华东师范大学学报（自然科学版） >

2022 , Vol. 2022 >Issue 2: 135 - 142

DOI: https://doi.org/10.3969/j.issn.1000-5641.2022.02.016

物理学与电子学

主动关联马赫-曾德尔干涉仪中多参数相位估值的极限

  • 王强 ,
  • 曾杰 ,
  • 焦高锋 ,
  • 袁春华
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  • 华东师范大学 物理与电子科学学院, 上海　200241

收稿日期: 2021-04-13

  录用日期: 2021-11-26

  网络出版日期: 2022-03-28

基金资助

国家自然科学基金(1197411)

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Limit of multi-parameter phase estimation in an actively correlated Mach-Zehnder interferometer

  • WANG Qiang ,
  • ZENG Jie ,
  • JIAO Gaofeng ,
  • YUAN Chunhua
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  • School of Physics and Electronic Science, East China Normal University, Shanghai　200241, China

Received date: 2021-04-13

  Accepted date: 2021-11-26

  Online published: 2022-03-28

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摘要

基于量子费歇尔信息和量子费希尔信息矩阵理论, 研究了三端口输入的主动关联马赫-曾德尔(Mach-Zehnder, MZ)干涉仪在两种不同输入态下的相位估值极限. 研究结果得到, 在单个端口输入任意光场的情况下, 利用相位平均和量子费歇尔信息矩阵理论消除了输入光场的涨落对相位估值极限的影响; 而在双端口输入相干态的情况下, 无法消除光场涨落对估值极限的影响, 且相位估值极限依赖于输入的双相干光的初始相位.

关键词： 主动关联马赫-曾德尔干涉仪; 量子费歇尔信息矩阵; 相位估值; 非线性分束器

本文引用格式

王强, 曾杰, 焦高锋, 袁春华. 主动关联马赫-曾德尔干涉仪中多参数相位估值的极限[J]. 华东师范大学学报（自然科学版）, 2022, 2022(2): 135-142. DOI: 10.3969/j.issn.1000-5641.2022.02.016

Abstract

In this paper, the phase estimation limits of an active-related Mach-Zehnder interferometer with three port inputs and two different input states was studied using quantum Fisher information and quantum Fisher information matrix theory. In the case of an arbitrary light field input to a single port, the effect of the input field fluctuation on the limit of phase estimation is eliminated by the theory of phase averaging and the quantum Fischer information matrix. In the case of a dual port input coherent state, the effect of the fluctuating light field on the estimation limit cannot be eliminated, and the phase estimation limit depends on the initial phase of the two input coherent states.

Key words： actively correlated Mach-Zehnder interferometer; quantum Fisher information matrix; phase estimation; nonlinear beam splitter

参考文献

1 KAY S M. Fundamentals of Statistical Signal Processing: Estimation Theory [M]. Upper Saddle River, New Jersey: Prentice-Hall Inc, 1993.
2 BRAUNSTEIN S L, CAVES C M. Statistical distance and the geometry of quantum states. Physical Review Letters, 1994, 72 (22): 3439- 3443.
3 HELSTROM C W. Quantum Detection and Estimation Theory [M]. New York: Academic Press, 1976.
4 YOU C L, ADHIKARI S, CHI Y X, et al. Multiparameter estimation with single photons-linearly-optically generated quantum entanglement beats the shotnoise limit[J]. Journal of Optics, 2017, 19(12): 124002.
5 CAVES C M. Quantum-mechanical noise in an interferometer. Physical Review D, 1981, 23, 1693- 1708.
6 DOWLING J P. Quantum optical metrology – the lowdown on high-N00N states. Contemporary Physics, 2008, 49 (2): 125- 143.
7 CAMPOS R A, GERRY C C, BENMOUSSA A. Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements. Physical Review A, 2003, 68 (2): 023810.
8 ANISIMOV P M, RATERMAN G M, CHIRUVELLI A, et al. Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit. Physical Review Letters, 2010, 104, 10360210.
9 YURKE B, MCCALL S L, KLAUDER J R. SU(2) and SU(1, 1) interferometers. Physical Review A, 1986, 33 (6): 4033- 4054.
10 PLICK W N, DOWLING J P, AGARWAL G S. Coherent-light-boosted, sub-shot noise, quantum interferometry. New Journal of Physics, 2010, (12): 083014.
11 OU Z Y. Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer. Physical Review A, 2012, 85 (2): 023815.
12 MARINO A M, CORZO TREJO N V, LETT P D. Effect of losses on the performance of an SU(1, 1) interferometer. Physical Review A, 2012, 86 (2): 023844.
13 LI D, YUAN C H, OU Z Y, et al. The phase sensitivity of an SU(1, 1) interferometer with coherent and squeezed-vacuum light. New Journal of Physics, 2014, 16, 073020.
14 GABBRIELLI M, PEZZE L, SMERZI A. Spin-mixing interferometry with Bose-Einstein condensates. Physical Review Letters, 2015, 115 (16): 163002.
15 CHEN Z D, YUAN C H, MA H M, et al. Effects of losses in the atom-light hybrid SU(1, 1) interferometer. Optics Express, 2016, 24 (16): 17766- 17778.
16 SPARACIARI C, OLIVARES S, PARIS M G A. Gaussian-state interferometry with passive and active elements. Physical Review A, 2016, 93 (2): 023810.
17 LI D, GARD B T, GAO Y, et al. Phase sensitivity at the Heisenberg limit in an SU(1, 1) interferometer via parity detection. Physical Review A, 2016, 94 (6): 063840.
18 GONG Q K, HU X L, LI D, et al. Intramode-correlation-enhanced phase sensitivities in an SU(1, 1) interferometer. Physical Review A, 2017, 96 (3): 033809.
19 GIESE E, LEMIEUX S, MANCEAU M, et al. Phase sensitivity of gain-unbalanced nonlinear interferometers. Physical Review A, 2017, 96 (5): 053863.
20 HU X, LI D, CHEN L Q, et al. Phase estimation for an SU(1, 1) interferometer in the presence of phase diffusion and photon losses. Physical Review A, 2018, 98 (2): 023803.
21 CAVES C M. Reframing SU(1, 1) interferometry. Advanced Quantum Technologies, 2020, 3 (11): 1900138.
22 JING J T, LIU C J, ZHOU Z F, et al. Realization of a nonlinear interferometer with parametric amplifiers. Applied Physics Letters, 2011, 99 (1): 011110.
23 HUDELIST F, KONG J, LIU C J, et al. Quantum metrology with parametric amplifier-based photon correlation interferometers [J]. Nature Communications, 2014(5): Article number 3049.
24 CHEN B, QIU C, CHEN S Y, et al. Atom-light hybrid interferometer. Physical Review Letters, 2015, 115 (4): 043602.
25 QIU C, CHEN S Y, CHEN L Q, et al. Atom-light superposition oscillation and Ramsey-like atom-light interferometer. Optica, 2016, 3 (7): 775- 780.
26 LINNEMANN D, STROBEL H, MUESSEL W, et al. Quantum-enhanced sensing based on time reversal of nonlinear dynamics. Physical Review Letters, 2016, 117 (1): 013001.
27 LEMIEUX S, MANCEAU M, SHARAPOVA P R, et al. Engineering the frequency spectrum of bright squeezed vacuum via group velocity dispersion in an SU(1, 1) interferometer. Physical Review Letters, 2016, 117 (18): 183601.
28 MANCEAU M, LEUCHS G, KHALILI F, et al. Detection loss tolerant supersensitive phase measurement with an SU(1, 1) interferometer. Physical Review Letters, 2017, 119 (22): 223604.
29 ANDERSON B E, GUPTA P, SCHMITTBERGER B L, et al. Phase sensing beyond the standard quantum limit with a variation on the SU(1, 1) interferometer. Optica, 2017, 4 (7): 752- 756.
30 GUPTA P, SCHMITTBERGER B L, ANDERSON B E, et al. Optimized phase sensing in a truncated SU(1, 1) interferometer. Optics Express, 2018, 26 (1): 391- 401.
31 DU W, JIA J, CHEN J F, et al. Absolute sensitivity of phase measurement in an SU(1, 1) type interferometer. Optics Letters, 2018, 43 (5): 1051- 1054.
32 JIAO G F ZHANG K Y, CHEN L Q, et al. Nonlinear phase estimation enhanced by an actively correlated Mach-Zehnder interferometer. Physical Review A, 2020, 102 (3): 033520.
33 JARZYNA M, DEMKOWICZ-DOBRZANSKI R. Quantum interferometry with and without an external phase reference. Physical Review A, 2012, 85 (1): 018011.
34 FUJIWARA A, IMAI H. A fibre bundle over manifolds of quantum channels and its application to quantum statistics. Journal of Physics A, 2008, 41 (25): 255304.
35 DU W, KONG J, JIA J, et al. SU(2)-in-SU(1, 1) nested interferometer [EB/OL]. (2020-04-29)[2021-05-06]. https://arxiv.org/pdf/2004.14266v1.pdf.
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