  We observe natural exceptional points in the excitation spectrum of an
exciton-polariton system by optically tuning the light-matter interactions. The
observed exceptional points do not require any spatial or polarization degrees
of freedom and result solely from the transition from weak to strong
light-matter coupling. We demonstrate that they do not coincide with the
threshold for photon lasing, confirming previous theoretical predictions [Phys.
Rev. Lett. 122, 185301 (2019), Optica 7, 1015 (2020) ]. Using a technique where
a strong coherent laser pump induces up-converted excitations, we encircle the
exceptional point in the parameter space of coupling strength and particle
momentum. Our method of local optical control of light-matter coupling paves
the way to investigation of fundamental phenomena including dissipative phase
transitions and non-Hermitian topological states.
