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We use the mean-field method, the Quantum Monte-carlo method and the Density matrix renormalization group method to study the trimer superfluid phase and the quantum phase diagram of the Bose-Hubbard model in an optical lattice, with explicit trimer tunneling term.Theoretically, we derive the explicit trimer hopping terms, such as ta3+1a3j, by the Schrieffer-Wolf transformation.In practice, the trimer superfluid described by these terms is driven by photoassociation.