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It has been recently suggested that the Bose-Einstein condensate formed byexcitons in the dilute limit must be dark, i.e., not coupled to photons. Here,we show that, under a density increase, the dark exciton condensate mustacquire a bright component due to carrier exchange in which dark excitons turnbright. This however requires a density larger than a threshold which seems tofall in the forbidden region of the phase separation between a dilute excitongas and a dense electron-hole plasma. The BCS-like condensation which is likelyto take place on the dense side, must then have a dark and a bright component -which makes it "gray". It should be possible to induce an internal Josephsoneffect between these two coherent components, with oscillations of thephotoluminescence as a strong proof of the existence for this "gray" BCS-likeexciton condensate.

"Gray" BCS condensate of excitons and internal Josephson effect