We investigate the quantum properties of the well-known process of sum
frequency generation, showing that it is potentially a very useful source of
non-classical states of the electromagnetic field, some of which are not
possible with the more common techniques. We show that it can produce
quadrature squeezed light, bright bichromatic entangled states and symmetric
and asymmetric demonstrations of the Einstein-Podolsky-Rosen paradox. We also
show that the semiclassical equations totally fail to describe the mean-field
dynamics when the cavity is strongly pumped
