Mean field analysis of quantum phase transitions in a periodic optical   superlattice
  In this paper we analyze the various phases exhibited by a system of ultracold bosons in a periodic optical superlattice using the mean field decoupling approximation. We investigate for a wide range of commensurate and incommensurate densities. We find the gapless superfluid phase, the gapped Mott insulator phase, and gapped insulator phases with distinct density wave orders. 
Arya Dhar, Manpreet Singh, Ramesh V. Pai, B. P. Das
cond-mat.quant-gas