  The property of superfluidity, first discovered in liquid 4He, is closely
related to Bose-Einstein condensation (BEC) of interacting bosons. However,
even at zero temperature, when one would expect the whole bosonic quantum
liquid to become condensed, a fraction of it is excited into higher momentum
states via interparticle interactions and quantum fluctuations -- the
phenomenon of quantum depletion. Quantum depletion of weakly interacting atomic
BECs in thermal equilibrium is well understood theoretically but is difficult
to measure. This is even more challenging in driven-dissipative systems such as
exciton-polariton condensates(photons coupled to electron-hole pairs in a
semiconductor), since their nonequilibrium nature is predicted to suppress
quantum depletion. Here, we observe quantum depletion of an optically trapped
high-density exciton-polariton condensate by directly detecting the spectral
branch of elementary excitations populated by this process. Analysis of the
population of this branch in momentum space shows that quantum depletion of an
exciton-polariton condensate can closely follow or strongly deviate from the
equilibrium Bogoliubov theory, depending on the fraction of matter (exciton) in
an exciton-polariton. Our results reveal the effects of exciton-polariton
interactions beyond the mean-field description and call for a deeper
understanding of the relationship between equilibrium and nonequilibrium BECs.
