  An important and continuing theme of modern solid state physics is the
realization of exotic excitations in materials (e.g. quasiparticles) that have
no analogy (or have not yet been observed) in the actual physical vacuum of
free space. Although they are not fundamental particles, such quasiparticles do
constitute the most basic description of the excited states of the "vacuum" in
which they reside. In this regard the magnetic textures of the excited states
of spin ices, magnetic pyrochlore oxides with dominant Ising interactions, are
proposed to be modeled as effective magnetic charge monopoles. Recent inelastic
neutron scattering experiments have established the pyrochlore material
Yb$_2$Ti$_2$O$_7$ (YbTO) as a quantum spin ice, where in addition to the Ising
interactions there are substantial transverse terms that may induce quantum
dynamics and - in principle - coherent monopole motion. Here we report a
combined time domain terahertz spectroscopy (TDTS) and microwave cavity study
of YbTO to probe its complex dynamic magnetic susceptibility. We find that the
form of the susceptibility is consistent with monopole motion and a magnetic
monopole conductivity can be defined and measured. Using the unique phase
sensitive capabilities of these techniques, we observe a sign change in the
reactive part of the magnetic response. In generic models of monopole motion
this is only possible through introducing inertial effects, e.g. a mass
dependent term, to the equations of motion. Analogous to conventional electric
charge systems, measurement of the conductivity's spectral weight allows us to
derive a value for the magnetic monopole mass, which we find to be
approximately 1800 electron masses. Our results establish the magnetic
monopoles of quantum spin ice as true coherently propagating quasiparticles of
this system.
