# Excitation spectrum of a trapped dipolar supersolid and its experimental evidence

## TL;DR

This paper investigates the excitation spectrum of a dipolar Bose gas transitioning from superfluid to supersolid, revealing two distinct excitation branches linked to crystal and superfluid orders, supported by experimental evidence.

## Contribution

It provides a theoretical and experimental analysis of the elementary excitations in a dipolar supersolid, demonstrating the coexistence of crystal and superfluid excitation modes.

## Key findings

- Two excitation branches appear in the supersolid phase.
- Experimental two-frequency response confirms broken symmetries.
- Finite-size effects are minimal in the excitation spectrum.

## Abstract

We study the spectrum of elementary excitations of a dipolar Bose gas in a three-dimensional anisotropic trap across the superfluid-supersolid phase transition. Theoretically, we show that, when entering the supersolid phase, two distinct excitation branches appear, respectively associated with dominantly crystal and superfluid excitations. These results confirm infinite-system predictions, showing that finite-size effects play only a small qualitative role, and connect the two branches to the simultaneous occurrence of crystal and superfluid orders. Experimentally, we probe compressional excitations in an Er quantum gas across the phase diagram. While in the Bose-Einstein condensate regime the system exhibits an ordinary quadrupole oscillation, in the supersolid regime we observe a striking two-frequency response of the system, related to the two spontaneously broken symmetries.