A Measure of Monopole Inertia in the Quantum Spin Ice Yb$_{2}$Ti$_{2}$O$_{7}$

We report a time domain terahertz spectroscopy study of quantum spin ice material Yb$_{2}$Ti$_{2}$O$_{7}$. We measure the complex dynamic susceptibility of Yb$_{2}$Ti$_{2}$O$_{7}$ in the temperature range between 1.4K and 20K. The data are consistent with a picture where the emergent magnetic monopoles are the principle degrees of freedom. Among other measures, we observe a zero crossing in the real part of the frequency dependent susceptibility. Such a feature is not possible without introducing inertial effects e.g. a mass dependent term to the equations of motion. Through a comparison of the magnetic spectral weight with numerical data that estimates the low temperature monopole density, we derive a value for the magnetic monopole mass.