  The adiabatic passage scheme for quantum state synthesis, in which atomic
Zeeman coherences are mapped to photon states in an optical cavity, is extended
to the general case of two degenerate cavity modes with orthogonal
polarization. Analytical calculations of the dressed-state structure and Monte
Carlo wave-function simulations of the system dynamics show that, for a
suitably chosen cavity detuning, it is possible to generate states of photon
multiplets that are maximally entangled in polarization. These states display
nonclassical correlations of the type described by Greenberger, Horne, and
Zeilinger (GHZ). An experimental scheme to realize a GHZ measurement using
coincidence detection of the photons escaping from the cavity is proposed. The
correlations are found to originate in the dynamics of the adiabatic passage
and persist even if cavity decay and GHZ state synthesis compete on the same
time scale. Beyond entangled field states, it is also possible to generate
entanglement between photons and the atom by using a different atomic
transition and initial Zeeman state.
