Abstract
A theoretical investigation of the nonlinear response of the Bose-Einstein condensate of an electron-hole plasma in a direct-gap semiconductor quantum-well reveals the existence of a second-order response, which is absent in the normal state of the plasma because of inversion symmetry. We propose a two-beam optical experiment to detect the second-order response as a test for Bose-Einstein condensation of excitons. The signal is sensitive to the intrinsic pair-coherence and is dominated by a long-wavelength collective mode inside the gap. Consequently, the signal is estimated to be much stronger than four-wave mixing, not even counting the extra factor of external field needed for the latter.
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