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Quantum non-demolition (QND) measurement is an important tool in the field ofquantum information processing and quantum optics. The atom-light hybridinterferometer is of great interest due to its combination of atomic spin waveand optical wave, which can be utilized for photon number QND measurement viathe AC-Stark effect. In this paper, we present an SU(1,1)-SU(2)-concatenatedatom-light hybrid interferometer, and theoretically study the QND measurementof photon number. Compared to the traditional SU(2) interferometer, thesignal-to-noise ratio (SNR) in a balanced case is improved by a gain factor ofthe nonlinear Raman process (NRP) in this proposed interferometer. Furthermore,the condition of high-quality of QND measurement is analyzed. In the presenceof losses, the measurement quality is reduced. We can adjust the gain parameterof the NRP in readout stage to reduce the impact due to losses. Moreover, thisscheme is a multiarm interferometer, which has the potential of multiparameterestimation with many important applications in the detection of vector fields,quantum imaging and so on.

Quantum non-demolition measurement based on an SU(1,1)-SU(2)-concatenated atom-light hybrid interferometer