  Using two-photon Bragg spectroscopy, we study the energy of particle-like
excitations in a strongly interacting homogeneous Bose-Einstein condensate, and
observe dramatic deviations from Bogoliubov theory. In particular, at large
scattering length $a$ the shift of the excitation resonance from the
free-particle energy changes sign from positive to negative. For an excitation
with wavenumber $q$, this sign change occurs at $a \approx 4/(\pi q)$, in
agreement with the Feynman energy relation and the static structure factor
expressed in terms of the two-body contact. For $a \gtrsim 3/q$ we also see a
breakdown of this theory, and better agreement with calculations based on the
Wilson operator product expansion. Neither theory explains our observations
across all interaction regimes, inviting further theoretical efforts.

Quantum Gases;Statistical Mechanics;Atomic Physics;Quantum Physics