  We describe the operating characteristics of a new type of quantum oscillator
that is based on a two-photon stimulated emission process. This two-photon
laser consists of spin-polarized and laser-driven $^{39}$K atoms placed in a
high-finesse transverse-mode-degenerate optical resonator, and produces a beam
with a power of $\sim $0.2 $\mu $W at a wavelength of 770 nm. We observe
complex dynamical instabilities of the state of polarization of the two-photon
laser, which are made possible by the atomic Zeeman degeneracy. We conjecture
that the laser could emit polarization-entangled twin beams if this degeneracy
is lifted.
