By performing two local displacement operations (LDOs) inside an SU(1,1) interferometer, called as the displacement-assisted SU(1,1) [DSU(1,1)], both the phase sensitivity based on homodyne detection and quantum Fisher information (QFI) with and without photon losses are investigated in this paper. In this DSU(1,1) interferometer, we focus our attention on the extent to which the introduced LDO affects the phase sensitivity and the QFI, even in the realistic scenario. Our analyses show that the estimation performance of DSU(1,1) interferometer is always better than that of SU(1,1) interferometer without the LDO, especially for the phase precision of the former in the ideal scenario closer to the Heisenberg limit via the increase of the LDO strength. Different from the latter, the robustness of the former can be also enhanced markedly by regulating and controlling the LDO. Our findings would open an useful view for quantum-improved phase estimation of optical interferometers.
By performing two local displacement operations (LDOs) inside an SU(1,1) interferometer, called as the displacement-assisted SU(1,1) [DSU(1,1)], both the phase sensitivity based on homodyne detection and quantum Fisher information (QFI) with and without photon losses are investigated in this paper. In this DSU(1,1) interferometer, we focus our attention on the extent to which the introduced LDO affects the phase sensitivity and the QFI, even in the realistic scenario. Our analyses show that the estimation performance of DSU(1,1) interferometer is always better than that of SU(1,1) interferometer without the LDO, especially for the phase precision of the former in the ideal scenario closer to the Heisenberg limit via the increase of the LDO strength. Different from the latter, the robustness of the former can be also enhanced markedly by regulating and controlling the LDO. Our findings would open an useful view for quantum-improved phase estimation of optical interferometers.
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.
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.
We propose a novel method for enhancing phase estimation in the displacement-assisted SU(1,1) [DSU(1,1)] interferometer by incorporating the photon recycling technique, evaluated under both single-intensity detection (SID) and homodyne detection (HD) schemes. Our analysis shows that utilizing the photon recycling technique, the photon-recycled DSU(1,1) interferometer performs better than the conventional DSU(1,1) interferometer under certain conditions. We also demonstrate that this improvement is achievable in both SID and HD schemes. In addition, to discuss the maximum sensitivity achieved by our proposed model, we have calculated the quantum Cramér–Rao bound (QCRB) within the framework and found that our proposed model approaches the QCRB. Therefore, we believe that our findings offer a promising new approach to improving phase sensitivity through photon recycling.
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.
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.
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.