Generating accessible entanglement in bosons via pair-correlated tunneling

We consider an extended Bose-Hubbard model that includes pair-correlated tunneling. We demonstrate that a minimal four-mode implementation of this model exhibits a pair-correlated regime in addition to Mott insulator and superfluid regimes. We propose a low complexity variational subspace for the ground state of the system in the pair-correlated regime, which we find to be numerically exact in pure pair-tunneling limit. Additionally, we propose a parameter-free high fidelity model wave function that qualitatively captures the features of the ground state in the pair-correlated regime. Due to particle number conservation, the operationally accessible entanglement vanishes deep inside the Mott insulator and superfluid regimes, however in the pure pair-correlated tunneling limit we find that the accessible entanglement entropy grows logarithmically with the number of particles. Additionally, we demonstrate that upon application of a unitary beamsplitter operation, the pair-correlated ground state is transformed into a state with completely accessible entanglement that is not limited by super-selection rules.