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We study the multistability of fixed points for a dimerized system of Rydberg atoms driven by two laser fields and trapped in a two-dimensional (2D) square lattice. For identical driving fields, the fixed points of this system exhibit stable uniform, unstable uniform, stable nonuniform, or oscillating nonuniform phases in the presence of a bistable region. For different driving fields, however, all (stable, unstable, or oscillating) phases become nonuniform instead, which then results in two islets isolated from the mainland of Rydberg excitation. We also show that a tristable region may stretch out from the (nonuniform) bistable region near the islets, indicating that a richer phase diagram can be attained by tuning the Rabi frequencies and/or detunings of the driving fields. Last but not least, the fixed points can adiabatically evolve from the islets to the mainland but can not inversely evolve from the mainland to the islets.

We study in theory the single-photon Rydberg excitation in an ensemble of two-level cold atoms at finite low temperatures. Rydberg population plotted against laser detuning may exhibit a nonlinear bistable behavior arising from the dipole–dipole interactions manifested as a van der Waals (vdW) potential. We find that Doppler broadening can result in a remarkable reduction of the bistable region, which may disappear as the atomic temperature increases to a certain value, of the order of tens to hundreds of μK. This special temperature, depending critically on the vdW potential, can be largely raised by partially eliminating the Doppler effect, when a double-photon excitation scheme is used to replace the single-photon excitation scheme.

We study a double-cavity optomechanical system with two movable mirrors acting as mechanical oscillators coupled via a common girder. The fluctuation parts of mechanical oscillations induced by vacuum noises exhibit a limited quantum synchronization owing to the Heisenberg uncertainty. Exerting periodic modulations on the driving lasers or mechanical oscillators, we find that it is viable to attain a 50% ~ 75% enhancement on this quantum synchronization with appropriate modulation frequencies and amplitudes. A direct comparison shows that the optimal modulations on driving lasers are more favorable than the optimal modulations on mechanical oscillators in that the former could result in a greater enhancement than the latter. Our findings should be instructive for further studies on multi-cavity optomechanical systems to pursue a promising platform for quantum information processing.