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Journal of the Optical Society of America B

Optimal phase point for SU(1,1) interferometer

Jun Xin, Xiao-Ming Lu, Xingmin Li, Guolong Li

Published Sep 16, 2019• 10 citations
Publisher

Abstract

Optimal phase point, where the best phase sensitivity can be achieved, plays an important role in the operation of an interferometer. In this paper, we theoretically investigate the optimal phase point of an SU(1,1) interferometer in joint intensity detection and joint homodyne detection, respectively. We demonstrate that for joint intensity detection, the optimal phase point of the SU(1,1) interferometer happens nearby the dark fringe with realistic factors considered. The divergence of the optimal phase point from the dark fringe can be dependent on the initial injection scheme of the SU(1,1) interferometer, the strength of the parametric amplifier inside the interferometer, and the internal losses of the system. In addition, we find that for joint homodyne detection, the optimal phase point of the SU(1,1) interferometer can happen only at the bright or dark fringe. Our results may pave the way to real applications of the SU(1,1) interferometer.

DOI
10.1364/josab.36.002824

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Optimal phase point, where the best phase sensitivity can be achieved, plays an important role in the operation of an interferometer. In this paper, we theoretically investigate the optimal phase point of an SU(1,1) interferometer in joint intensity detection and joint homodyne detection, respectively. We demonstrate that for joint intensity detection, the optimal phase point of the SU(1,1) interferometer happens nearby the dark fringe with realistic factors considered. The divergence of the optimal phase point from the dark fringe can be dependent on the initial injection scheme of the SU(1,1) interferometer, the strength of the parametric amplifier inside the interferometer, and the internal losses of the system. In addition, we find that for joint homodyne detection, the optimal phase point of the SU(1,1) interferometer can happen only at the bright or dark fringe. Our results may pave the way to real applications of the SU(1,1) interferometer.
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.
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.
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.
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 theoretically study the phase sensitivity of an SU(1,1) interferometer with a coherent state in one input port and a squeezed-vacuum state in the other input port using the method of homodyne detection. In this interferometer, beam splitting and recombination are generated by the parametric amplifiers instead of the beam splitters. Compared with the traditional Mach–Zehnder interferometer, the phase sensitivity of this interferometer can be improved due to the amplification process of the parametric amplifiers. Combined with the squeezed state input, the sensitivity can be improved further due to the noise reduction. The phase sensitivity of our scheme can approach the Heisenberg limit and the associated optimal condition is analyzed. The scheme can be implemented with current experimental technology.
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.