# Long-lived and transient supersolid behaviors in dipolar quantum gases

## TL;DR

This study combines theory and experiments to demonstrate long-lived supersolid states in dipolar quantum gases of erbium and dysprosium, revealing differences in their stability and lifetime due to atom loss rates.

## Contribution

It provides the first detailed experimental observation of long-lived supersolid behavior in dipolar quantum gases and identifies the parameter regimes for different phases.

## Key findings

- Supersolid states coexist with density modulation and phase coherence.
- Dysprosium exhibits longer supersolid lifetime than erbium.
- Long-lived supersolids achieved via evaporative cooling from thermal gases.

## Abstract

By combining theory and experiments, we demonstrate that dipolar quantum gases of both $^{166}$Er and $^{164}$Dy 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 $^{166}$Er and $^{164}$Dy 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 $^{166}$Er the supersolid behavior only survives a few tens of milliseconds, we observe coherent density modulations for more than $150\,$ms in $^{164}$Dy. 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.