Postselected amplification and photon recycling applied to optical sensing of magnetic fields

Abstract: We apply the combined technique of postselected amplification and photon-recycling to an optical setup of magnetic field precision measurement. We propose two recycling schemes and carry out analytic expressions for the amplified signal and measurement sensitivity. The results show significant improvement of performance over conventional measurement. The underlying reason is twofold. On one aspect, introducing the technique of recycling eliminates the shortcoming of data discarding in postselection, thus maintains similar noise level of conventional measurement (without postselection). On the other aspect, performing intentional postselection within the recycling framework, which was originally proposed in the context of gravitational wave detection, can amplify the signal. Thus, the measurement signal-to-noise ratio is enhanced.