Interference of light with localized atomic wave functions

Veniamin P. Chebotayev, A. P. Kasantsev, Valery P. Yakovlev +1 more

We consider the interference of atoms caused by the wave nature of their motion. Coherently interfering beams of particles may be obtained by using the diffraction of atoms from separated standing waves resonant with the transition between the ground and excited states of the atoms. Interference arises with and without spatial separation of the diffracted atomic beams. A problem concerning two-quantum perturbation of the wave function of an atom in the ground state by a standing-wave field has been solved. Both amplitude and phase perturbation are taken into account. We show that in spite of the absence of coherence in the incident beam and a rapid decay of the coherence induced by the standing wave for scattered spatially overlapping beams, the interference can be observed for the conditions of an echo. We first consider the phenomenon of an echo under the quantum-mechanical action of light on the translational degrees of freedom. We show that owing to this phenomenon phase memory can be transferred through the ground state over unlimitedly large distances. Owing to the interference of the density harmonics, a periodic structure in the spatial distribution of the atomic density with a period of less than one wavelength of the light is localized at distances of the order of the distance between the fields. The harmonic amplitude is calculated for instantaneous excitation in the case in which the duration of the excitation is comparable with the backward Doppler linewidth in the beam and for scattering under Bragg conditions. In the latter case we show that the effective temperature of the atoms participating in the interference is less than one recoil energy.

B Ya Dubetskiĭ, A. P. Kazantsev, V. P. Chebotaev +1 more

D. Arsenović, Mirjana Božić

The visibility of the interference pattern in Feynman's atomic light microscope is studied theoretically using the evolution of the wave function of individual atoms passing through a double slit grating and interacting with laser light (of the wave vector ki). Assuming that the slits' width (δ) is much smaller than the slits' distance (d), the expressions for visibility as functions of dki were derived for uniform and for Mandel distribution of transferred momentum during photon atom resonance scattering. The decreasing of oscillations of visibility with increasing dki was explained taking into account the wave functions of individual atoms and the statistics of transverse momentum transferred to atoms. The influence of nonnegligible slits' width on visibility was studied numerically. It is found that revivals are present for infinitesimally wide slits as well as when slits have finite width.

Alexandr Petrovich Davydov, Tatiana Pavlovna Zlydneva

Abstract The general results of constructing and modeling the photon wave function in the coordinate representation in the framework of quantum mechanics are presented in order to explain single-photon interference phenomena, in particular Young’s experiment. The relevance of this function is emphasized in connection with modern single-photon and two-photon experiments. The necessity of replacing the explanation of obtaining coherent light sources using the concept of a train of supposedly real electromagnetic waves emitted by one atom, by the conditional emission by this atom of the photon wave function in the coordinate representation, which then experiences diffraction and interference, is substantiated. A single-photon wave function is simulated based on the consideration of the electric dipole radiation of an atom in classical electrodynamics, and a conclusion is drawn on the possibility to explain Young’s experiment. It is argued that although the photon wave function (as well as of particles having mass) is not a physical object, the application of this function significantly weakens the problem of wave-particle duality of light. It is assumed the “nature” of this function reflects the properties of a physical vacuum, but new experiments are required to clarify it.

Crispin W. Gardiner