Experimental realization of a Bose-Hubbard model with long-range interactions

Manuele Landini, Renate Landig, Lorenz Hruby, Nishant Dogra, Rafael Mottl, Ferdinand Brenneke, Tobias Donner, and Tilman Esslinger

Institute for Quantum Electronics, ETH Zürich, Switzerland

The combination of strongly correlated systems with long-range interactions gives rise to rich physics with a variety of complex phases, which are often very little understood. Realizing such systems with ultracold atoms offers the perspective to address open questions in a highly controlled way. For example, in the case of cavity-mediated long-range interactions, the competition with short-range interactions is expected to lead to a supersolid, a charge density wave as well as a checkerboard Mott insulating phase. In our experiment, we couple the external degree of freedom of a quantum gas of Rb-87 to an optical high-finesse cavity. When increasing the cavity-mediated long-range interactions, the quantum gas exhibits a phase transition from a superfluid (SS) to a self-organized state with checkerboard density modulation. We distinguish four phases in the phase diagram. At low cavity coupling a standard SF to Mott-insulator (MI) phase transition takes place. Increasing the coupling the SF state develops density modulation as a result of a phase transition to a super-solid (SS) state. Increasing density in the SS phase a different MI state is reached which inherits the chequerboard density pattern typical of the SS phase. Two order parameters distinguish the different phases. The first one is associated with the presence of density modulations in the Bose gas, which gives rise to a nonzero light field transmitted by the cavity. The second one is associated with the presence of phase coherence in the system as extracted from time-of-flight pictures of the expanding cloud. We demonstrate first experimental results on the phase diagram of a Bose-Hubbard model with long-range interactions.