  We propose to realize an exotic Haldane superfluid (HSF) phase in an extended
Bose-Hubbard model on the two-leg ladder (i.e., a two-species mixture of
interacting bosons). The proposal is confirmed by means of large-scale quantum
Monte Carlo simulations, with a significant part of the ground-state phase
diagram being revealed. Most remarkably, the newly discovered HSF phase
features both superfluidity and the non-local topological Haldane order. The
effects induced by varying the number of legs are furthermore explored. Our
results shed light on how topological superfluid emerges in bosonic systems.

Strongly Correlated Electrons;Quantum Gases;Statistical Mechanics