Off-diagonal long-range order in arrays of dipolar droplets

We report quantum Monte Carlo results of harmonically confined quantum Bose dipoles within a range of interactions covering the evolution from a gas phase to the formation of an array of droplets. Scaling the experimental setup to a computationally accessible domain we characterize that evolution in qualitative agreement with experiments. Our microscopic approach generates ground-state results free from approximations, albeit with some controlled statistical noise. The simultaneous estimation of the static structure factor and the one-body density matrix allows for a better knowledge of the quantum coherence between droplets. Our results show a narrow window of interaction strengths where diagonal and off-diagonal long-range order can coexist. This domain, which is the key signal of a supersolid state, is reduced with respect to the one predicted by the extended Gross-Pitaevskii equation. Differences are probably due to an increase of attraction in our model, observed previously in the calculation of critical atom numbers for single dipolar drops.