  The topological structure associated with the branchpoint singularity around
an exceptional point (EP) provides new tools for controlling the propagation of
electromagnetic waves and their interaction with matter. To date, observation
of EPs in light-matter interactions has remained elusive and has hampered
further progress in applications of EP physics. Here, we demonstrate the
emergence of EPs in the electrically controlled interaction of light with a
collection of organic molecules in the terahertz regime at room temperature. We
show, using time-domain terahertz spectroscopy, that the intensity and phase of
terahertz pulses can be controlled by a gate voltage which drives the device
across the EP. This fully electrically-tuneable system allows reconstructing
the Riemann surface associated with the complex energy landscape and provides a
topological control of light by tuning the loss-imbalance and frequency
detuning of interacting modes. We anticipate that our work could pave the way
for new means of dynamic control on the intensity and phase of terahertz field,
developing topological optoelectronics, and studying the manifestations of EP
physics in the quantum correlations of the light emitted by a collection of
emitters coupled to resonators.
