  It is widely assumed that photons cannot be manipulated using electric or
magnetic fields. Even though hybridization of photons with electronic
polarization to form exciton-polaritons has paved the way to a number of
ground-breaking experiments in semiconductor microcavities, the neutral bosonic
nature of these quasiparticles has severely limited their response to external
gauge fields. Here, we demonstrate polariton acceleration by external electric
and magnetic fields in the presence of nonperturbative coupling between
polaritons and itinerant electrons, leading to formation of new quasiparticles
termed polaron-polaritons. We identify the generation of electron density
gradients by the applied fields to be primarily responsible for inducing a
gradient in polariton energy, which in turn leads to acceleration along a
direction determined by the applied fields. Remarkably, we also observe that
different polarization components of the polaritons can be accelerated in
opposite directions when the electrons are in $\nu = 1$ integer quantum Hall
state.
