Dr. Michal Karski  

We report on image processing techniques and experimental procedures to determine the latticesite positions of single atoms in an optical lattice with high reliability, even for limited acquisition time or optical resolution. Determining the positions of atoms beyond the diffraction limit relies on parametric deconvolution in close analogy to methods employed in superresolution microscopy. We develop a deconvolution method that makes effective use of the prior knowledge of the optical transfer function, noise properties, and discreteness of the optical lattice. We show that accurate knowledge of the image formation process enables a dramatic improvement on the localization reliability. This allows us to demonstrate superresolution of the atoms' position in closely packed ensembles where the separation between particles cannot be directly optically resolved. Furthermore, we demonstrate experimental methods to precisely reconstruct the point spread function with subpixel resolution from fluorescence images of single atoms, and we give a mathematical foundation thereof. We also discuss discretized image sampling in pixel detectors and provide a quantitative model of noise sources in electron multiplying CCD cameras. The techniques developed here are not only beneficial to neutral atom experiments, but could also be employed to improve the localization precision of trapped ions for ultra precise force sensing.
Engineering quantum particle systems, such as quantum simulators and quantum cellular automata, relies on full coherent control of quantum paths at the single particle level. Here we present an atom interferometer operating with single trapped atoms, where single particle wave packets are controlled through spindependent potentials. The interferometer is constructed from a sequence of discrete operations based on a set of elementary building blocks, which permit composing arbitrary interferometer geometries in a digital manner. We use this modularity to devise a spacetime analogue of the wellknown spin echo technique, yielding insight into decoherence mechanisms. We also demonstrate mesoscopic delocalization of single atoms with a separationtolocalization ratio exceeding 500; this result suggests their utilization beyond quantum logic applications as nanoresolution quantum probes in precision measurements, being able to measure potential gradients with precision 5×10^{4} in units of gravitational acceleration g.
We have directly observed spindependent transport of single cesium atoms in a 1D optical lattice. A superposition of two circularly polarized standing waves is generated from two counter propagating, linearly polarized laser beams. Rotation of one of the polarizations by π causes displacement of the σ^{+} and σ^{–}lattices by one lattice site. Unidirectional transport over several lattice sites is achieved by rotating the polarization back and forth and flipping the spin after each transport step. We have analyzed the transport efficiency over 10 and more lattice sites, and discussed and quantified relevant error sources.