  Competing interactions in the so-called spin-ice compounds stabilize a
frustrated ground-state with finite zero-point entropy and, interestingly,
emergent magnetic monopole excitations. The properties of these monopoles are
at the focus of recent research with particular emphasis on their quantum
dynamics. It is predicted that each monopole also possesses an electric dipole
moment, which allows to investigate their dynamics via the dielectric function
\epsilon(\nu). Here, we report on broadband spectroscopic measurements of
\epsilon(\nu) in Dy2Ti2O7 down to temperatures of 200mK with a specific focus
on the critical endpoint present for a magnetic field along the
crystallographic [111] direction. Clear critical signatures are revealed in the
dielectric response when, similarly as in the liquid-gas transition, the
density of monopoles changes in a critical manner. Surprisingly, the dielectric
relaxation time \tau\ exhibits a critical speeding-up with a significant
enhancement of 1/\tau\ as the temperature is lowered towards the critical
temperature. Besides demonstrating the magnetoelectric character of the
emergent monopole excitations, our results reveal unique critical dynamics near
the monopole condensation transition.
