We theoretically analyze the phase sensitivity of an $\operatorname{SU}(1,1)$ interferometer with various input states by product detection in this paper. This interferometer consists of two parametric amplifiers that play the role of beam splitters in a traditional Mach–Zehnder interferometer. The product of the amplitude quadrature of one output mode and the momentum quadrature of the other output mode is measured via balanced homodyne detection. We show that product detection has the same phase sensitivity as parity detection for most cases, and it is even better in the case with two coherent states at the input ports. The phase sensitivity is also compared with the Heisenberg limit and the quantum Cramér–Rao bound of the $\operatorname{SU}(1,1)$ interferometer. This detection scheme can be easily implemented with current homodyne technology, which makes it highly feasible. It can be widely applied in the field of quantum metrology.

中文翻译：

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\(\operatorname{SU}(1,1)\) 干涉仪通过乘积检测的相位灵敏度

本文通过产品检测从理论上分析了具有各种输入状态的$\operatorname{SU}(1,1)$干涉仪的相位灵敏度。该干涉仪由两个参量放大器组成，它们在传统的 Mach-Zehnder 干涉仪中起到分束器的作用​​。一种输出模式的振幅正交与另一种输出模式的动量正交的乘积是通过平衡零差检测来测量的。我们表明，在大多数情况下，乘积检测与奇偶校验检测具有相同的相位灵敏度，在输入端口具有两个相干状态的情况下甚至更好。相位灵敏度还与 $\operatorname{SU}(1,1)$ 干涉仪的海森堡极限和量子克拉梅-拉奥界进行了比较。使用当前的零差技术可以轻松实现这种检测方案，这使它非常可行。可广泛应用于量子计量领域。