  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.
