Localization–delocalization transition of dipolar bosons in a four-well potential

We study interacting dipolar atomic bosons in a four-well potential within a ring geometry and outline how a four-site Bose–Hubbard (BH) model including next–nearest–neighbor interaction terms can be derived for the above four-well system. We analyze the ground state of dipolar bosons by varying the strength of the (effective) interaction between particles in next–nearest-neighbor wells. We perform this analysis both numerically and analytically by reformulating the dipolar-boson model within the continuous variable picture applied in Buonsante et al (2011 Phys. Rev. A 84 061601(R)). By using this approach we show that when the (effective) next-nearest–neighbor interaction crosses a precise value of the on-site interaction, the ground state exhibits a change from the uniform state (pertaining to the delocalization regime) to a macroscopic two-pulse state, with strongly localized bosons (localization regime). These predictions are confirmed by the results obtained by diagonalizing numerically the four-site extended BH Hamiltonian.