We propose a scheme that a dynamically evolving atom-molecule condensate maps onto an SU(1, 1) interferometer, which includes a nonlinear medium (nonlinear phase encoding). We give an analytical result of the phase uncertainty from the error propagation by measuring the particle number at the output and demonstrate the optimal quantum metrology, which is obtained with a time-reversal protocol. We show the phase sensitivity of the nonlinear medium with time-reversal protocol scales as 1/(2.1 N 2 ), which overcome the conventional sensitivity limit of 1/ N . Finally, the effect of the poor particle resolution detection on the phase sensitivity is discussed.

中文翻译：

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通过非线性相位编码提高SU（1，1）干涉仪的相位灵敏度

我们提出了一种方案，将动态演化的原子-分子冷凝物映射到SU（1，1）干涉仪上，该干涉仪包括非线性介质（非线性相位编码）。我们通过测量输出处的粒子数，从误差传播中给出了相位不确定性的分析结果，并演示了最佳的量子计量学，这是通过时间反转协议获得的。我们展示了时间逆向协议标度为1 /（2.1 N 2）的非线性介质的相位灵敏度，该相位灵敏度克服了常规灵敏度极限1 /N。最后，讨论了较差的颗粒分辨率检测对相位灵敏度的影响。