$\mathbb{Z}_2$ phases and Majorana spectroscopy in paired Bose-Hubbard chains

TL;DR

This paper explores a novel gapped $ abla_2$ Ising phase in a paired Bose-Hubbard chain, revealing its potential for macroscopic qubits and Majorana states, with implications for cold-atom experiments.

Contribution

It introduces a new $ abla_2$ phase in the Bose-Hubbard model with pairing, linking it to Majorana physics and proposing an experimental realization.

Findings

Identification of a $ abla_2$ Ising phase with unique properties.

Mapping of the bosonic system to a fermionic Kitaev chain.

Proposal for cold-atom experiments to observe Majorana states.

Abstract

We investigate the Bose-Hubbard chain in the presence of nearest-neighbor pairing. The pairing term gives rise to an unusual gapped $\mathbb{Z}_2$ Ising phase that has number fluctuation but no off-diagonal long range order. This phase has a strongly correlated many-body doubly degenerate ground state which is effectively a gap-protected macroscopic qubit. In the strongly interacting limit, the system can be mapped onto an anisotropic transverse spin chain, which in turn can be mapped to the better-known fermionic sister of the paired Bose-Hubbard chain: the Kitaev chain which hosts zero-energy Majorana bound states. While corresponding phases in the fermionic and bosonic systems have starkly different wavefunctions, they share identical energy spectra. We describe a possible cold-atom realization of the paired Bose-Hubbard model in a biased zig-zag optical lattice with reservoir-induced pairing, opening a possible route towards experimental Kitaev chain spectroscopy.