  For low-density plasmas, the classical limit described by the Debye-H\"uckel
theory is still considered as an appropriate description even though a clear
experimental proof of this paradigm is lacking due to the problems in
determining the plasma-induced shift of single-particle energies in atomic
systems. We show that Rydberg excitons in states with a high principal quantum
number are highly sensitive probes for their surrounding making it possible to
unravel accurately the basic properties of low-density non-degenerate
electron-hole plasmas. To this end, we accurately measure the parameters of
Rydberg excitons such as energies and linewidths in absorption spectra of bulk
cuprous oxide crystals in which a tailored electron-hole plasma has been
generated optically. Since from the absorption spectra exciton energies, as
well as the shift of the single-particle energies given by the band edge, can
be directly derived, the measurements allow us to determine the plasma density
and temperature independently, which has been a notoriously hard problem in
semiconductor physics. Our analysis shows unambiguously that the impact of the
plasma cannot be described by the classical Debye model, but requires a quantum
many-body theory, not only for the semiconductor plasma investigated here, but
in general. Furthermore, it reveals a new exciton scattering mechanism with
coupled plasmon-phonon modes becoming important even at very low plasma
densities.
