feeding these results back to a piezoelectric translation stage, we track the Brownian motion of fluorescent polymer microspheres in aqueous solution in the plane transverse to the laser axis. We discuss the estimation of particle diffusion statistics from closed-loop position measurements, and we present a generalized theory of fluorescence correlation spectroscopy for the case that the motion of a single fluorescent particle is actively tracked by a time-dependent laser intensity. We model the motion of a tracked particle using Ornstein-Uhlenbeck statistics, using a general theory that contains a umber of existing results as specific cases. We find good agreement between our theory and experimental results, and discuss possible future applications of these techniques to passive, single-shot, single-molecule fluorescence measurements with many orders of magnitude in time resolution

Interaction of a ring-reinforced shell and a fluid medium

Transient dynamic response of periodically ring- reinforced, infinitely long, circular cylindrical shell to uniform pressure applied through surrounding acoustic mediu

On the noise-induced passage through an unstable periodic orbit II: General case

Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the system's first exit from the interior of the unstable orbit occurs, typically displays the phenomenon of cycling: The distribution of first-exit locations is translated along the unstable periodic orbit proportionally to the logarithm of the noise intensity as the noise intensity goes to zero. We show that for a large class of such systems, the cycling profile is given, up to a model-dependent change of coordinates, by a universal function given by a periodicised Gumbel distribution. Our techniques combine action-functional or large-deviation results with properties of random Poincar\'e maps described by continuous-space discrete-time Markov chains.Comment: 44 pages, 4 figure

Feedback localization of freely diffusing fluorescent particles near the optical shot-noise limit

We report near-optimal tracking of freely diffusing fluorescent particles in a quasi-two-dimensional geometry via photon counting and real-time feedback. We present a quantitative statistical model of our feedback network and find excellent agreement with the experiment. We monitor the motion of a single fluorescent particle with a sensitivity of 15 nm/sqrt Hz while collecting fewer than 5000 fluorescence photons/s. Fluorescent microspheres (diffusion coefficient 1.3 μm^2/s) are tracked with a root-mean-square tracking error of 170 nm, within a factor of 2 of the theoretical limit set by photon counting shot noise

The effect of additive noise on dynamical hysteresis

We investigate the properties of hysteresis cycles produced by a one-dimensional, periodically forced Langevin equation. We show that depending on amplitude and frequency of the forcing and on noise intensity, there are three qualitatively different types of hysteresis cycles. Below a critical noise intensity, the random area enclosed by hysteresis cycles is concentrated near the deterministic area, which is different for small and large driving amplitude. Above this threshold, the area of typical hysteresis cycles depends, to leading order, only on the noise intensity. In all three regimes, we derive mathematically rigorous estimates for expectation, variance, and the probability of deviations of the hysteresis area from its typical value.Comment: 30 pages, 5 figure

Femtosecond wavepacket interferometry using the rotational dynamics of a trapped cold molecular ion

A Ramsey-type interferometer is suggested, employing a cold trapped ion and two time-delayed off-resonant femtosecond laser pulses. The laser light couples to the molecular polarization anisotropy, inducing rotational wavepacket dynamics. An interferogram is obtained from the delay dependent populations of the final field-free rotational states. Current experimental capabilities for cooling and preparation of the initial state are found to yield an interferogram visibility of more than 80\%. The interferograms can be used to determine the polarizability anisotropy with an accuracy of about $\pm 2\%$, respectively $\pm 5\%$, provided the uncertainty in the initial populations and measurement errors are confined to within the same limits

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 timescale 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 Forster theory. With further characterization we believe that FRET photon statistics could provide a unique tool for studying DNA mechanics on timescales from 10^-9 to 10^-3 s.Comment: 4 pages, 4 figures, submitted to Physical Review Letter