Trimer superfluid and supersolid on two-dimensional optical lattices

What is it about?

By the photoassociation method, the trimer superfluid phase disappears in the one dimensional state-dependent optical lattice if the ratio of the three-body interaction W to the trimer tunneling Jis kept at W/J=12 [Phys Rev A. {\bf 90}, 033622(2014)]. To search for a trimer superfluid and trimer supersolid, we load the cold atom into two-dimensional lattices, whose coordinate number z and kinetic energy -zJ are respectively larger and lower than those of a one dimensional lattice. Herein, we study the Bose-Hubbard model, which has an additional trimer tunneling term, a three-body interaction and a next-nearest repulsion. The on-site trimer and trimer superfluid exist if the on-site two-body repulsion and three-body repulsion are smaller than some thresholds. With atom-tunneling terms, the phase transitions from trimer superfluid phase to both atom superfluid and atom supersolid phases are first order. With W/J=12, in a one dimensional lattice, the trimer superfluid phase does not exist at all. In contrast, the trimer superfluid phase, exists in the lower density regions 0 \textless \rho \textless2 on the square lattice if J is not very large. The trimer superfluid phase emerges in a wider range 0 \textless \rho \textless3 in the triangular lattice, or in the cubic lattice (z=6). When the three-body interaction is turned on, a trimer supersolid phase emerges due to the classical degeneracy between the quasi trimer solid and the trimer solid being broken by the quantum fluctuation. The phase transitions from the trimer supersolid phase to quasi trimer solid are first order and the phase transition from the trimer supersolid phase to trimer solid is continuous. Our results, obtained by mean-field and quantum Monte Carlo methods, will be helpful in realizing the trimer superfluid and supersolid by cold atom experiments.

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Photo by Leon JL on Unsplash

Photo by Leon JL on Unsplash

Why is it important?

This models superfluids and supersolids with a mean-field Bose-Hubbard model including a 3-body interaction. This is equivalent to a nonlinear Schrodinger Equation. The results will be helpful in realizing the trimer superfluid and supersolid by cold atom experiments

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