  Spontaneous symmetry breaking occurs in a physical system whenever the ground
state does not share the symmetry of the underlying theory, e.g., the
Hamiltonian. It gives rise to massless Nambu-Goldstone modes and massive
Anderson-Higgs modes. These modes provide a fundamental understanding of matter
in the Universe and appear as collective phase/amplitude excitations of an
order parameter in a many-body system. The amplitude excitation plays a crucial
role in determining the critical exponents governing universal non-equilibrium
dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the
amplitude excitations in a spin-1 condensate and measure their energy gap for
different phases of the quantum phase transition. At the quantum critical point
of the transition, finite size effects lead to a non-zero gap. Our measurements
are consistent with this prediction, and furthermore, we demonstrate an
adiabatic quench through the phase transition, which is forbidden at the mean
field level. This work paves the way toward generating entanglement through an
adiabatic phase transition.
