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Optics Express

Phase shifting interferometry of cold atoms

Tzu-Ping Ku, Chi‐Yuan Huang, Bor-Wen Shiau, Dian-Jiun Han

Published Feb 11, 2011• 6 citations
Publisher

Abstract

We propose a scheme to engage phase shifting interferometry on cold atomic samples and present the simulation results under several experimentally achievable conditions nowadays. This method allows far-detuning, low power probing, and is intrinsically nondestructive. This novel detection means yields image quality superior to the conventional phase contrast imaging at certain conditions and could be experimentally realized. Furthermore, the longitudinal resolution of imaging by this manner is mainly set by optical interference and can be better than the diffraction limit. This scheme also provides special advantages to diagnose the surface-trapped clouds, with which phase imaging on the fabricated wires and atoms altogether is possible as well.

DOI
10.1364/oe.19.003730

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We propose a scheme to engage phase shifting interferometry on cold atomic samples and present the simulation results under several experimentally achievable conditions nowadays. This method allows far-detuning, low power probing, and is intrinsically nondestructive. This novel detection means yields image quality superior to the conventional phase contrast imaging at certain conditions and could be experimentally realized. Furthermore, the longitudinal resolution of imaging by this manner is mainly set by optical interference and can be better than the diffraction limit. This scheme also provides special advantages to diagnose the surface-trapped clouds, with which phase imaging on the fabricated wires and atoms altogether is possible as well.
We propose a lens-free nondestructive imaging method for cold atomic clouds using a Gaussian beam accompanied with phase shifting interferometry. This scheme requires no imaging lens. Hence, aberrations associated with it are completely eliminated and mechanical focusing can be avoided. Compared with the common single-beam nondestructive means, our proposed scheme lowers the energy per probe pulse delivered to the cold samples by almost three orders of magnitude, due to signal enhancement inherently provided in the two-beam configuration. Moreover, higher image resolution is attainable by magnifying the far-field interference distribution using a divergent Gaussian beam. We examine this novel lensless detection means for in situ imaging on typical cold atomic clouds under experimentally achievable conditions. Our simulations show the cloud position can be precisely determined, depending upon the cloud size and probe parameters, with an uncertainty from a few hundreds of micrometers to only a few micrometers, and the spatial resolution of the retrieved phase image can reach the diffraction limit.
We report experimental realization of lensless imaging on cold rubidium atoms confined in a magneto-optical trap. This imaging scheme relies on the off-resonant light refraction from the cold atoms and is employed in a phase-tunable Mach–Zehnder interferometer, accompanied with phase-shifting interferometry. With this setup, it allows obtaining the probe light phase distribution in the far field after passing the atoms, from which the near-field phase image of the atomic cloud is retrieved using the Fresnel–Kirchhoff integral. We show the phase images can be effectively reconstructed, and the measured two-dimensional phase distributions are in good agreement with the theory.
We demonstrate a new method for nondestructive imaging of laser-cooled atoms. This spatial heterodyne technique forms a phase image by interfering a strong reference laser beam with a weak probe beam that passes through the cold atom cloud. The figure of merit equals or exceeds that of phase-contrast imaging, and the technique can be used over a wider range of spatial scales. We show images of a dark-spot magneto-optic trap taken with imaging fluences as low as 61 pJ/cm(2) at a detuning of 11? , resulting in 0.0004 photons scattered per atom.
Point source atom interferometry (PSI) uses the velocity distribution in a cold atom cloud to simultaneously measure one axis of acceleration and two axes of rotation from the spatial distribution of interferometer phase in an expanded cloud of atoms. Previously, the interferometer phase has been found from the phase, orientation, and period of the resulting spatial atomic interference fringe images. For practical applications in inertial sensing and precision measurement, it is important to be able to measure a wide range of system rotation rates, corresponding to interferograms with far less than one full interference fringe to very many fringes. Interferogram analysis techniques based on image processing used previously for PSI are challenging to implement for low rotation rates that generate less than one full interference fringe across the cloud. We introduce a new experimental method that is closely related to optical phase-shifting interferometry that is effective in extracting rotation values from signals consisting of fractional fringes as well as many fringes without prior knowledge of the rotation rate. The method finds the interferometer phase for each pixel in the image from four interferograms, each with a controlled Raman laser phase shift, to reconstruct the underlying atomic interferometer phase map without image processing.
Point source atom interferometry (PSI) uses the velocity distribution in a cold atom cloud to simultaneously measure one axis of acceleration and two axes of rotation from the spatial distribution of interferometer phase in an expanded cloud of atoms. Previously, the interferometer phase has been found from the phase, orientation, and period of the resulting spatial atomic interference fringe images. For practical applications in inertial sensing and precision measurement, it is important to be able to measure a wide range of system rotation rates, corresponding to interferograms with far less than one full interference fringe to very many fringes. Interferogram analysis techniques based on image processing used previously for PSI are challenging to implement for low rotation rates that generate less than one full interference fringe across the cloud. We introduce a new experimental method that is closely related to optical phase-shifting interferometry that is effective in extracting rotation values from signals consisting of fractional fringes as well as many fringes without prior knowledge of the rotation rate. The method finds the interferometer phase for each pixel in the image from four interferograms, each with a controlled Raman laser phase shift, to reconstruct the underlying atomic interferometer phase map without image processing.