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Double-well optical lattice in an insulating state is considered. Theinfluence of atomic vibrations and mesoscopic disorder on the properties of thelattice are studied. Vibrations lead to the renormalization of atomicinteractions. The occurrence of mesoscopic disorder results in the appearanceof first-order phase transitions between the states with different levels ofatomic imbalance. The existence of a nonuniform external potential, such astrapping potential, essentially changes the lattice properties, suppressing thedisorder fraction and rising the transition temperature.

Double-Well Optical Lattices with Atomic Vibrations and Mesoscopic Disorder