Space Localization of the Photon

O. O. Chumak, N. Sushkova

The possibility to describe the evolution of an electromagnetic field by means of the photon distribution function in the phase space (r, q-space) is studied. This function defined by analogy with the coarse-grained Mandel operator of photon density in the configuration space is used to characterize the local density of photons with a given momentum. Approximate eigenfunctions and eigenvalues of the distribution function, corresponding to one-photon localized states of the electromagnetic field, are obtained. It is shown that the photon transport is governed by the Newton mechanics if the "external force" acting on photons is a slowly varying function of spatial variables. It is shown that the distribution function at any time can be expressed via the initialdistribution and photon's trajectories.

John F. Clauser

Kam Wai Clifford Chan, C. K. Law, Joseph H. Eberly

We solve the joint open problems of photon localization and single-photon wave functions in the context of spontaneous emission from an excited atom in free space. Our wave functions are well-defined members of a discrete orthonormal function set. Both the degree and shape of the localization are controlled by entanglement mapping onto the atom wave function, even though the atom is remote from the photon.

Steven B. Berger

Iwo Białynicki‐Birula

It is shown that photons can be localized in space with an exponential falloff of the energy density and photodetection rates. The limits of localization are determined by the fundamental Paley-Wiener theorem. A direct mathematical connection between the spatial localization of photons and the decay in time of quantum mechanical systems is established.

Subhasish Chakraborty, Miriam Scherer