Quantum theory of Rayleigh scattering

TL;DR

This paper presents a quantum theory of Rayleigh scattering, describing how incident photons interact with atoms, form entangled states, and produce elastic scattered light with narrow linewidths, without relying on virtual levels.

Contribution

It introduces a quantum framework for Rayleigh scattering that models the process as photon relaxation into reservoir modes, avoiding phenomenological virtual levels.

Findings

Scattered light spectrum peaks at the incident mode frequency even without atomic resonance.

The linewidth of scattered light is significantly narrower than spontaneous emission.

Entanglement between atom and photon prevents complete photon absorption.

Abstract

We develop a quantum theory of atomic Rayleigh scattering. Scattering is considered as a relaxation of incident photons from a selected mode of free space to the reservoir of the other free space modes. Additional excitations of the reservoir states which appear are treated as scattered light. We show that an entangled state of the excited atom and the incident photon is formed during the scattering. Due to entanglement, a photon is never completely absorbed by the atom. We show that even if the selected mode frequency is incommensurable with any atomic transition frequency, the scattered light spectrum has a maximum at the frequency of the selected mode. The linewidth of scattered light is much smaller than that of the spontaneous emission of a single atom, therefore, the process can be considered as elastic. The developed theory does not use the phenomenological concept of virtual level.