Bose-Einstein statistics of an excitonic gas in two dimensions: Excitons and biexcitons in a GaAs quantum well

Intense photoexcitation of a GaAs quantum well produces a dense gas of free excitons that can pairwise combine to form biexcitons. At sufficiently high density where interparticle spacing is comparable to the thermal deBroglie wavelength, such a two-component gas confined to two-dimensional motion may exhibit quantum-statistical behavior. In this paper, we theoretically show how quantum statistics modifies the equilibrium-density relationship between excitons and biexcitons from that of a classical square law. We also experimentally examine a gas of excitons and biexcitons in GaAs quantum wells and find the predicted signature of Bose-Einstein statistics: a saturation of the exciton density with a continued growth of the biexciton density, as the pair density is increased. For a two-dimensional excitonic gas at a temperature of 5 K inside a 100-Å GaAs quantum well, the calculated pair density at the onset of excitonic saturation is only about $1\times {10}^{11}{\mathrm{cm}}^{-2},$ a density readily attained by photoexcitation with 5-ps laser pulses focused to a $3-\mu \mathrm{m}$ spot. Concurrent with the saturation behavior with increasing density, we observe a gradual broadening and blueshifting of the luminescence peaks, indicating the onset of many-particle effects. Also, the deduced ratio of the total radiative rate of a biexciton to that of an exciton is considerably smaller than what might be expected from simple kinetic arguments. Thus, it seems that a rigorous understanding of the spectral line shapes and luminescence intensities is needed to support our interpretation of Bose-Einstein statistics in this system.