  We report spin and intensity coupling of an exciton-polariton condensate to
the mechanical vibrations of a circular membrane microcavity. We optically
drive the microcavity resonator at the lowest mechanical resonance frequency
while creating an optically-trapped spin-polarized polariton condensate in
different locations on the microcavity, and observe spin and intensity
oscillations of the condensate at the vibration frequency of the resonator.
Spin oscillations are induced by vibrational strain driving, whilst the
modulation of the optical trap due to the displacement of the membrane causes
intensity oscillations in the condensate emission. Our results demonstrate
spin-phonon coupling in a macroscopically coherent condensate.
