Optimal phase point for SU(1,1) interferometer

Optimal phase point, where the best phase sensitivity can be achieved, plays an important role in the operation of an interferometer. In this paper, we theoretically investigate the optimal phase point of an SU(1,1) interferometer in joint intensity detection and joint homodyne detection, respectively. We demonstrate that for joint intensity detection, the optimal phase point of the SU(1,1) interferometer happens nearby the dark fringe with realistic factors considered. The divergence of the optimal phase point from the dark fringe can be dependent on the initial injection scheme of the SU(1,1) interferometer, the strength of the parametric amplifier inside the interferometer, and the internal losses of the system. In addition, we find that for joint homodyne detection, the optimal phase point of the SU(1,1) interferometer can happen only at the bright or dark fringe. Our results may pave the way to real applications of the SU(1,1) interferometer.