  The photoluminescence (PL) spectra of a two-dimensional electron system
induced in a Be-delta-doped GaAs/AlGaAs quantum well (QW) with a back gate are
measured. The electron density is controlled from 1 X 10^{9} cm^{-2} to 2.5 X
10^{11} cm^{-2} by changing the back gate voltage. There is a linear increase
in the acceptor PL spectrum around 1.49 eV with an increase in the back gate
voltage and the PL disappears from the exciton bound to neutral donors (D^{0}X)
around 1.51 eV at 1.2 X 10^{10} cm^{-2}.
