Light scattering by ultracold atoms in an optical lattice

TL;DR

This paper develops a quantum theoretical framework for light scattering by ultracold atoms in optical lattices, analyzing how atomic states influence scattering and revealing effects of photon recoil on atomic tunneling.

Contribution

It introduces a comprehensive quantum model for atom-photon interactions across the Mott-insulator to superfluid transition, linking atomic states to scattering properties and photon recoil effects.

Findings

Photon recoil induces atomic site-to-site hopping affecting scattering.

The scattering cross section varies with atomic phase and emission direction.

Interference between recoil-induced hopping and tunneling alters scattering signals.

Abstract

We investigate theoretically light scattering of photons by ultracold atoms in an optical lattice in the linear regime. A full quantum theory for the atom-photon interactions is developed as a function of the atomic state in the lattice along the Mott-insulator -- superfluid phase transition, and the photonic scattering cross section is evaluated as a function of the energy and of the direction of emission. The predictions of this theory are compared with the theoretical results of a recent work on Bragg scattering in time-of-flight measurements [A.M. Rey, {\it et al.}, Phys. Rev. A {\bf 72}, 023407 (2005)]. We show that, when performing Bragg spectroscopy with light scattering, the photon recoil gives rise to an additional atomic site to site hopping, which can interfere with ordinary tunneling of matter waves and can significantly affect the photonic scattering cross section.