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In this letter, by the use of the generalized effective potential theory,with the help of process-chain approach under the framework of Kato formulationof perturbation expansion, we calculate out the quantum phase diagram up to8-th order for an ultracold Bose system in a square optical superlattice. Baseon these perturbative data, with the help of the linear fit extrapolationtechnique, more accurate results are gotten, which are in excellent agreementwith recent Monte-Carlo numerical results. Moreover, by employing thegeneralized re-summed Green's function method and cumulant expansion, themomentum distribution function of the system is also calculated analyticallyand the time-of-flight absorption pictures of the system are plotted.

Quantum Phase diagram and time-of-flight absorption pictures of ultracold Bose system in a square optical superlattice