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Chinese Physics B

Phase sensitivity of a lossy truncated SU(1,1) interferometer with double-port homodyne detection

Yu-Wei 煜伟 Xiao 肖, Yue Ji, Jun Wei, Jiandong Zhang, Li-Li 丽丽 Hou 侯

Published Aug 20, 2025• 1 citation
Publisher

Abstract

Abstract We theoretically investigate the phase sensitivity of a truncated SU(1,1) interferometer fed with a two-mode coherent state and employing double-port homodyne detection. On the one hand, we analytically demonstrate that the two-mode coherent state provides better phase sensitivity than the single-mode coherent state. In addition, we show that the double-port homodyne detection is a quasi-optimal measurement. For a bright coherent-state input, the sensitivity of this scheme saturates the phase-sensitivity bound determined by the quantum Fisher information. On the other hand, we quantitatively illustrate the advantage of double-port homodyne detection over the single-port scheme under ideal conditions and in the presence of photon loss, respectively. Furthermore, our analysis indicates that the scheme we propose is robust against photon loss.

DOI
10.1088/1674-1056/adfd46

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Abstract We theoretically investigate the phase sensitivity of a truncated SU(1,1) interferometer fed with a two-mode coherent state and employing double-port homodyne detection. On the one hand, we analytically demonstrate that the two-mode coherent state provides better phase sensitivity than the single-mode coherent state. In addition, we show that the double-port homodyne detection is a quasi-optimal measurement. For a bright coherent-state input, the sensitivity of this scheme saturates the phase-sensitivity bound determined by the quantum Fisher information. On the other hand, we quantitatively illustrate the advantage of double-port homodyne detection over the single-port scheme under ideal conditions and in the presence of photon loss, respectively. Furthermore, our analysis indicates that the scheme we propose is robust against photon loss.
We provide a general theoretical derivation of the phase sensitivity achieved by SU(1,1) interferometers under homodyne detection. The general expressions obtained accommodate arbitrary input states and include internal and external losses. In this systematic review, both full SU(1,1) interferometers with two parametric amplifiers and the truncated interferometers with only one parametric amplifier are examined. We investigate scenarios involving both single-output ports and joint homodyne detection, and consider parametric amplifiers with equal gains or with a boosted gain second amplifier. Our analytical formulation provides physical insight and understanding of the improvements in the sensitivity, which are shown to originate from noise reduction and/or signal amplification, depending on the configurations and practical implementations. Surprisingly, the configuration with single-output mode detection and parametric amplifiers with equal gains exhibits the highest robustness to very high internal losses. We finally apply this framework to a ubiquitous ∣α,0⟩|α,0\rangle∣α,0⟩ input two-mode coherent probe state. This approach permits the comparison of different strategies and the optimization of the interferometer performance in the presence of losses. In particular, we determine which amplification and detection configurations provide the best performance, depending on the level of losses. This exemplifies how this general analytical approach provides a powerful tool to design quantum-enhanced interferometers and achieve optimal sensitivity with selected probe states and homodyne detection.
Homodyne detection is often used for interferometers based on nonlinear optical gain media. For the configuration of a seeded, "truncated SU(1,1)" interferometer Anderson, et al. [ Phys. Rev. A95, 063843 (2017)] showed how to optimize the homodyne detection scheme and demonstrated theoretically that it can saturate the quantum Cramer-Rao bound for phase estimation. In this work we extend those results by taking into account loss in the truncated SU(1,1) interferometer and determining the optimized homodyne detection scheme for phase measurement. Further, we build a truncated SU(1,1) interferometer and experimentally demonstrate that this optimized scheme achieves a reduction in noise level, corresponding to an enhanced potential phase sensitivity, compared to a typical homodyne detection scheme for a two-mode squeezed state. In doing so, we also demonstrate an improvement in the degree to which we can beat the standard quantum limit with this device.
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 scheme that is used for the enhancement of phase sensitivity. The SU(1,1) interferometer with a two-mode squeezed coherent state input, using balanced homodyne detection (BHD) and intensity detection (ID), is shown. Our results demonstrate that the phase sensitivity achieved via BHD outperforms that of ID. The optimal phase sensitivity via BHD surpasses the Heisenberg limit (HL) and approaches the quantum Cramér–Rao bound. A larger photon number and parameter strength can make the phase sensitivity better. Furthermore, we show the effects of internal and external losses on phase sensitivity in detail. When external loss reaches 10%, the phase sensitivity can reach the HL. Next, we have a detailed discussion on the impact of the squeezing parameter and photon number on phase sensitivity, which shows that our scheme has better phase sensitivity and enhanced robustness. This interferometer system thus holds significant potential for applications in quantum precision measurement.
We study the phase sensitivity in the conventional SU(2) and nonconventional SU(1,1) interferometers with a coherent and squeezed vacuum input state via quantum Cramer-Rao bound. We explicitly construct the detection scheme that gives the optimal phase sensitivity. For practical purposes, we show that in the presence of photon loss, both interferometers with proper homodyne detections are nearly optimal. We also find that unlike the coherent state and the squeezed vacuum state, the effects of imperfect detector on the phase sensitivity cannot be asymptotically removed for a generic coherent-squeezed state.