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Résumé:

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 1⁄4 0 ! J0 1⁄4 1 narrow atomic transition. As a side result, we resolve a controversy for the occurrence of a spectral gap in a fcc lattice.