Abstract
Access to collective excitations lies at the heart of our understanding of quantum many-body systems. We study the Higgs and Goldstone modes in a supersolid quantum gas that is created by coupling a Bose-Einstein condensate symmetrically to two optical cavities. The cavity fields form a U(1)-symmetric order parameter that can be modulated and monitored along both quadratures in real time. This enables us to measure the excitation energies across the superfluid-supersolid phase transition, establish their amplitude and phase nature, as well as characterize their dynamics from an impulse response. Furthermore, we can give a tunable mass to the Goldstone mode at the crossover between continuous and discrete symmetry by changing the coupling of the quantum gas with either cavity.