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Physical Review A

Phase estimation via a number-conserving operation inside a SU(1,1) interferometer

Qingqian Kang, Zekun Zhao, Teng Zhao, Cunjin Liu, Liyun Hu

Published Aug 23, 2024• 11 citations
Publisher

Abstract

Utilizing nonlinear elements, SU(1,1) interferometers demonstrate superior phase sensitivity compared to passive interferometers. However, the precision is significantly impacted by photon losses, particularly internal losses. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing a number-conserving operation (NCO), i.e., $a{a}^{\ifmmode\dagger\else\textdagger\fi{}}$ and ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$, inside the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We analyze the effects of the NCO on the phase sensitivity, the quantum Fisher information (QFI), and the quantum Cram\'er-Rao bound under both ideal and photon-loss scenarios. Our findings reveal that the internal non-Gaussian operations can enhance the phase sensitivity and the QFI and effectively improve the robustness of the SU(1,1) interferometer against internal photon losses. Notably, the ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$ scheme exhibits superior improvement in both the ideal and photon-loss cases in terms of phase sensitivity. Moreover, in the ideal case, the $a{a}^{\ifmmode\dagger\else\textdagger\fi{}}$ scheme slightly outperforms the ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$ scheme in terms of the QFI. However, in the presence of high photon losses, the ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$ scheme demonstrates a greater advantage.

DOI
10.1103/physreva.110.022432

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Utilizing nonlinear elements, SU(1,1) interferometers demonstrate superior phase sensitivity compared to passive interferometers. However, the precision is significantly impacted by photon losses, particularly internal losses. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing a number-conserving operation (NCO), i.e., aa\ifmmode†\else\textdagger\fia{a}^{\ifmmode\dagger\else\textdagger\fi{}}aa\ifmmode†\else\textdagger\fi and a\ifmmode†\else\textdagger\fia{a}^{\ifmmode\dagger\else\textdagger\fi{}}aa\ifmmode†\else\textdagger\fia, inside the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We analyze the effects of the NCO on the phase sensitivity, the quantum Fisher information (QFI), and the quantum Cram'er-Rao bound under both ideal and photon-loss scenarios. Our findings reveal that the internal non-Gaussian operations can enhance the phase sensitivity and the QFI and effectively improve the robustness of the SU(1,1) interferometer against internal photon losses. Notably, the a\ifmmode†\else\textdagger\fia{a}^{\ifmmode\dagger\else\textdagger\fi{}}aa\ifmmode†\else\textdagger\fia scheme exhibits superior improvement in both the ideal and photon-loss cases in terms of phase sensitivity. Moreover, in the ideal case, the aa\ifmmode†\else\textdagger\fia{a}^{\ifmmode\dagger\else\textdagger\fi{}}aa\ifmmode†\else\textdagger\fi scheme slightly outperforms the a\ifmmode†\else\textdagger\fia{a}^{\ifmmode\dagger\else\textdagger\fi{}}aa\ifmmode†\else\textdagger\fia scheme in terms of the QFI. However, in the presence of high photon losses, the a\ifmmode†\else\textdagger\fia{a}^{\ifmmode\dagger\else\textdagger\fi{}}aa\ifmmode†\else\textdagger\fia scheme demonstrates a greater advantage.
Utilizing nonlinear elements, SU(1,1) interferometers demonstrate superior phase sensitivity compared to passive interferometers. However, the precision is significantly impacted by photon losses, particularly internal losses. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing number-conserving operations (PA-then-PS and PS-then-PA) within the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We analyze the effects of number-conserving operations on the phase sensitivity, the quantum Fisher information, and the quantum Cramer-Rao bound under both ideal and photon losses scenarios. Our findings reveal that the internal non-Gaussian operations can enhance the phase sensitivity and the quantum Fisher information, and effectively improve the robustness of the SU(1,1) interferometer against internal photon losses. Notably, the PS-then-PA scheme exhibits superior improvement in both ideal and photon losses cases in terms of phase sensitivity. Moreover, in the ideal case, PA-then-PS scheme slightly outperforms PS-then-PA scheme in terms of the quantum Fisher information and the Quantum Cramer-Rao. However, in the presence of photon losses, PS-then-PA scheme demonstrates a greater advantage.
Abstract To improve the phase sensitivity, multi-photon subtraction schemes (multi-PSS) within the SU(1,1) interferometer are proposed. The input states are the coherent state and the vacuum state, and the detection method is homodyne detection. The effects of multi-photon subtraction on phase sensitivity, quantum Fisher information (QFI), and quantum Cramér-Rao bound (QCRB) are analyzed under both ideal and photon losses situations. It is shown that the internal subtraction operation can improve the phase sensitivity, which becomes better performance by increasing subtraction number. It can also efficiently improve the robustness of the SU(1,1) interferometer against internal photon losses. By comparing separatively arbitrary photon subtraction on the two-mode inside SU(1,1) interferometer, the performance differences under different conditions are analyzed, including the asymmetric properties of non-Gaussian operations on the phase precision and the QFI. Our proposed scheme represents a valuable method for achieving quantum precision measurements.
Compared with passive interferometers, SU(1,1) interferometers demonstrate superior phase sensitivity due to the incorporation of nonlinear elements that enhance their ability to detect phase shifts. Nevertheless, the measurement precision of these interferometers is considerably impacted by photon losses, particularly internal losses, thereby restricting the overall accuracy of measurements. Addressing these issues is essential to fully realize the advantages of SU(1,1) interferometers in practical applications. Among the available resources in quantum metrology, squeezing stands out as one of the most practical and efficient approaches. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing the single-path local squeezing operation (LSO) inside the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We not only analyze the effects of the single-path LSO scheme on the phase sensitivity and the quantum Fisher information (QFI) under both ideal and photon-loss cases but also compare the impact of different squeezing parameters r on the system performance. Our findings reveal that the internal single-path LSO scheme can significantly enhance the phase sensitivity and QFI by strengthening intramode correlations while weakening intermode correlations, thereby effectively improving the robustness of the SU(1,1) interferometer against photon losses.
Compared to passive interferometers, SU(1,1) interferometers exhibit superior phase sensitivity due to the incorporation of nonlinear elements that enhance their ability to detect phase shifts. However, the precision of these interferometers is significantly affected by photon losses, especially internal losses, which can limit the overall measurement accuracy. Addressing these issues is essential to fully realize the advantages of SU(1,1) interferometers in practical applications. Among the known resources of quantum metrology, one of the most practical and efficient is squeezing. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing the single-path local squeezing operation (LSO) inside the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We not only analyze the effects of the single-path LSO scheme on the phase sensitivity and the quantum Fisher information (QFI) under both ideal and photon-loss cases but also compare the effects of different squeezing parameters r on the system performance. Our findings reveal that the internal single-path LSO scheme can enhance the phase sensitivity and the QFI, effectively improving the robustness of the SU(1,1) interferometer against internal and external photon losses. Additionally, a larger squeezing parameter r leads to a better performance of the interferometer.
We propose a high-precision phase estimation scheme in a hybrid interferometer by synergistically combining a Kerr nonlinear phase shifter and multi-photon subtraction operations. Using a coherent state and a vacuum state as input resources, we systematically evaluate the phase sensitivity via homodyne detection and analyze the quantum Fisher information as well as the quantum Cramér-Rao bound under both ideal and lossy conditions. Our results show that the joint integration of Kerr nonlinearity and multi-photon subtraction yields remarkable advantages over either technique used alone. The proposed scheme enables the phase sensitivity to surpass the standard quantum limit, exceed the conventional Heisenberg scaling (1/N1/N1/N), and approach the super-Heisenberg scaling (1/N21/N^{2}1/N2)-a direct consequence of Kerr nonlinearity. More precisely, the super-Heisenberg scaling $\propto $ 1/N21/N^{2}1/N2 is the ultimate precision limit permitted by the k=2k=2k=2 Kerr nonlinearity and does not violate the fundamental Heisenberg limit for linear phase accumulation. Even under moderate internal photon loss, the system maintains high precision and exhibits enhanced robustness to decoherence. The Kerr nonlinearity introduces an intensity-dependent phase shift proportional to the squared photon number, while multi-photon subtraction tailors non-Gaussian states to strengthen phase information extraction. Compared with existing schemes based on hybrid interferometers or SU(1,1) interferometers, our architecture achieves superior precision and stronger loss resilience. All components are experimentally accessible with current quantum optical technologies. This work provides a promising route for practical high-precision quantum metrology and quantum sensing.
In the field of quantum precision measurement, enhancing phase sensitivity is crucial for various applications, including quantum metrology and quantum sensing technologies. We theoretically investigate the improvement in phase sensitivity and quantum Fisher information achieved through multiphoton subtraction operations at the output port of an SU(1,1) interferometer under conditions of photon loss. We use vacuum and coherent states as the inputs and detect the outputs by intensity detection. The results indicate that internal photon losses within the SU(1,1) interferometer have a more significant impact on the phase sensitivity compared to external photon losses. Moreover, increasing the number of photon subtractions m effectively enhances both the phase sensitivity and the quantum Fisher information. Notably, even under conditions of severe photon loss, the multiphoton subtraction operations can enable the phase sensitivity to surpass the standard quantum limit, approaching both the Heisenberg limit and the quantum Cramér-Rao bound. This study provides a new theoretical basis for enhancing the phase sensitivity in the SU(1,1) interferometer.