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arXiv:2012.04236 · Physical Review A

Phase sensitivity approaching the quantum Cramér-Rao bound in a modified SU(1,1) interferometer

Jiandong Zhang, Chenglong You, Chuang Li, Shuai Wang

Published Mar 29, 2021• 32 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.103.032617

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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.
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.
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.
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 of an SU(1,1) interferometer from two aspects, i.e., the phase estimation determined by the error propagation formula and that by the quantum Cramér-Rao bound (QCRB). The results show that the phase sensitivity by using the intensity detection reaches the sub-shot-noise limit with a coherent state and an m-photon-added squeezed vacuum state (m-PA-SVS) as inputs. The phase sensitivity gradually approaches the Heisenberg limit for increasing m, and the ultimate phase precision improves with the increase of m. In addition, the QCRB can be saturated by the intensity detection with inputting the m-PA-SVS.
Improving interferometric phase sensitivity is crucial for high-precision measurements in rapidly developing quantum technologies. The Mach–Zehnder interferometer (MZI) is a versatile tool for analyzing this phenomenon. By splitting and recombining a light beam using beam splitters, the MZI allows for precise phase sensitivity analysis using tools like the quantum Cramér–Rao bound (QCRB) and the quantum Fisher information (QFI). This paper analyzes the phase sensitivity of an MZI in various scenarios using different detection schemes and input states. We compare the single- and two-parameter quantum estimation and their associated QCRB for three phase-shift situations: in both arms; only in the upper arm (asymmetric); and in both arms symmetrically. We then investigate the phase sensitivity under three detection schemes: intensity difference; single-mode intensity; and balanced homodyne. Additionally, we explore the use of Perelomov and Barut–Girardello coherent states, two types of SU(1,1) coherent states, in all scenarios. Notably, we demonstrate that, under optimal conditions, all detection schemes can achieve the QCRB by utilizing SU(1,1) coherent states as input states.