Experiments towards a periodically pumped single-photon source are presented. The lateral piezoelectric field of a surface acoustic wave dissociates laser-generated two-dimensional excitons into electrons and holes. These carriers are separated by the wave potential and are transported over macroscopic length scales without recombining. When reaching a stress-induced quantum dot in the quantum well they periodically populate the zero-dimensional states and recombine, emitting single photons periodically in time according to the surface acoustic-wave frequency. We have successfully reduced the number of pumped quantum dots down to 100 and have detected a strong blinking photoluminescence signal. By further reducing the number of quantum dots down to 1 a periodically pumped single photon source could be realized.