  The frustrated pyrochlore magnet Yb$_2$Ti$_2$O$_7$ has the remarkable
property that it orders magnetically, but has no propagating magnons over wide
regions of the Brillouin zone. Here we use inelastic neutron scattering to
follow how the spectrum evolves in cubic-axis magnetic fields. At high fields
we observe in addition to dispersive magnons also a two-magnon continuum, which
grows in intensity upon reducing the field and overlaps with the one-magnon
states at intermediate fields leading to strong renormalization of the
dispersion relations, and magnon decays. Using heat capacity measurements we
find that the low and high field regions are smoothly connected with no sharp
phase transition, with the spin gap increasing monotonically in field. Through
fits to an extensive data set we re-evaluate the spin Hamiltonian finding
dominant quantum exchange terms, which we propose are responsible for the
anomalously strong fluctuations and quasiparticle breakdown effects observed at
low fields.
