  Three-dimensional quantum gases of strongly dipolar atoms can undergo a
crossover from a dilute gas to a dense macrodroplet, stabilized by quantum
fluctuations. Adding a one-dimensional optical lattice creates a platform where
quantum fluctuations are still unexplored, and a rich variety of new phases may
be observable. We employ Bloch oscillations as an interferometric tool to
assess the role quantum fluctuations play in an array of quasi-two-dimensional
Bose-Einstein condensates. Long-lived oscillations are observed when the
chemical potential is balanced between sites, in a region where a macrodroplet
is extended over several lattice sites. Further, we observe a transition to a
state that is localized to a single lattice plane$-$driven purely by
interactions$-$marked by the disappearance of the interference pattern in the
momentum distribution. To describe our observations, we develop a discrete
one-dimensional extended Gross-Pitaevskii theory, including quantum
fluctuations and a variational approach for the on-site wavefunction. This
model is in quantitative agreement with the experiment, revealing the existence
of single and multisite macrodroplets, and signatures of a two-dimensional
bright soliton.
