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Journal of Physics B Atomic Molecular and Optical Physics

Supersensitive phase estimation for hybrid interferometer using balanced homodyne detection

Tao Shao, Minyang Zhang, Chenlu Li, Yuanxiang Wang, Youyou Hu, Mingming Zhang, Jun Liu

Published Oct 24, 2023• 3 citations
Publisher

Abstract

Abstract We have theoretically investigated the phase sensitivity of the hybrid interferometer with two coherent beams using the method of balance homodyne detection. The measurement device is a nonlinear–linear hybrid interferometer consisting of an optical parametric amplifier and a beam splitter. We prove that the phase sensitivity can beat the shot noise limit in the optimal conditions. Furthermore, we derive the quantum Cramér–Rao bound of the hybrid interferometer. The effects of transmission loss and detection loss on the measurement accuracy are discussed. The detection accuracy of this scheme is compared with that of the conventional SU (1,1) interferometer. Our results show that this scheme outperforms the conventional SU (1,1) interferometer scheme at high parametric strength. This scheme can be implemented with existing experimental techniques and will have important applications in quantum precision measurements.

DOI
10.1088/1361-6455/ad065c

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Abstract We have theoretically investigated the phase sensitivity of the hybrid interferometer with two coherent beams using the method of balance homodyne detection. The measurement device is a nonlinear–linear hybrid interferometer consisting of an optical parametric amplifier and a beam splitter. We prove that the phase sensitivity can beat the shot noise limit in the optimal conditions. Furthermore, we derive the quantum Cramér–Rao bound of the hybrid interferometer. The effects of transmission loss and detection loss on the measurement accuracy are discussed. The detection accuracy of this scheme is compared with that of the conventional SU (1,1) interferometer. Our results show that this scheme outperforms the conventional SU (1,1) interferometer scheme at high parametric strength. This scheme can be implemented with existing experimental techniques and will have important applications in quantum precision measurements.
Estimating nonlinear phase shifts is useful to analyze many dynamical processes. In this work, with respect to the second-order nonlinear phase shifts, we propose an estimation scheme with a coherent state as the input and balanced homodyne detection as the readout strategy. The measurement setup is a nonlinear-linear hybrid interferometer composed of an optical parametric amplifier and a beam splitter. We analyze the precision and determine the optimal parameters of our scheme. The precision is compared with the quantum Cramér–Rao bound as well as the precision of a conventional nonlinear interferometer. In view of the fact that photon loss is ubiquitous, the effects of transmission loss and detection loss on the precision are addressed. At low gain, our scheme is superior to the scheme using a conventional nonlinear interferometer, and the precision can saturate the quantum Cramér–Rao bound.
Abstract We investigate the enhancement of phase sensitivity of a nonlinear-linear hybrid interferometer with the input of the two-mode squeezed coherent state (TMSCS). With the TMSCS produced by four-wave mixing, the quantum Cramér-Rao bounds (QCRB) can beat the Heisenberg limit (HL). Under the phase matched conditions, the optimal phase sensitivity with the balanced homodyne detection measurement can beat the HL and approach QCRB. The effects of internal and external losses on the measurement accuracy are also discussed. The results demonstrate that the scheme is robustness against to internal losses and this protocol can resist external detection loss which is up to 39%. Our results improve the performance of hybrid interferometers and this scheme can find important practical applications in quantum metrology.
Phase sensitivity of an SU⁡(1,1)\operatorname{SU}(1,1)SU(1,1) interferometer via product detection
Abstract We theoretically analyze the phase sensitivity of an SU⁡(1,1)\operatorname{SU}(1,1)SU(1,1) SU ( 1 , 1 ) interferometer with various input states by product detection in this paper. This interferometer consists of two parametric amplifiers that play the role of beam splitters in a traditional Mach–Zehnder interferometer. The product of the amplitude quadrature of one output mode and the momentum quadrature of the other output mode is measured via balanced homodyne detection. We show that product detection has the same phase sensitivity as parity detection for most cases, and it is even better in the case with two coherent states at the input ports. The phase sensitivity is also compared with the Heisenberg limit and the quantum Cramér–Rao bound of the SU⁡(1,1)\operatorname{SU}(1,1)SU(1,1) SU ( 1 , 1 ) interferometer. This detection scheme can be easily implemented with current homodyne technology, which makes it highly feasible. It can be widely applied in the field of quantum metrology.
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 consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach–Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer–Rao bound than the pure active (e.g., SU(1,1)) interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [ Phys. Rev. D 23 1693 (1981)], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves’ scheme.
SU(1,1) interferometers, based on the usage of nonlinear elements, are superior to passive interferometers in phase sensitivity. However, the SU(1,1) interferometer cannot make full use of photons carrying phase information as the second nonlinear element annihilates some of the photons inside. Here we focus on improving phase sensitivity and propose a different protocol based on a modified SU(1,1) interferometer, where the second nonlinear element is replaced by a beam splitter. We utilize two coherent states as inputs and implement balanced homodyne measurement at the output. Our analysis suggests that the protocol we propose can achieve the sub-shot-noise-limited phase sensitivity and is robust against photon loss as well as background noise. Our work is important for practical quantum metrology using SU(1,1) interferometers.