We describe the operating characteristics of a new type of quantum oscillat
or that is based on a two-photon stimulated emission process. This two-phot
on laser consists of spin-polarized and laser-driven K-39 atoms placed in a
high-finesse transverse-mode-degenerate optical resonator and produces a b
eam with a power of similar to0.2 muW at a wavelength of 770 nm. We observe
complex dynamical instabilities of the state of polarization of the two-ph
oton laser, which are made possible by the atomic Zeeman degeneracy. We con
jecture that the laser could emit polarization-entangled twin beams if this
degeneracy is lifted.