Evolution of the interband absorption threshold with the density of a two-dimensional electron gas

We have obtained absolute interband absorption spectra from a series of modulation-doped GaAs/${\mathrm{Al}}_{0.3}$ ${\mathrm{Ga}}_{0.7}$As multiple quantum wells covering a wide range of two-dimensional electron densities. The evolution of the threshold line shape from an exciton to a Fermi-edge singularity is quantified. We discuss the influence of the doubly occupied bound state ($X^{-}$) on the line shape and compare the results with realistic many-body calculations.