Spectrum of Light in a Quantum Fluctuating Periodic Structure

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.

4 pages, 1 figure; introduction, conclusion and title changed

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• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Collective generation of quantum states of light by entangled atoms
• Fano-Hopfield model and photonic band gaps for an arbitrary atomic lattice
• Optical properties of atomic Mott insulators: from slow light to dynamical Casimir effects
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