# The Fate of the Higgs Mode in a Trapped Dipolar Supersolid

## TL;DR

This paper theoretically explores the excitation spectrum of a trapped dipolar quantum gas during the BEC-supersolid phase transition, revealing distinct Higgs and Nambu-Goldstone modes and their evolution.

## Contribution

It provides a detailed analysis of the Higgs mode behavior in a finite-size dipolar supersolid, connecting symmetry breaking to excitation spectra.

## Key findings

- Identification of Higgs and Nambu-Goldstone modes at the phase transition
- Rapid increase in Higgs mode energy on the supersolid side
- Strong coupling of Higgs mode to higher-lying modes

## Abstract

We theoretically investigate the spectrum of elementary excitations of a trapped dipolar quantum gas across the BEC-supersolid phase transition. Our calculations reveal the existence of distinct Higgs and Nambu-Goldstone modes that emerge from the softening roton modes of the dipolar BEC at the phase transition point. On the supersolid side of the transition, the energy of the Higgs mode increases rapidly, leading to a strong coupling to higher-lying modes. Our study highlights how the symmetry-breaking nature of the supersolid state translates to finite-size systems.