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arXiv:1805.02358 · Journal of the Optical Society of America B

Effects of loss on the phase sensitivity with parity detection in an SU(1,1) interferometer

Dong Li, Chun-Hua Yuan, Yao Yao, Wei Jiang, Mo Li, Weiping Zhang

Published Apr 11, 2018• 31 citations
arXivHTMLPDF

Abstract

We theoretically study the effects of loss on the phase sensitivity of an SU(1,1) interferometer with parity detection with various input states. We show that although the sensitivity of phase estimation decreases in the presence of loss, it can still beat the shot-noise limit with small loss. To examine the performance of parity detection, the comparison is performed among homodyne detection, intensity detection, and parity detection. Compared with homodyne detection and intensity detection, parity detection has a slightly better optimal phase sensitivity in the absence of loss but has a worse optimal phase sensitivity with a significant amount of loss with one-coherent state or coherent ⊗ squeezed state input.

DOI
10.1364/josab.35.001080

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We theoretically study the effects of loss on the phase sensitivity of an SU(1,1) interferometer with parity detection with various input states. We show that although the sensitivity of phase estimation decreases in the presence of loss, it can still beat the shot-noise limit with small loss. To examine the performance of parity detection, the comparison is performed among homodyne detection, intensity detection, and parity detection. Compared with homodyne detection and intensity detection, parity detection has a slightly better optimal phase sensitivity in the absence of loss but has a worse optimal phase sensitivity with a significant amount of loss with one-coherent state or coherent ⊗ squeezed state input.
We theoretically study the phase sensitivity of an SU(1,1) interferometer with a thermal state and a squeezed vacuum state as inputs and parity detection as the measurement. We find that the phase sensitivity can beat the shot-noise limit and approaches the Heisenberg limit, with increasing input photon number, in an ideal situation. We also consider the effect of various noises, including photon loss, dark counts, and thermal photon noise. Our results show that the phase sensitivity is below the shot-noise limit with photon loss and dark counts, but cannot beat the shot-noise limit in the presence of thermal noise.
We theoretically study the phase sensitivity of an SU(1,1) interferometer with a thermal state and a squeezed vacuum state as inputs and parity detection as the measurement. We find that the phase sensitivity can beat the shot-noise limit and approaches the Heisenberg limit, with increasing input photon number, in an ideal situation. We also consider the e ect of various noises, including photon loss, dark counts, and thermal photon noise. Our results show that the phase sensitivity is below the shot-noise limit with photon loss and dark counts, but cannot beat the shot-noise limit in the presence of thermal noise.
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.
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 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.
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.