Andrew J. Berglund

Optimal diffusion coefficient estimation in single-particle tracking

Single-particle tracking is increasingly used to extract quantitative parameters on single molecules and their environment, while advances in spatial and temporal resolution of tracking techniques inspire new questions and avenues of investigation. Correspondingly, sophisticated analytical methods are constantly developed to obtain more refined information from measured trajectories. Here we point out some fundamental limitations of these approaches due to the finite length of trajectories, the presence of localization error, and motion blur, focusing on the simplest motion regime of free diffusion in an isotropic medium (Brownian motion). We show that two recently proposed algorithms approach the theoretical limit of diffusion coefficient uncertainty. We discuss the practical performance of the algorithms as well as some important implications of these results for single-particle tracking.

Fast, bias-free algorithm for tracking single particles with variable size and shape.

We introduce a fast and robust technique for single-particle tracking with nanometer accuracy. We extract the center-of-mass of the image of a single particle with a simple, iterative algorithm that efficiently suppresses background-induced bias in a simplistic centroid estimator. Unlike many commonly used algorithms, our position estimator requires no prior information about the shape or size of the tracked particle image and uses only simple arithmetic operations, making it appropriate for future hardware implementation and real-time feedback applications. We demonstrate it both numerically and experimentally, using an inexpensive CCD camera to localize 190 nm fluorescent microspheres to better than 5 nm.

Manipulating Quantum Dots to Nanometer Precision by Control of Flow

We present a method for manipulating preselected quantum dots (QDs) with nanometer precision by flow control. The accuracy of this approach scales more favorably with particle size than optical trapping, enabling more precise positioning of nanoscopic particles. We demonstrate the ability to position a single QD in a 100 microm working region to 45 nm accuracy for holding times exceeding one hour and the ability to take active quantum measurements on the dynamically manipulated QD.

Narrow-Line Magneto-Optical Cooling and Trapping of Strongly Magnetic Atoms

Laser cooling on weak transitions is a useful technique for reaching ultracold temperatures in atoms with multiple valence electrons. However, for strongly magnetic atoms a conventional narrow-line magneto-optical trap (MOT) is destabilized by competition between optical and magnetic forces. We overcome this difficulty in Er by developing an unusual narrow-line MOT that balances optical and magnetic forces using laser light tuned to the blue side of a narrow (8 kHz) transition. The trap population is spin polarized with temperatures reaching below 2 muK. Our results constitute an alternative method for laser cooling on weak transitions, applicable to rare-earth-metal and metastable alkaline earth elements.

Sub-Doppler laser cooling and magnetic trapping of erbium

We investigate cooling mechanisms in magneto-optically and magnetically trapped erbium. We find efficient sub-Doppler cooling in our trap, which can persist even in large magnetic fields due to the near degeneracy of two Lande g factors. Furthermore, a continuously loaded magnetic trap is demonstrated where we observe temperatures below 25 {mu}K. These favorable cooling and trapping properties suggest a number of scientific possibilities for rare-earth-metal atomic physics, including narrow linewidth laser cooling and spectroscopy, unique collision studies, and degenerate bosonic and fermionic gases with long-range magnetic dipole coupling.

Super-resolution Optical Measurement of Nanoscale Photoacid Distribution in Lithographic Materials

We demonstrate a method using photoactivation localization microscopy (PALM) in a soft-material system, with a rhodamine-lactam dye that is activated by both ultraviolet light and protonation, to reveal the nanoscale photoacid distribution in a model photoresist. Chemically amplified resists are the principal lithographic materials used in the semiconductor industry. The photoacid distribution generated upon exposure and its subsequent evolution during post-exposure bake is a major limiting factor in determining the resolution and lithographic quality of the final developed resist image. Our PALM data sets resolve the acid distribution in a latent image with subdiffraction limit accuracy. Our overall accuracy is currently limited by residual mechanical drift.

Simultaneous positioning and orientation of a single nano-object by flow control: theory and simulations

In this paper, we theoretically describe a method to simultaneously control both the position and orientation of single nano-objects in fluids by precisely controlling the flow around them. We develop and simulate a control law that uses electro-osmotic flow (EOF) actuation to translate and rotate rigid nano-objects in two spatial dimensions. Using EOF to control nano-objects offers advantages as compared to other approaches: a wide class of objects can be manipulated (no magnetic or electric dipole moments are needed), the object can be controlled over a long range (>100 μm) with sub-micrometer accuracy, and control may be achieved with simple polydimethylsiloxane (PDMS) devices. We demonstrate the theory and numerical solutions that will enable deterministic control of the position and orientation of a nano-object in solution, which can be used, for example, to integrate nanostructures in circuits and orient sensors to probe living cells.

Theoretical model of errors in micromirror-based three-dimensional particle tracking.

Several recently developed particle-tracking and imaging methods have achieved three-dimensional sensitivity through the introduction of angled micromirrors into the observation volume of an optical microscope. We model the imaging response of such devices and show how the direct and reflected images of a fluorescent particle are affected. In particle-tracking applications, asymmetric image degradation manifests itself as systematic tracking errors. Based on our results, we identify strategies for reducing systematic errors to the 10nm level in practical applications.

Optimal laser scan path for localizing a fluorescent particle in two or three dimensions

Localizing a fluorescent particle by scanning a focused laser beam in its vicinity and analyzing the detected photon stream provides real-time information for a modern class of feedback control systems for particle tracking and trapping. We show for the full range of standard merit functions based on the Fisher information matrix (1) that the optimal path coincides with the positions of maximum slope of the square root of the beam intensity rather than with the intensity itself, (2) that this condition matches that derived from the theory describing the optimal design of experiments and (3) that in one dimension it is equivalent to maximizing the signal to noise ratio. The optimal path for a Gaussian beam scanned in two or three dimensions is presented along with the Cramer-Rao bound, which gives the ultimate localization accuracy that can be achieved by analyzing the detected photon stream. In two dimensions the optimum path is independent of the chosen merit function but this is not the case in three dimensions. Also, we show that whereas the optimum path for a Gaussian beam in two dimensions can be chosen to be continuous, it cannot be continuous in three dimensions.

Controlled placement of single photon sources for quantum integration

Controlled manipulation of quantum dots with nanometer precision is an essential capability for basic science as well as for scalable engineering of nanophotonic and quantum optical devices. The most common methods for manipulation of particles use optical or dielectric trapping forces which scale poorly with particle size, making it difficult to manipulate single quantum dots. Here we demonstrate a particle manipulation technique that achieves nanometer positioning by controlling the flow of the surrounding liquid. This approach scales much more favorable with particle size, enabling the position of colloidal quantum dots with better precision. Using this approach we demonstrate the capture, quantum optical characterization, and manipulation of individually selected single quantum dots with up to 45.5 nm precision for times exceeding one hour. This technique can be used to place pre-selected single photon sources in nanophotonic structures such as cavities and waveguides for engineering of integrated quantum optical devices.