  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.
