  Highly excited Rydberg states of excitons in Cu$_2$O semiconductors provide a
promising approach to explore and control strong particle interactions in a
solid-state environment. A major obstacle has been the substantial absorption
background that stems from exciton-phonon coupling and lies under the Rydberg
excitation spectrum, weakening the effects of exciton interactions. Here, we
demonstrate that two-photon excitation of Rydberg excitons under conditions of
electromagnetically induced transparency (EIT) can be used to control this
background. Based on a microscopic theory that describes the known
single-photon absorption spectrum, we analyze the conditions under which
two-photon EIT permits separating the optical Rydberg excitation from the
phonon-induced absorption background, and even suppressing it entirely. Our
findings thereby pave the way for the exploitation of Rydberg blockade with
Cu$_2$O excitons in nonlinear optics and other applications.
