Opt Express. 2023 Feb 13;31(4):6499-6513. doi: 10.1364/OE.476822.
We propose an alternative scheme for phase estimation in a Mach-Zehnder interferometer (MZI) with photon recycling. It is demonstrated that with the same coherent-state input and homodyne detection, our proposal possesses a phase sensitivity beyond the traditional MZI. For instance, it can achieve an enhancement factor of ∼9.32 in the phase sensitivity compared with the conventional scheme even with a photon loss of 10% on the photon-recycled arm. From another point of view, the quantum Cramér-Rao bound (QCRB) is also investigated. It is found that our scheme is able to achieve a lower QCRB than the traditional one. Intriguingly, the QCRB of our scheme is dependent of the phase shift ϕ while the traditional scheme has a constant QCRB regardless of the phase shift. Finally, we present the underlying mechanisms behind the enhanced phase sensitivity. We believe that our results provide another angle from which to enhance the phase sensitivity in a MZI via photon recycling.
我们提出了一种在具有光子回收的马赫-曾德尔干涉仪（MZI）中进行相位估计的替代方案。结果表明，在相同的相干态输入和外差检测下，我们的方案具有超越传统 MZI 的相位灵敏度。例如，与传统方案相比，即使在光子回收臂上有 10%的光子损耗，它也可以实现约 9.32 的相位灵敏度增强因子。从另一个角度来看，我们还研究了量子克拉默-罗不等式（QCRB）。结果发现，我们的方案能够比传统方案实现更低的 QCRB。有趣的是，我们方案的 QCRB 依赖于相移 ϕ，而传统方案的 QCRB 则与相移无关，无论相移如何，其 QCRB 都是恒定的。最后，我们提出了增强相位灵敏度背后的基本机制。我们相信，我们的结果为通过光子回收增强 MZI 中的相位灵敏度提供了另一个角度。
