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We present a cluster Gutzwiller mean-field study for ground states andtime-evolution dynamics in the Bose-Hubbard ladder (BHL), which can be realizedby loading Bose atoms in double-well optical lattices. In our clustermean-field approach, we treat each double-well unit of two lattice sites as acoherent whole for composing the cluster Gutzwiller ansatz, which may remainsome residual correlations in each two-site unit. For a unbiased BHL, inaddition to conventional superfluid phase and integer Mott insulator phases, wefind that there are exotic fractional insulator phases if the inter-chaintunneling is much stronger than the intra-chain one. The fractional insulatorphases can not be found by using a conventional mean-field treatment based uponthe single-site Gutzwiller ansatz. For a biased BHL, we find there appearsingle-atom tunneling and interaction blockade if the system is dominated bythe interplay between the on-site interaction and the inter-chain bias. In themany-body Landau-Zener process, in which the inter-chain bias is linearly sweptfrom negative to positive or vice versa, our numerical results arequalitatively consistent with the experimental observation [Nat. Phys.\textbf{7}, 61 (2011)]. Our cluster bosonic Gutzwiller treatment is ofpromising perspectives in exploring exotic quantum phases and time-evolutiondynamics of bosonic particles in superlattices.

Cluster Gutzwiller study of Bose-Hubbard ladder: ground-state phase diagram and many-body Landau-Zener dynamics