The Phase Sensitivities for Different Phase-Shift Configurations in an SU(1,1) Interferometer**Supported by the National Natural Science Foundation of China under Grant Nos. 11747161 and 11974189 and the China Postdoctoral Science Foundation under Grant No. 2018M642293

Abstract

We theoretically study the phase sensitivities of two different phase-shift configurations in an SU(1,1) interferometer with coherent ⊗ squeezed vacuum states. According to quantum Cramér-Rao theorem, we analytically obtain the ultimate phase sensitivities for two types of phase shift accumulating in one- and two-arm. Compared with the case of one-arm phase shift, the model with phase shift encoding in both arms may provide a better sensitivity when the strength of squeezed vacuum state is large enough. Furthermore, we discuss the achievable sensitivities with the homodyne measurement by invoking of error-propagation formula. In addition, we study the effect of internal and outernal photon losses on the phase sensitivity of the SU(1,1) interferometer and find that the unbalanced interferometer is helpful to improve precision even with high external losses.