  We report on the selective excitation of single impurity-bound exciton states
in a GaAs double quantum well (DQW). The structure consists of two quantum
wells (QWs) coupled by a thin tunnel barrier. The DQW is subject to a
transverse electric field to create spatially indirect inter-QW excitons with
electrons and holes located in different QWs. We show that the presence of
intra-QW charged excitons (trions) blocks carrier tunneling across the barrier
to form indirect excitons, thus opening a gap in their emission spectrum. This
behavior is attributed to the low binding energy of the trions. Within the
tunneling blockade regime, emission becomes dominated by processes involving
excitons bound to single shallow impurities, which behave as two-level centers
activated by resonant tunneling. The quantum nature of the emission is
confirmed by the anti-bunched photon emission statistics. The narrow
distribution of emission energies ($\sim 10$~meV) and the electrical connection
to the QWs make these single-exciton centers interesting candidates for
applications in single-photon sources.
