  Output entanglement is a key element in quantum information processing. Here,
we show how to obtain optimal entanglement between two filtered output fields
in a three-mode optomechanical system. First, we obtain the key analytical
expression of optimal time delay between the two filtered output fields, from
which we can obtain the optimal coupling for output entanglement without time
delay. In this case, our linearized analysis predicts that the entanglement
saturates to an optimal value as the optomechanical coupling is increased.
Furthermore, we obtain the optimal output entanglement with time delay. These
results should be very helpful in conceiving new optomechanical schemes of
quantum information processing with their efficiency depending critically on
the degree of output entanglement.
