  A promising route to novel quantum technologies are hybrid quantum systems,
which combine the advantages of several individual quantum systems. We have
realized a hybrid atomic-mechanical experiment consisting of a SiN membrane
oscillator cryogenically precooled to 500 mK and optically coupled to a cloud
of laser cooled Rb atoms. Here, we demonstrate active feedback cooling of the
oscillator to a minimum mode occupation of n = 16 corresponding to a mode
temperature of T = 200 {\mu}K. Furthermore, we characterize in detail the
coupling of the membrane to the atoms by means of sympathetic cooling. By
simultaneously applying both cooling methods we demonstrate the possibility of
preparing the oscillator near the motional ground state while it is coupled to
the atoms. Realistic modifications of our setup will enable the creation of a
ground state hybrid quantum system, which opens the door for coherent quantum
state transfer, teleportation and entanglement as well as quantum enhanced
sensing applications.
