Long-Lived and Transient Supersolid Behaviors in Dipolar Quantum Gases

By combining theory and experiments, we demonstrate that dipolar quantum gases of both ¹⁶⁶Er and ¹⁶⁴Dy support a state with supersolid properties, where a spontaneous density modulation and a global phase coherence coexist. This paradoxical state occurs in a well-defined parameter range, separating the phases of a regular Bose-Einstein condensate and of an insulating droplet array, and is rooted in the roton mode softening, on the one side, and in the stabilization driven by quantum fluctuations, on the other side. Here, we identify the parameter regime for each of the three phases. In the experiment, we rely on a detailed analysis of the interference patterns resulting from the free expansion of the gas, quantifying both its density modulation and its global phase coherence. Reaching the phases via a slow interaction tuning, starting from a stable condensate, we observe that ¹⁶⁶Er and ¹⁶⁴Dy exhibit a striking difference in the lifetime of the supersolid properties, due to the different atom loss rates in the two systems. Indeed, while in ¹⁶⁶Er the supersolid behavior survives only a few tens of milliseconds, we observe coherent density modulations for more than 150 ms in ¹⁶⁴Dy. Building on this long lifetime, we demonstrate an alternative path to reach the supersolid regime, relying solely on evaporative cooling starting from a thermal gas.