Fermi edge singularity in neutral electron-hole plasma

We studied e-h systems created by optical excitation in separated electron and hole layers in GaAs/AlGaAs coupled quantum well heterostructure. The layer separation increases the e-h recombination time and, in turn, the density for a given optical excitation by orders of magnitude and, as a result, enables the realization of a dense and cold e-h system, with the density controlled by the excitation power. We found a strong enhancement of photoluminescence intensity at the Fermi energy of the neutral dense ultracold e-h plasma that evidences the emergence of excitonic Fermi edge singularity due to the Cooper-pair-like excitons at the Fermi energy. The photoluminescence lineshape and spontaneous coherence measurements show a crossover from BEC to BCS-like exciton condensate with increasing density, consistent with the theory predicting a smooth BEC - BCS transition. The Fermi edge singularity is the distinctive feature of the BCS-like exciton condensate.