  We consider a wide family of optical coherent feedback loops acting on an
optomechanical system operating in the linearized regime. We assess the
efficacy of such loops in improving key operations, such as cooling,
steady-state squeezing and entanglement, as well as optical to mechanical state
transfer. We find that mechanical sideband cooling can be enhanced through
passive, interferometric coherent feedback, achieving lower steady-state
occupancies and considerably speeding up the cooling process; we also quantify
the detrimental effect of non-zero delay times on the cooling performance.
Steady state entanglement generation in the blue sideband can also be assisted
by passive interferometric feedback, which allows one to stabilise otherwise
unstable systems, though active feedback (including squeezing elements) does
not help to this aim. We show that active feedback loops only allow for the
generation of optical, but not mechanical squeezing. Finally, we prove that
passive feedback can assist state transfer at transient times for red-sideband
driven systems in the strong coupling regime.
