  We investigate theoretically the magnetoplasmon (cyclotron) resonance in a
hybrid system consisting of spatially separated two-dimensional layers of
electron and dipolar exciton gases coupled via the Coulomb forces. We study the
dynamics of this system under the action of weak alternating external
electromagnetic field in the presence of uniform magnetic field, perpendicular
to the layers. We reveal that the electromagnetic power absorption exhibits a
double-resonance spectrum. We show that the first resonance is associated with
the conventional well-studied magnetoplasmon excitations of the electron gas
and it has a standard Lorentzian shape, whereas the second resonance is a
peculiarity attributed to the Bose-condensed exciton gas. Further, we
explicitly demonstrate that the spectrum of the system exhibits an asymmetric
Fano-type profile, where the excitonic peak is extremely narrow in comparison
with the magnetoplasmon one. We show that the shape of the resonance and the
position of the peaks depends on the magnitude of the applied magnetic field,
exciton condensate density and exciton-impurity scattering time. In particular,
the Fano profile turns into a Lorentzian shape with decreasing exciton-impurity
scattering time and the position of the plasmon-associated resonance is mainly
sensitive and determined by the magnetic field strength, whereas the
exciton-condensate peak position is determined by exciton condensate density.
It opens the experimental possibility to determine the latter quantity in
cyclotron resonance experiment.
