Physics Problem Solving: ISAAC-II

Abstract

The quantum analogue of ptychography, a powerful coherent diffractive imaging technique, is a simple method for reconstructing <i>d</i>-dimensional pure states. It relies on measuring partially overlapping parts of the input state in a single orthonormal basis and feeding the outcomes to an iterative phase retrieval algorithm for postprocessing. We provide a proof of concept demonstration of this method by determining pure states given by superpositions of <i>d</i> transverse spatial modes of an optical field. A set of <i>n</i> rank-<i>r</i> projectors, diagonal in the spatial mode basis, is used to generate <i>n</i> partially overlapping parts of the input, and each part is projectively measured in the Fourier transformed basis. For <i>d</i> up to 32, we successfully reconstructed hundreds of random states using <i>n</i>=5 and <i>n</i>=<i>d</i> rank-⌈<i>d</i>/2⌉ projectors. The extension of quantum ptychography for other types of photonic spatial modes is outlined.