Detecting quantum coherence of Bose gases in optical lattices by scattering light intensity in cavity.

We propose a new method of detecting quantum coherence of a Bose gas trapped in a one-dimensional optical lattice by measuring the light intensity from Raman scattering in cavity. After pump and displacement process, the intensity or amplitude of scattering light is different for different quantum states of a Bose gas, such as superfluid and Mott-Insulator states. This method can also be useful to detect quantum states of atoms with two components in an optical lattice.