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Quantum Information Processing

Approaching quantum-limited phase tracking with a large photon flux in a fiber Mach–Zehnder interferometer

Fang Liu, Kaimin Zheng, Liu Wang, Chuan Xu, Lidan Zhang, TianXin Wang, YuChang Liu, Xiang Li, Lijian Zhang, Yong Zhang, Min Xiao

Published May 1, 2021• 3 citations
Publisher
DOI
10.1007/s11128-021-03097-x

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Recent advances in quantum photonics have enabled increasingly robust protocols in optical phase estimation, achieving precisions beyond the standard quantum limit and approaching the Heisenberg limit. While intrinsic losses hinder the realization of unconditional super-sensitivity, reaching quantum advantage, defined as sensitivity surpassing that of any classical counterpart with identical resources, remains achievable. Here we experimentally demonstrate such an advantage using a fully fibered Mach-Zehnder-type interferometer operating at telecom wavelengths, free of post-selection. The scheme relies on the conversion of polarization-entangled photon pairs, a degree of freedom commonly favored for experimental convenience, into energy-time entanglement, which is particularly well suited for scalable fiber-based sensors. All system imperfections, including asymmetric losses and detector inefficiencies, are accounted for in the Fisher information analysis, yielding a measured quantum advantage of 10%. This result highlights the practicality of compact, alignment-free quantum interferometers for real-world sensing applications.
Quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters. Similar to the estimation of a constant phase, there is a standard quantum limit for stochastic phase estimation, which can be obtained with the Mach–Zehnder interferometer and coherent input state. Recently, it has been shown that the stochastic standard quantum limit can be surpassed with nonclassical resources such as squeezed light. However, practical methods to achieve quantum enhancement in the stochastic phase estimation remain largely unexplored. Here we propose a method utilizing the SU(1,1) interferometer and coherent input states to estimate a stochastic optical phase. As an example, we investigate the Ornstein–Uhlenback stochastic phase. We analyze the performance of this method for three key estimation problems: prediction, tracking, and smoothing. The results show significant reduction of the mean square error compared with the Mach–Zehnder interferometer under the same photon number flux inside the interferometers. In particular, we show that the method with the SU(1,1) interferometer can achieve fundamental quantum scaling, achieve stochastic Heisenberg scaling, and surpass the precision of the canonical measurement.
In this paper, a Mach–Zehnder interferometer is analyzed with a single photon Gaussian wave packet at one of its input ports and vacuum state at the other input port. Various noises arising in the Mach–Zehnder interferometer such as photon flux noise and quadrature noise are mathematically analyzed. The effect of variation in device parameters on the power spectral density at the output ports of the Mach–Zehnder interferometer is studied. It is observed that the power spectral density of photon flux noise autocorrelation at the output ports of a Mach–Zehnder interferometer is a function of phase shift, whereas the power spectral density of quadrature noise autocorrelation at the output ports of a Mach–Zehnder interferometer is a function of frequency of a single photon wave packet and the phase shift. The analysis carried out in this paper will be helpful in understanding the quantum fluctuations in the design of quantum logic devices and circuits where the Mach–Zehnder interferometer is a core building block.