Sagnac effect enhancement with single-mode number squeezing in the presence of photon loss

The precision of gyroscope can be improved with Sagnac effect enhancement. We show that Sagnac effect can be enhanced with single-mode number squeezing technique by calculating the quantum Fisher information (QFI) of coherent state and Fock state and obtain the minimum phase uncertainty with parity measurement in ideal case. Considering that photon losses almost cannot be avoidable in the practical application, a lossy interferometer is modeled by inserting a beam splitter theoretically to calculate the QFI in the presence of photon losses. Through theoretical analysis, the effective transmission rate (or the maximum loss rate) which can enhance Sagnac effect is obtained. For instance, if the average photon number of coherent state | α | 2 is far more than the average photon number of Fock state N and N = 20 , sub-shot-noise phase uncertainty can be achieved when loss rate is less than 85%, which indicates the prospect of practical application with the proposed scheme.