Phase diagram of Rydberg atoms in a nonequilibrium optical lattice*

We study the quantum nonequilibrium dynamics of ultra-cold three-level atoms trapped in an optical lattice, which are excited to their Rydberg states via a two-photon excitation with non-negligible spontaneous emission. Rich quantum phases, including the uniform phase, the antiferromagnetic phase, and the 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 blueshifted and the latter ratio is less than 1, bistability exists among the phases. Actually, this ratio controls the Rydberg-blockade and Rydberg-antiblockade effects, thus, the phase transition in this system can be considered as a possible approach to study both effects.