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Open Physics

Atom number calibration in absorption imaging at very small atom numbers

Gregory Konstantinidis, Melina Pappa, Gustav Wikström, Paul C. Condylis, Daniel Sahagún, Mark A. Baker, Olivier Morizot, Wolf von Klitzing

Published Jul 20, 2012• 10 citations
Publisher

Abstract

Abstract Cold atom experiments often use images of the atom clouds as their exclusive source of experimental information. The most commonly used technique is absorption imaging, which provides accurate information about the shapes of the atom clouds, but requires care when seeking the absolute atom number for small atom samples. In this paper, we present an independent, absolute calibration of the atom numbers. We directly compare the atom number detected using dark-ground imaging to the one observed by fluorescence imaging of the same atoms in a magneto-optical trap. We normalise the signal using single-atom resolved fluorescence imaging. In order to be able to image the absorption of the very low atom numbers involved, we use diffractive dark-ground imaging as a novel, ultra-sensitive method of in situ imaging for untrapped atom clouds down to only 100 atoms. We demonstrate that the Doppler shift due to the acceleration of the atoms by the probe beam has to be taken into account when measuring the atom-number.

DOI
10.2478/s11534-012-0108-x

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Abstract Cold atom experiments often use images of the atom clouds as their exclusive source of experimental information. The most commonly used technique is absorption imaging, which provides accurate information about the shapes of the atom clouds, but requires care when seeking the absolute atom number for small atom samples. In this paper, we present an independent, absolute calibration of the atom numbers. We directly compare the atom number detected using dark-ground imaging to the one observed by fluorescence imaging of the same atoms in a magneto-optical trap. We normalise the signal using single-atom resolved fluorescence imaging. In order to be able to image the absorption of the very low atom numbers involved, we use diffractive dark-ground imaging as a novel, ultra-sensitive method of in situ imaging for untrapped atom clouds down to only 100 atoms. We demonstrate that the Doppler shift due to the acceleration of the atoms by the probe beam has to be taken into account when measuring the atom-number.
Quantum degenerate Fermi gases and Bose–Einstein condensates give access to a vast new class of quantum states. The resulting multi-particle correlations place extreme demands on the detection schemes. Here we introduce diffractive dark-ground imaging as a novel ultra-sensitive imaging technique. Using only moderate detection optics, we image clouds of less than 30 atoms with near-atom shot-noise-limited signal-to-noise ratio and show Stern–Gerlach separated spinor condensates with a minority component of only seven atoms. This presents an improvement of more than one order of magnitude when compared to our standard absorption imaging. We also examine the optimal conditions for absorption imaging, including saturation and fluorescence contributions. Finally, we discuss potentially serious imaging errors of small atom clouds whose size is near the resolution of the optics.
Abstract The accurate determination of atom numbers is an ubiquitous problem in the field of ultracold atoms. For modest atom numbers, absolute calibration techniques are available, however, for large numbers and high densities, the available techniques neglect many-body scattering processes. Here, a spatial calibration technique for time-of-flight absorption images of ultracold atomic clouds is presented. The calibration is obtained from radially averaged absorption images and we provide a practical guide to the calibration process. It is shown that the calibration coefficient scales linearly with optical density and depends on the absorbed photon number for the experimental conditions explored here. This allows for the direct inclusion of a spatially dependent calibration in the image analysis. For typical ultracold atom clouds the spatial calibration technique leads to corrections in the detected atom number up to ≈ 12 % and temperature up to ≈ 14 % in comparison to previous calibration techniques. The technique presented here addresses a major difficulty in absorption imaging of ultracold atomic clouds and prompts further theoretical work to understand the scattering processes in ultracold dense clouds of atoms for accurate atom number calibration.
We develop a theoretical model for calibrating the absorption imaging of cold atoms under high magnetic fields. Particularly it also works when the hyperfine structure is decoupled and cannot provide good quantum numbers anymore. Compared with zero or low magnetic fields, for high magnetic fields the efficiency of the absorption imaging is lower, while an additional correction factor is required to obtain the absolute atom number under the Beer-Lambert law. Our model is based on the rate equations and can account for many experimental imperfections, such as Zeeman level crossing, off-resonant couplings, and low repumping efficiency. On the basis of this method, we can precisely calculate the correction factor for atom-number measurement without any empirical or fitting parameters. Meanwhile, we use a cold-atom apparatus based on 85Rb{}^{85}\mathrm{Rb}85Rb to experimentally verify our model. In addition, we find our work can also serve as a benchmark to measure the polarization impurity of a circularly polarized laser beam with high sensitivity. We believe this work will be beneficial for most cold-atom experiments using absorption imaging.
We describe an experimental method to calibrate an absorption imaging system for ultracold atom clouds. Optical density profiles of an atom cloud are obtained for various probe beam intensities and are analyzed to determine the correction factor for the effective probe beam intensity directly from saturation effects. We find that the temporal shape of the probe-beam pulse needs to be taken into account for a quantitative analysis of the optical density measured in saturation absorption imaging. We show that this pulse-shape effect can lead to distortion of the density profile due to its nonlinear dependence on the optical depth.
A majority of ultracold atom experiments utilize resonant absorption imaging techniques to obtain the atomic density. To make well-controlled quantitative measurements, the optical intensity of the probe beam must be precisely calibrated in units of the atomic saturation intensity I sat . In quantum gas experiments, the atomic sample is enclosed in an ultra-high vacuum system that introduces loss and limits optical access; this precludes a direct determination of the intensity. Here, we use quantum coherence to create a robust technique for measuring the probe beam intensity in units of I sat via Ramsey interferometry. Our technique characterizes the ac Stark shift of the atomic levels due to an off-resonant probe beam. Furthermore, this technique gives access to the spatial variation of the probe intensity at the location of the atomic cloud. By directly measuring the probe intensity just before the imaging sensor our method in addition yields a direct calibration of imaging system losses as well as the quantum efficiency of the sensor.
We propose and demonstrate an experimental method to measure by absorption imaging the size and local column density of a cloud of atoms, even when its smallest dimension is smaller than the resolution of the imaging system. To do this, we take advantage of the fact that, for a given total number of atoms, a smaller and denser cloud scatters less photons when the gas is optically thick. The method relies on making an ansatz on the cloud shape along the unresolved dimension(s) and on providing an additional information, such as the total number of atoms. We demonstrate the method on in situ absorption images of elongated 87Sr^{87}\mathrm{Sr}87Sr Fermi gases. We find significant nonlinear corrections to the estimated size and local density of the cloud compared to a standard analysis. This allows us to recover an undistorted longitudinal density profile and to measure transverse sizes as small as one-fourth of our imaging resolution. The ultimate limit of our method is the wavelength that is used for imaging.