We theoretically study the transmission of a weak probe field under the
influence of a strong pump field in a coupled nanomechanical
resonator-superconducting microwave cavity system. Using the standard
input-output theory, we find that both pulse delay (slow light effect) and
advancement (fast light effect) of the probe field can appear in this coupled
system provided that we choose the suitable detuning of the pump field from
cavity resonance. The magnitude of the delay (advancement) can be tuned
continuously by adjusting the power of the pump field. This technique
demonstrates great potential in applications including microwave phase shifter
and delay line.Comment: 12pages, 3 figure
