Cooling of a Mechanical Oscillator and Normal Mode Splitting in Optomechanical Systems with Coherent Feedback

The ground state cooling of a mechanical oscillator and strong optomechanical coupling are necessary prerequisites for realizing quantum control of the macroscopic mechanical oscillator. Here, we show that the resolved-sideband cooling of a mechanical oscillator in an optomechanical system can be enhanced by a simple coherent feedback scheme, in which a portion of the output field from the cavity is fed back into the cavity using an asymmetric beam splitter. Moreover, we show that the normal mode splitting in the spectra of the movable mirror and the output field in a weakly coupled optomechanical system can be induced by the feedback scheme due to a reduced effective cavity decay rate. We find that the peak separation becomes larger and two peaks of the spectra become narrower and higher with increasing the reflection coefficient r of the beam splitter.