Abstract
We demonstrate a new imaging technique for cold atom clouds based on phase retrieval from a single diffraction measurement. Most single-shot diffractive imaging methods for cold atoms assume a monomorphic object to extract the column density. The method described here allows quantitative imaging of an inhomogeneous cloud, enabling recovery of either the atomic density or the refractive index, provided the other is known. Using ideas borrowed from density functional theory, we calculate the approximate paraxial diffracted intensity derivative from the measured diffracted intensity distribution and use it to solve the Transport of Intensity Equation (TIE) for the phase of the wave at the detector plane. Back-propagation to the object plane yields the object exit surface wave and then provides a quantitative measurement of either the atomic column density or refractive index. Images of homogeneous clouds showed good quantitative agreement with conventional techniques. An inhomogeneous cloud was created using a cascade electromagnetically induced transparency scheme and images of both phase and amplitude parts of refractive index across the cloud were separately retrieved, showing good agreement with theoretical results.
Highlights
Measurement of the spatial distribution of cold atoms has become increasingly important with the development of ultracold atom trapping and experiments in a diverse range of applications
We are interested in imaging of cold atoms as a means of controlling electron bunch shapes generated from Ultracold Plasma (UCP)
Electron bunches extracted from an UCP are potentially much brighter than conventional thermal sources [8] and in the long-term offer the possibility of sufficient brightness for single-shot diffractive imaging of bio-molecules
Summary
Measurement of the spatial distribution of cold atoms has become increasingly important with the development of ultracold atom trapping and experiments in a diverse range of applications. Atomic coherence processes, such as generation of entangled states in the Rydberg blockade regime [2, 3], Electromagnetically Induced Transparency (EIT) [4] and slow light [5] are all typically investigated using simple probe beam techniques which do not provide spatially resolved information. Each with a spatially varying intensity profile, will interact with the cold atoms to produce the UCP The effect of these fields on the refractive index of the cloud will result in an inhomogeneous atom cloud. Electron bunches extracted from an UCP are potentially much brighter than conventional thermal sources [8] and in the long-term offer the possibility of sufficient brightness for single-shot diffractive imaging of bio-molecules
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