Résumé
We address the general problem of the excitation spectrum for light coupled to scatterers havingquantum fluctuating positions around the sites of a periodic lattice. In addition to providing an imaginarypart to the spectrum, we show that these quantum fluctuations affect the real part of the spectrum, in a waythat we determine analytically. Our predictions may be observed with ultracold atoms in an optical lattice,on a J 1⁄4 0 ! J0 1⁄4 1 narrow atomic transition. As a side result, we resolve a controversy for theoccurrence of a spectral gap in a fcc lattice.