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Physical Review A

State-selective imaging of cold atoms

David V. Sheludko, Simon C. Bell, R. P. Anderson, C. S. Hofmann, Edgar J. D. Vredenbregt, Robert E Scholten

Published Mar 5, 2008• 30 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.77.033401

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Atomic coherence phenomena are usually investigated using single beam techniques without spatial resolution. Here we demonstrate state-selective imaging of cold 85Rb^{85}\text{R}\text{b}85Rb 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.
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.
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.
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.
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.
Cold atoms are a quantum system well-isolated from the environment. Since the 80s, they have been used to make high-sensitivity atomic sensors and to deepen the understanding of quantum physics phenomena. At low temperatures, degenerate atomic gas regimes can be reached. They are characterized by a macroscopic quantum state that can be manipulated and controlled by lasers. Placing such atomic wave function in optical lattices provide a way to study the dynamics of complex many-body systems. In this context, diffraction-limited quantum gas microscopes have emerged as standard tools to probe such complex systems and to measure atomic density correlations between lattice sites. By further reducing the optical lattices dimensions, the energy scales are strongly enhanced and favor novel quantum phases. Such reduction of optical lattice dimensions requires novel trapping and imaging techniques to manipulate cold-atoms with subwavelength spatial resolutions.In this PhD thesis, we experimentally perform subwavelength imaging of ultra-cold atoms of Rubidium 87 using a dressed excited state method, initially proposed for generating subwavelength trapping potentials. The measurement are performed using in situ absorption imaging. A quantitative comparison of data and theory lead us to reinterprete and modify a method for atom number calibrations that is commonly used in the community. This reinterpretation requires a fine understanding of the interaction of a single quantum multi-level system and a coherent saturating field. The measurement of the in situ transmission of a coherent probe shows a linear reduction of the single-atom scattering cross-section with the optical density for which we propose a physical interpretation and a model. Once calibrated, we use our subwavelength imaging method that reaches down to 20 nm resolution in a few microseconds to super-resolve a tiny quantum object : the longitudinal wave function of a BEC in a very tight lattice.