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We construct an interferometer with parametric amplifiers as beam splitters. Because of the gain in the parametric amplifiers, the maximum output intensity of the interferometer can be much bigger than the input intensity as well as the intensity inside the interferometer (the phase sensing intensity). We find that the fringe intensity depends quadratically on the intensity of the phase sensing field at high gain. This type of nonlinear interferometer has better sensitivity than the traditional linear interferometer made of beam splitters with the same phase sensing intensity.
Jing et al. (Mon,) studied this question.