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