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Physical Review A

Measuring the quantum state of an electromagnetic field using the atomic Talbot effect

Bernd Rohwedder, L. Davidovich, Nicim Zagury

Published Jul 1, 1999• 9 citations
Publisher

Abstract

Fractional Talbot images in the de Broglie near field of atoms diffracted by a dispersive light grating allow the measurement of the quantum state of an electromagnetic field in a cavity, in the optical domain. In particular, the photon-number statistics may be obtained, in principle, through a single experimental realization. It may be expressed as a Fourier transform of the atomic density on a plane situated at one-fourth of the Talbot distance from the light grating. The proposed measurement of the density matrix of a standing light wave using ``Talbot fingerprints'' should be feasible within the present state of the art.

DOI
10.1103/physreva.60.480

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Atom Optical Elements Based on Near-field Grating Sequences

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Fortschritte der Physik•Dec 1, 1999•11 citations
Fractional Talbot images in the de Broglie near field of atoms diffracted by a dispersive light grating allow the measurement of the quantum state of an electromagnetic field in a cavity, in the optical domain. In particular, the photon-number statistics may be obtained, in principle, through a single experimental realization. It may be expressed as a Fourier transform of the atomic density on a plane situated at one-fourth of the Talbot distance from the light grating. The proposed measurement of the density matrix of a standing light wave using ``Talbot fingerprints'' should be feasible within the present state of the art.
We have demonstrated the Talbot-Lau effect for atomic de Broglie waves in the time domain. This effect is based on Fresnel diffraction of matter waves from an incoherent source. In the experiment, de Broglie waves of atoms in a particular internal state have been manipulated and the resulting density directly imaged by resonant optical fields. These experiments allow us to probe the quantum dynamics of the atomic center of mass. We have also used this effect to create patterns in the density of the atoms with period as small as 1∕101∕101∕10 of the optical wavelength, demonstrating the potential application of this technique for atom nanofabrication.
We report the first experimental observation of quantum Talbot effects with single photons and entangled photon pairs. Both the first- and second-order quantum Talbot self-images are observed experimentally. They exhibit unique properties, which are different from those produced by coherent and incoherent classical light sources. In particular, our experiments show that the revival distance of two-photon Talbot imaging is twice the usual classical Talbot length and there is no net improvement in the resolution, due to the near-field effect of Fresnel diffraction, which is different from the case of previous proof-of-principle quantum lithography experiments in the far field.