Bloch oscillations and matter-wave localization of a dipolar quantum gas in a one-dimensional lattice

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 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. Quantum fluctuations stabilize dense self-bound macroscopic quantum states in quantum gases. This work places an Erbium dipolar ultracold atomic gas with dominantly attractive long-range interactions in a 1D periodic lattice, and uses interferometric techniques and numerical modeling to characterize the importance of beyond mean-field effects, revealing the emergence of spatially-extended and single-site localized (2D) droplets and signatures of an anisotropic 2D soliton.