  We show that far field diffraction image of spontaneously scattered Stokes
photons can be used for detection of spin entanglement and for metrology of
fields gradients in cold atomic ensembles. For many-body states with small or
maximum uncertainty in spin-excitation number, entanglement is simply witnessed
by the presence of a sharp diffraction peak or dip. Gradient vector of external
fields is measured by the displacement of a diffraction peak due to
inhomogeneous spin precessions, which suggests a new possibility for precision
measurement beyond the standard quantum limit without entanglement. Monitoring
temporal decay of the diffraction peak can also realize non-demolition probe of
temperature and collisional interactions in trapped cold atomic gases. The
approach can be readily generalized to cold molecules, trapped ions, and solid
state spin ensembles.
