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arXiv:cond-mat/9904032 · Physical Review A

Atom holography

O. Zobay, Elena V. Goldstein, P. Meystre

Published Nov 1, 1999• 15 citations
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Abstract

We study the conditions under which atomic condensates can be used as holographic recording media and then suggest a scheme which allows us to reconstruct the original object with an atomic reading beam. The recording method relies on the observation that the shape of a condensate in the Thomas-Fermi limit closely follows the form of the confining potential. Holographic information can thus be stored as density modulations. The reading scheme proceeds in analogy to optical Fresnel sideband holography with an atomic beam replacing the reading laser.

DOI
10.1103/physreva.60.3999

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We study the conditions under which atomic condensates can be used as holographic recording media and then suggest a scheme which allows us to reconstruct the original object with an atomic reading beam. The recording method relies on the observation that the shape of a condensate in the Thomas-Fermi limit closely follows the form of the confining potential. Holographic information can thus be stored as density modulations. The reading scheme proceeds in analogy to optical Fresnel sideband holography with an atomic beam replacing the reading laser.
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Bose-Einstein condensates are interesting systems for studying quantum mechanics. Absorption imaging and phase-contrast imaging are two methods that are often used to determine the absolute number of atoms in a condensate. This thesis proposes a third method: holographic imaging. This method relies on the interference of a probe beam, which passes through the condensate, and a reference beam. The phase shift of the light due to the atoms and the optical density of the condensate are reconstructed with the use of Fourier transformation. Up to 300 images can be taken \\textit{in situ}.\n\nThere are two interesting applications of holographic imaging. The first is the refractive index, which can be measured directly with holographic imaging. The Hartree-Fock model is used to relate the real and imaginary part of the refractive index to the degeneracy of the condensate. However, the preliminary results are ambiguous and require further study.\n\nThe second is spin-dependent imaging, in which two orthogonally polarized reference beams are used to reconstruct polarization dependent information. This can be applied to study the dynamics of spinor condensates. In this thesis, a proof of concept for this method is given.
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The temporal evolution of atomic wave packets interacting with object and reference electromagnetic waves is investigated, and an analytical solution for the off-resonant density matrix is presented. It is shown that, under certain physical conditions, the diffraction of an ultracold atomic beam by an inhomogeneous laser field can be interpreted as if the beam passes through a three-dimensional hologram. We show that high diffraction efficiencies can be realized if one restricts the extent of the atomic hologram in the time domain rather than in space. The hologram, thus, can work in a pulsed regime pumping atoms from the beam or from the initial wave packet into the reconstructed matter wave. The suggested regime is well compatible with the Raman cooling methods and the recent realization of an atom laser, which are capable of repeatedly reproducing coherent, or almost coherent, atomic wave packets necessary for the actual implementation of the reading beam. It is found that the diffraction efficiency of such a hologram may reach 100% and is determined by the duration of laser pulses. On this basis, a new method for the reconstruction of the object image with matter waves is offered. The latter may have useful practical applications, ranging from atom lithography, to the manufacturing of microstructures, and quantum microfabrication.