In a conventional atomic interferometer employing $N$ atoms, the phase sensitivity is at the standard quantum limit: $1/\sqrt N$. Under usual spin squeezing, the sensitivity is increased by lowering the quantum noise. It is also possible to increase the sensitivity by leaving the quantum noise unchanged while producing phase amplification. Here we show how to increase the sensitivity, to the Heisenberg limit of $1/N$, while increasing the quantum noise by $\sqrt N$ and amplifying the phase by a factor of $N$. Because of the enhancement of the quantum noise and the large phase magnification, the effect of excess noise is highly suppressed. The protocol uses a Schrödinger cat state representing a maximally entangled superposition of two collective states of $N$ atoms. The phase magnification occurs when we use either atomic state detection or collective state detection; however, the robustness against excess noise occurs only when atomic state detection is employed. We show that for one version of the protocol, the signal amplitude is $N$ when $N$ is even, and is vanishingly small when $N$ is odd, for both types of detection. We also show how the protocol can be modified to reverse the nature of the signal for odd versus even values of $N$. Thus, for a situation where the probability of $N$ being even or odd is equal, the net sensitivity is within a factor of $\sqrt 2$ of the Heisenberg limit. Finally, we discuss potential experimental constraints for implementing this scheme via one-axis-twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed because of the increased quantum noise and the large phase magnification inherent to the protocol. As a result, we find that the maximum improvement in sensitivity can be close to the ideal limit for as many as 10 million atoms.

中文翻译：

---

使用增加的量子噪声将原子干涉仪的灵敏度提高到海森堡极限

在采用$ N $原子的常规原子干涉仪中，相位灵敏度处于标准量子极限：$ 1 / \ sqrt N $。在通常的自旋压缩下，通过降低量子噪声来提高灵敏度。通过在产生相位放大的同时保持量子噪声不变，还可以提高灵敏度。在这里，我们展示了如何将灵敏度提高到$ 1 / N $的Heisenberg极限，同时将量子噪声增加$ \ sqrt N $并将相位放大了$ N $倍。由于量子噪声的增强和大的相位放大率，过量噪声的影响得到了高度抑制。该协议使用Schrödinger猫状态，该状态表示$ N $原子的两个集体状态的最大纠缠叠加。当我们使用原子状态检测或集体状态检测时，会发生相位放大。但是，仅当采用原子状态检测时，才会产生抗过度噪声的鲁棒性。我们表明，该协议的一个版本，信号幅度为$ N $当$ N $是偶数，并且是微乎其微当$ N $为奇数，这两种类型的检测。我们还展示了如何修改协议以反转信号奇数和偶数值的性质$ N $。因此，对于$ N $是偶数还是奇数的概率相等的情况，净灵敏度在Heisenberg限制的$ \ sqrt 2 $的范围内。最后，我们讨论了采用腔反馈方案通过单轴扭曲压缩实施该方案的潜在实验约束条件，并表明由于量子噪声增加和固有的大相位放大率，腔衰变和自发发射的影响得到了高度抑制协议。结果，我们发现灵敏度的最大提高可以接近多达1000万个原子的理想极限。