Onset of a modulational instability in trapped dipolar Bose-Einstein condensates

We explore the phase diagram of a finite-sized dysprosium dipolar Bose-Einstein condensate in a cylindrical harmonic trap. We monitor the final state after the scattering length is lowered from the repulsive BEC regime to the quantum droplet regime. Either an adiabatic transformation between a BEC and a quantum droplet is obtained or, above a critical trap aspect ratio ${\ensuremath{\lambda}}_{\mathrm{c}}=1.87(14)$, a modulational instability results in the formation of multiple droplets. This is in full agreement with the predicted structure of the phase diagram with a crossover region below ${\ensuremath{\lambda}}_{\mathrm{c}}$ and a multistable region above. Our results provide the missing piece connecting the previously explored regimes resulting in a single or multiple dipolar quantum droplets.