Optical signatures of a fully dark exciton condensate

We propose optical means to reveal the presence of a dark exciton condensate that does not yield any photoluminescence at all. We show that (i) the dark exciton density can be obtained from the blueshift of the excitonic absorption line induced by dark excitons; (ii) the polarization of the dark condensate can be deduced from the blueshift dependence on probe photon polarization and also from Faraday effect, linearly polarized dark excitons leaving unaffected the polarization plane of an unabsorbed photon beam. These effects result from carrier exchanges between dark and bright excitons.