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Different quantum states of atoms in optical lattices can be nondestructivelymonitored by off-resonant collective light scattering into a cavity. Angleresolved measurements of photon number and variance give information aboutatom-number fluctuations and pair correlations without single-site access.Observation at angles of diffraction minima provides information on quantumfluctuations insensitive to classical noise. For transverse probing, no photonis scattered into a cavity from a Mott insulator phase, while the photon numberis proportional to the atom number for a superfluid.Comment: 4 pages, 3 figures, to published in Phys. Rev. Lett. (March 2007

Cavity-Enhanced Light Scattering in Optical Lattices to Probe Atomic Quantum Statistics