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

Fractional Talbot images in the de Broglie near field of atoms diffracted b y a dispersive light grating allow the measurement of the quantum state of an electromagnetic held in a cavity, in the optical domain. In particular, the photon-number statistics may be obtained, in principle, through a singl e experimental realization, It may be expressed as a Fourier transform of t he 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. [S1050-2947(99)02407-5].