  We study the quantum nonequilibrium dynamics of ultracold three-level atoms
trapped in an optical lattice, which are excited to their Rydberg states via a
two-photon excitation with nonnegligible spontaneous emission. Rich quantum
phases including uniform phase, antiferromagnetic phase and oscillatory phase
are identified. We map out the phase diagram and find these phases can be
controlled by adjusting the ratio of intensity of the pump light to the control
light, and that of two-photon detuning to the Rydberg interaction strength.
When the two-photon detuning is blue-shifted and the latter ratio is less than
1, bistability exists among the phases. Actually, this ratio controls the
Rydberg-blockade and antiblockade effect, thus the phase transition in this
system can be considered as a possible approach to study both effects.
