Realizing Z₂ phases and Majorana Spectroscopy in nearest-neighbor paired Bose-Hubbard systems

The connection between transverse XY spin chains and the fermionic Kitaev chain with nearest-neighbor hopping and pairing has been well known for decades, and has lately drawn attention for its rich phase diagram and relevance to realizations of Majorana fermions. Here, we study the novel system comprised of a Bose-Hubbard chain connected to a reservoir that can generate analogous pairing terms for bosons. We describe a cold-atom realization of such a system in a biased zig-zag optical lattice. We show that in certain limits, the Bosonic Kitaev chain maps on to the XY spin chain, resulting in an unsual Z₂ phase that has number fluctuation but no off-diagonal long range order associated with boson condensation. Noteworthy features include the possibility of a strongly correlated many-body qubit ground state and the potential for cold-atom measurements of the Kitaev chain energy spectrum, including degenerate zero-energy states corresponding to Majorana fermionic bound states.