Unique signatures for Bose-Einstein condensation in the decay luminescence lineshape of weakly interacting excitons in a potential trap

We calculate the spatially resolved optical emission spectrum of a weakly interacting Bose gas of excitons confined in a three dimensional potential trap due to interband transitions involving weak direct and phonon mediated exciton-photon interactions. Applying the local density approximation, we show that for a non-condensed system the spatio-spectral lineshape of the direct process reflects directly the shape of the potential. The existence of a Bose-Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Typical examples are given for parameters of the lowest yellow excitons in cuprous oxide.