  Theoretical studies of the tunnelling current and emission spectrum of a
single electron transistor (SET) under optical pumping are presented. The
calculation is performed via Keldysh Green's function method within the
Anderson model with two energy levels. It is found that holes in the quantum
dot (QD) created by optical pumping lead to new channels for the electron
tunnelling from emitter to collector. As a consequence, an electron can tunnel
through the QD via additional channels, characterized by the exciton, trion and
biexciton states. It is found that the tunnelling current as a function of the
gate voltage displays a series of sharp peaks and the spacing between these
peaks can be used to determine the exciton binding energy as well as the
electron-electron Coulomb repulsion energy. In addition, we show that the
single-photon emission associated with the electron-hole recombination in the
exciton complexes formed in the QD can be controlled both electrically and
optically.
