  Spontaneous symmetry breaking is a central paradigm of elementary particle
physics, magnetism, superfluidity and superconductivity. According to
Goldstone's theorem, phase transitions that break continuous symmetries lead to
the existence of gapless excitations in the long-wavelength limit. These
Goldstone modes generally dominate the low-energy excitations, showing that
symmetry breaking has a profound impact on the physical properties of matter.
Here, we present the first comprehensive study of the elementary excitations in
a homogeneous strongly interacting Fermi gas through the crossover from a
Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC)
of molecules using two-photon Bragg spectroscopy. The spectra exhibit a
discrete Goldstone mode, associated with the broken symmetry superfluid phase,
as well as pair breaking single-particle excitations. Our techniques yield a
direct determination of the superfluid pairing gap and speed of sound in close
agreement with a strong-coupling theory.
