  Topological insulators have been predicted to exhibit a variety of
interesting phenomena including a quantized magnetoelectric response and novel
spintronics effects due to spin textures on their surfaces. However,
experimental observation of these phenomena has proved difficult due to the
finite bulk carrier density which may overwhelm the intrinsic topological
responses that are expressed at the surface. Here, we demonstrate a novel ionic
gel gating technique to tune the chemical potential of Bi$_{2}$Se$_{3}$ thin
films while simultaneously performing THz spectroscopy. We can tune the carrier
concentration by an order of magnitude and shift the Fermi energy, E$_{F} $ to
as low as $\simeq$ 10 meV above the Dirac point. At high bias voltage and
magnetic field, we observe a quantized Faraday angle consistent with the
topological magnetoelectric effect that can be tuned by ionic gel gating
through a number of plateau states
