We study semiconductor excitons confined in an electrostatic trap of a GaAs bilayer heterostructure. We evidence that optically bright excitonic states are strongly depleted while cooling to sub-Kelvin temperatures. In return, the other accessible and optically dark states become macroscopically occupied so that the overall exciton population in the trap is conserved. These combined behaviours constitute the spectroscopic signature for the mostly dark Bose-Einstein condensation of excitons, which in our experiments is restricted to a dilute regime within a narrow range of densities, below a critical temperature of about 1K.
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