Probing Bose-Einstein Condensation of Excitons with Electromagnetic Radiation

We examine the absorption spectrum of electromagnetic radiation from excitons, where an exciton in the $1s$ state absorbs a photon and makes a transition to the $2p$ state. We demonstrate that the absorption spectrum depends strongly on the quantum degeneracy of the exciton gas, and that it will generally manifest many-body effects. Based on our results we propose that absorption of infrared radiation could resolve recent contradictory experimental results on excitons in Cu$_2$O.