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Optics Express

Non-iterative imaging of inhomogeneous cold atom clouds using phase retrieval from a single diffraction measurement

David V. Sheludko, A. J. McCulloch, M. Jasperse, Harry M. Quiney, Robert E Scholten

Published Jan 13, 2010• 10 citations

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.

DOI: 10.1364/oe.18.001586

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We consider the inverse problem of in-line holography, applied to minimally destructive imaging of cold atom clouds. Absorption imaging near resonance provides a simple, but destructive measurement of atom column density. Imaging off resonance greatly reduces heating, and sequential images may be taken. Under the conditions required for off-resonant imaging, the generally intractable inverse problem may be linearized. A minimally destructive, quantitative and high-resolution image of the atom cloud column density is then retrieved from a single diffraction pattern.

Imaging cold atom samples provides interesting opportunities for studying not only the external atomic distribution, but also the internal atomic state, particularly for atoms prepared in a coherent state. We have previously developed techniques for off-resonant imaging of a cold atom cloud, without optical elements, computationally extracting the atomic column density map from a diffraction pattern (diffraction contrast imaging or DCI). We are now combining two lasers and three atomic states in a Λ-system to explore atomic coherence via two-dimensional imaging of electromagnetically induced transparency.

Atomic coherence phenomena are usually investigated using single beam techniques without spatial resolution. Here we demonstrate state-selective imaging of cold

^{85}\text{R}\text{b}

atoms in a three-level ladder system, where the atomic refractive index is sensitive to the quantum coherence state of the atoms. We use a phase-sensitive diffraction contrast imaging (DCI) technique which depends on the complex refractive index of the atom cloud. A semiclassical model allows us to analytically calculate the detuning-dependent refractive index of the system. The predicted Autler-Townes splitting and our experimental measurements are in excellent agreement. DCI provided a quantitative image of the distribution of the excited-state fraction, and compared with on-resonance absorption and blue cascade fluorescence techniques, was found to be experimentally simple and robust.

The propagation of light in moving media is dragged by atomic motion. The light-drag effect can be dramatically enhanced by reducing the group velocity with electromagnetically induced transparency (EIT). We develop a systematic procedure to accurately reconstruct the complex wavefront of the slow light with single-shot measurements, enabling precise, photon shot-noise-limited spectroscopic measurements of atomic response across EIT even in the presence of generic atomic number fluctuations. Applying the technique to an expanding cloud of cold atoms, we demonstrate simultaneous inference of the atomic density distribution and the velocity field from the complex imaging data. This inline imaging technique may assist a wide range of cold-atom experiments to access spectroscopic and phase-space information with in situ and minimally destructive measurements.

We have investigated state-selective diffraction contrast imaging (DCI) of cold 85 Rb atoms in the first excited (5 2 P 3/2 ) state. Excited-state DCI requires knowledge of the complex refractive index of the atom cloud, which was calculated numerically using a semi-classical model. The Autler-Townes splitting predicted by the model was verified experimentally, showing excellent agreement. 780 nm lasers were used to cool and excite atoms within a magneto-optical trap, and the atoms were then illuminated by a 776 nm imaging laser. Several excited-state imaging techniques, including blue cascade fluorescence, on-resonance absorption, and DCI have been demonstrated. Initial results show that improved signal-to-noise ratio (SNR) will be required to accurately determine the excited state fraction. We have demonstrated magnetic field gradient compression of the cold atom cloud, and expect that further progress on compression and additional cooling will achieve sufficient diffraction contrast for quantitative state-selective imaging.