首页 > 论文 > Photonics Research > 8卷 > 10期(pp:1653-1661)

Quantum-enhanced stochastic phase estimation with the SU(1,1) interferometer

  • 摘要
  • 论文信息
  • 参考文献
  • 被引情况
  • PDF全文
分享:

Abstract

Quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters. Similar to the estimation of a constant phase, there is a standard quantum limit for stochastic phase estimation, which can be obtained with the Mach–Zehnder interferometer and coherent input state. Recently, it has been shown that the stochastic standard quantum limit can be surpassed with nonclassical resources such as squeezed light. However, practical methods to achieve quantum enhancement in the stochastic phase estimation remain largely unexplored. Here we propose a method utilizing the SU(1,1) interferometer and coherent input states to estimate a stochastic optical phase. As an example, we investigate the Ornstein–Uhlenback stochastic phase. We analyze the performance of this method for three key estimation problems: prediction, tracking, and smoothing. The results show significant reduction of the mean square error compared with the Mach–Zehnder interferometer under the same photon number flux inside the interferometers. In particular, we show that the method with the SU(1,1) interferometer can achieve fundamental quantum scaling, achieve stochastic Heisenberg scaling, and surpass the precision of the canonical measurement.

广告组1.2 - 空间光调制器+DMD
补充资料

DOI:10.1364/PRJ.395682

所属栏目:Quantum Optics

基金项目:National Key Research and Development Program of China10.13039/501100012166; National Natural Science Foundation of China10.13039/501100001809; Fundamental Research Funds for the Central Universities10.13039/501100012226; Natural Science Foundation of Shanghai10.13039/100007219; Nanjing University Innovation and Creative Program for PhD candidate; Basic Research Project of Shanghai Science and Technology Commission;

收稿日期:2020-04-21

录用日期:2020-08-02

网络出版日期:2020-08-04

作者单位    点击查看

Kaimin Zheng:National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
Minghao Mi:National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
Ben Wang:National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
Liang Xu:National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
Liyun Hu:Center for Quantum Science and Technology, Jiangxi Normal University, Nanchang 330022, China
Shengshuai Liu:State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
Yanbo Lou:State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
Jietai Jing:State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China;Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China;e-mail: jtjing@phy.ecnu.edu.cn
Lijian Zhang:National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China;e-mail: lijian.zhang@nju.edu.cn

联系人作者:Jietai Jing(jtjing@phy.ecnu.edu.cn); Lijian Zhang(lijian.zhang@nju.edu.cn);

备注:National Key Research and Development Program of China10.13039/501100012166; National Natural Science Foundation of China10.13039/501100001809; Fundamental Research Funds for the Central Universities10.13039/501100012226; Natural Science Foundation of Shanghai10.13039/100007219; Nanjing University Innovation and Creative Program for PhD candidate; Basic Research Project of Shanghai Science and Technology Commission;

【1】M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor and W. P. Bowen. Biological measurement beyond the quantum limit. Nat. Photonics. 7, 229-233(2013).

【2】T. Ono, R. Okamoto and S. Takeuchi. An entanglement-enhanced microscope. Nat. Commun. 4, (2013).

【3】G. Brida, M. Genovese and I. R. Berchera. Experimental realization of sub-shot-noise quantum imaging. Nat. Photonics. 4, 227-230(2010).

【4】S. Pirandola, B. R. Bardhan, T. Gehring, C. Weedbrook and S. Lloyd. Advances in photonic quantum sensing. Nat. Photonics. 12, 724-733(2018).

【5】C. Degen, F. Reinhard and P. Cappellaro. Quantum sensing. Rev. Mod. Phys. 89, (2017).

【6】C. Bonato, M. S. Blok, H. T. Dinani, D. W. Berry, M. L. Markham, D. J. Twitchen and R. Hanson. Optimized quantum sensing with a single electron spin using real-time adaptive measurements. Nat. Nanotechnol. 11, 247-252(2015).

【7】G. M. D’Ariano and M. G. A. Paris. Arbitrary precision in multipath interferometry. Phys. Rev. A. 55, 2267-2271(1997).

【8】R. X. AdhikariR. X. Adhikari. Gravitational radiation detection with laser interferometry. Rev. Mod. Phys. 86, 121-151(2014).

【9】Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel and Y. Chen. Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement. Nat. Phys. 13, 776-780(2017).

【10】L. Pezzé and A. Smerzi. Mach-Zehnder interferometry at the Heisenberg limit with coherent and squeezed-vacuum light. Phys. Rev. Lett. 100, (2008).

【11】M. J. Holland and K. Burnett. Interferometric detection of optical phase shifts at the Heisenberg limit. Phys. Rev. Lett. 71, 1355-1358(1993).

【12】C. M. CavesC. M. Caves. Quantum-mechanical noise in an interferometer. Phys. Rev. D. 23, 1693-1708(1981).

【13】V. Giovannetti, S. Lloyd and L. Maccone. Advances in quantum metrology. Nat. Photonics. 5, 222-229(2011).

【14】N. Thomas-Peter, B. J. Smith, A. Datta, L. Zhang, U. Dorner and I. A. Walmsley. Real-world quantum sensors: evaluating resources for precision measurement. Phys. Rev. Lett. 107, (2011).

【15】M. Xiao, L.-A. Wu and H. J. Kimble. Precision measurement beyond the shot-noise limit. Phys. Rev. Lett. 59, 278-281(1987).

【16】S. Rosen, I. Afek, Y. Israel, O. Ambar and Y. Silberberg. Sub-Rayleigh lithography using high flux loss-resistant entangled states of light. Phys. Rev. Lett. 109, (2012).

【17】A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams and J. P. Dowling. Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit. Phys. Rev. Lett. 85, 2733-2736(2000).

【18】Y. Israel, S. Rosen and Y. Silberberg. Supersensitive polarization microscopy using NOON states of light. Phys. Rev. Lett. 112, (2014).

【19】D. W. Berry and H. M. Wiseman. Adaptive quantum measurements of a continuously varying phase. Phys. Rev. A. 65, (2002).

【20】K. Iwasawa, K. Makino, H. Yonezawa, M. Tsang, A. Davidovic, E. Huntington and A. Furusawa. Quantum-limited mirror-motion estimation. Phys. Rev. Lett. 111, (2013).

【21】M. Tsang, H. M. Wiseman and C. M. Caves. Fundamental quantum limit to waveform estimation. Phys. Rev. Lett. 106, (2011).

【22】H. Miao, R. X. Adhikari, Y. Ma, B. Pang and Y. Chen. Towards the fundamental quantum limit of linear measurements of classical signals. Phys. Rev. Lett. 119, (2017).

【23】R. Jiménez-Martnez, J. Ko?odyński, C. Troullinou, V. G. Lucivero, J. Kong and M. W. Mitchell. Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering. Phys. Rev. Lett. 120, (2018).

【24】D. W. Berry, M. Tsang, M. J. Hall and H. M. Wiseman. Quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation. Phys. Rev. X. 5, (2015).

【25】D. W. Berry, M. J. W. Hall and H. M. Wiseman. Stochastic Heisenberg limit: optimal estimation of a fluctuating phase. Phys. Rev. Lett. 111, (2013).

【26】H. T. Dinani and D. W. Berry. Adaptive estimation of a time-varying phase with a power-law spectrum via continuous squeezed states. Phys. Rev. A. 95, (2017).

【27】M. TsangM. Tsang. Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing. Phys. Rev. A. 80, (2009).

【28】M. Tsang, J. H. Shapiro and S. Lloyd. Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design. Phys. Rev. A. 79, (2009).

【29】M. TsangM. Tsang. Time-symmetric quantum theory of smoothing. Phys. Rev. Lett. 102, (2009).

【30】D. W. Berry and H. M. Wiseman. Adaptive phase measurements for narrowband squeezed beams. Phys. Rev. A. 73, (2006).

【31】T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa and E. H. Huntington. Adaptive optical phase estimation using time-symmetric quantum smoothing. Phys. Rev. Lett. 104, (2010).

【32】H. Yonezawa, D. Nakane, T. A. Wheatley, K. Iwasawa, S. Takeda, H. Arao, K. Ohki, K. Tsumura, D. W. Berry, T. C. Ralph, H. M. Wiseman, E. H. Huntington and A. Furusawa. Quantum-enhanced optical-phase tracking. Science. 337, 1514-1517(2012).

【33】B. Yurke, S. L. McCall and J. R. Klauder. SU(2) and SU(1, 1) interferometers. Phys. Rev. A. 33, 4033-4054(1986).

【34】C. Brif and A. Mann. Nonclassical interferometry with intelligent light. Phys. Rev. A. 54, 4505-4518(1996).

【35】J. Jing, C. Liu, Z. Zhou, Z. Y. Ou and W. Zhang. Realization of a nonlinear interferometer with parametric amplifiers. Appl. Phys. Lett. 99, (2011).

【36】Z. Y. OuZ. Y. Ou. Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer. Phys. Rev. A. 85, (2012).

【37】F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou and W. Zhang. Quantum metrology with parametric amplifier-based photon correlation interferometers. Nat. Commun. 5, (2014).

【38】B. E. Anderson, P. Gupta, B. L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K. M. Jones and P. D. Lett. Phase sensing beyond the standard quantum limit with a variation on the SU(1, 1) interferometer. Optica. 4, 752-756(2017).

【39】M. Manceau, G. Leuchs, F. Khalili and M. Chekhova. Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer. Phys. Rev. Lett. 119, (2017).

【40】S. Lemieux, M. Manceau, P. R. Sharapova, O. V. Tikhonova, R. W. Boyd, G. Leuchs and M. V. Chekhova. Engineering the frequency spectrum of bright squeezed vacuum via group velocity dispersion in an SU(1, 1) interferometer. Phys. Rev. Lett. 117, (2016).

【41】M. Gabbrielli, L. Pezzè and A. Smerzi. Spin-mixing interferometry with Bose-Einstein condensates. Phys. Rev. Lett. 115, (2015).

【42】D. Linnemann, H. Strobel, W. Muessel, J. Schulz, R. Lewis-Swan, K. Kheruntsyan and M. Oberthaler. Quantum-enhanced sensing based on time reversal of nonlinear dynamics. Phys. Rev. Lett. 117, (2016).

【43】S. S. Szigeti, R. J. Lewis-Swan and S. A. Haine. Pumped-up SU(1,1) interferometry. Phys. Rev. Lett. 118, (2017).

【44】M. BanM. Ban. Decomposition formulas for su(1, 1) and su(2) Lie algebras and their applications in quantum optics. J. Opt. Soc. Am. B. 10, 1347-1359(1993).

【45】G. Chiribella, G. M. D’Ariano and P. Perinotti. Applications of the group SU(1,1) for quantum computation and tomography. Laser Phys. 16, 1572-1581(2006).

【46】H. L. V. Trees and K. L. Bell. Detection Estimation and Modulation Theory. Part I: Detection, Estimation, and Filtering Theory. : Wiley, (2013).

【47】S. Liu, Y. Lou, J. Xin and J. Jing. Quantum enhancement of phase sensitivity for the bright-seeded SU(1,1) interferometer with direct intensity detection. Phys. Rev. Appl. 10, (2018).

引用该论文

Kaimin Zheng, Minghao Mi, Ben Wang, Liang Xu, Liyun Hu, Shengshuai Liu, Yanbo Lou, Jietai Jing, and Lijian Zhang, "Quantum-enhanced stochastic phase estimation with the SU(1,1) interferometer," Photonics Research 8(10), 1653-1661 (2020)

您的浏览器不支持PDF插件,请使用最新的(Chrome/Fire Fox等)浏览器.或者您还可以点击此处下载该论文PDF