  Presence of bound pairs (excitons) in a low-temperature electron-hole plasma
is accounted for by including correlation between fermions at the ladder level.
Using a simplified one-dimensional model with on-site Coulomb interaction, we
calculate the one-particle self-energies, chemical potential, and optical
response. The results are compared to those obtained in the Born approximation,
which does not account for bound pairs. In the self-consistent ladder
approximation the self-energy and spectral function show a characteristic
correlation peak at the exciton energy for low temperature and density. In this
regime the Born approximation overestimates the chemical potential. Provided
the appropriate vertex correction in the interaction with the photon is
included, both ladder and Born approximations reproduce the excitonic and free
pair optical absorption at low density, and the disappearance of the exciton
absorption peak at larger density. However, lineshapes and energy shifts with
density of the absorption and photoluminescence peaks are drastically
different. In particular, the photoluminescence emission peak is much more
stable in the ladder approximation. At low temperature and density a sizeable
optical gain is produced in both approximations just below the excitonic peak,
however this gain shows unphysical features in the Born approximation. We
conclude that at low density and temperature it is fundamental to take into
account the existence of bound pairs in the electron-hole plasma for the
calculation of its optical and thermodynamic properties. Other approximations
that fail to do so are intrinsically unphysical in this regime, and for example
are not suitable to address the problem of excitonic lasing.
