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 a one-dimensional optical lattice, with an explicit trimer-tunneling term. Theoretically, we derive the explicit trimer hopping terms, such as $a_i^{3†}{a}_j^3$, by the Schrieffer-Wolf transformation. In practice, the trimer superfluid described by these terms is driven by photoassociation. The phase transition between the trimer superfluid phase and other phases are also studied. Without the on-site interaction, the phase transition between the trimer superfluid phase and the Mott insulator phase is continuous. Turning on the on-site interaction, the phase transitions are first order with Mott insulators of atoms filling 1 and 2. With nonzero atom tunneling, the phase transition is first order from the atom superfluid to the trimer superfluid. In the trimer superfluid phase, the winding numbers can be divided by three without any remainder. The power-law decay exponent is $1/2$ for the nondiagonal correlation $a_i^{†3}{a}_j^3$, i.e., the same as the exponent of the correlation $a_i^{†}{a}_j$ in hardcore bosons. The density-dependent atom-tunneling term $n_i^2{a}_i^{†}{a}_j$ and pair-tunneling term $n_i{a}_i^{†2}{a}_j^2$ are also studied. With these terms, the phase transition from the empty phase to atom superfluid is first order and different from the cases without the density-dependent terms. The effects of finite three-body interactions and finite temperatures are also studied. Our results will be helpful in realizing the trimer superfluid by a cold-atom experiment.

• Received 26 May 2014
• Revised 20 August 2014

DOI:https://doi.org/10.1103/PhysRevA.90.033622