Spectrum of Light in a Quantum Fluctuating Periodic Structure

TL;DR

This paper analytically investigates how quantum fluctuations of scatterer positions in a periodic lattice influence the excitation spectrum of light, with potential experimental observations using ultracold atoms in optical lattices.

Contribution

It provides an analytical description of the impact of quantum positional fluctuations on both real and imaginary parts of the light spectrum in periodic structures.

Findings

Quantum fluctuations modify the real part of the spectrum.

Predictions applicable to ultracold atoms in optical lattices.

Resolved controversy about spectral gaps in fcc lattices.

Abstract

We address the general problem of the excitation spectrum for light coupled to scatterers having quantum fluctuating positions around the sites of a periodic lattice. In addition to providing an imaginary part to the spectrum, we show that these quantum fluctuations affect the real part of the spectrum, in a way that we determine analytically. Our predictions may be observed with ultracold atoms in an optical lattice, on a J=0->J'=1 narrow atomic transition. As a side result, we resolve a controversy for the occurrence of a spectral gap in a fcc lattice.