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Quantum entanglement possesses important applications in quantum computation, quantum communication, and quantum precision measurement. It is also an important method to improve the performance of quantum radar and quantum radio navigation. However, the penetration of light wave is poor due to the high frequency, which leads to detecting limitations in bad weather. In this context, quantum entanglement in the microwave domain has been extensively studied, and it is hopeful to overcome the above-mentioned defects in quantum optics. Although the entangled microwave preparation of continuous variable is achievable at present, there exist still some problems such as poor entanglement performance, low entanglement efficiency, complex signal processing and control, which restrict the development of entangled microwave sources. In order to improve the entanglement performance in microwave domain, a squeezing-angle locking scheme based on single photon counting is proposed. First, two Josephson parametric amplifiers (JPAs) are driven respectively by two pump signals to generate two single-mode squeezed states which are uncorrelated to each other. Next, the squeezing angle difference between the two single-mode squeezed states is adjusted to 180°, and then the two signals are mixed in a superconducting 180° hybrid ring coupler for two entangled microwave outputs. The outputs are single photon detected, and the results are sent to the data processor for solution. The squeezing angle difference between the input single-mode squeezed microwaves is estimated by Bayesian criterion and compared with the target value to calculate the error. Finally, the squeezing angle correction information is fed back into the JPA pump to control the squeezing angle of the single-mode squeezed microwave of the JPA output as well as the relative squeezing angle to reach the target value. Thus, the dual-path entangled microwave with the optimal entanglement performance is output. Comparing with the existing entangled microwave preparation schemes, a single photon counter is utilized in the scheme of this paper, which leads to a detection efficiency of 90%. In addition, the Bayesian criterion is used to estimate the output result, and the theoretical precision reaches the quantum Cramer-Rao lower bound. Meanwhile, the introduced noise level and operation difficulty are reduced, which greatly improves the property of dual-path entangled microwave preparation.
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Keywords:
- entangled microwave preparation /
- squeezing angle locking /
- microwave photon counting /
- Bayesian estimation
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图 1 基于超导180°混合环纠缠制备方案
Figure 1. Entanglement preparation scheme based on superconducting 180° hybrid ring coupler.
图 2 基于单transmon的微波光子探测系统
Figure 2. A scheme for single-photon detection using a transmon.
图 3 基于微波光子计数的压缩角锁定方案
Figure 3. Squeezing angle locking scheme based on microwave photon counter.
图 4 相对压缩角锁定前后输出特性
Figure 4. Output properties before and after locking squeezing angle.
图 5 相对压缩角锁定前后输出纠缠度(实线, 锁定前; 虚线, 锁定后)
Figure 5. Degree of output entanglement before and after locking squeezing angle (real line, before locking; dashed line, after locking).
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[1] Meschede D, Walther H, Müller G 1985 Phys. Rev. Lett. 54 551
Google Scholar
[2] Yurke B, Kaminsky P G, Miller R E, Whittaker E A, Smith A D, Silver A H, Simon R W 1988 Phys. Rev. Lett. 60 764
Google Scholar
[3] Flurin E, Roch N, Mallet F, Devoret M H, Huard B 2012 Phys. Rev. Lett. 109 183901
Google Scholar
[4] Menzel E P, Candia R D, Deppe F, Eder P, Zhong L, Ihmig M, Haeberlein M, Baust A, Hoffmann E, Ballester D, Inomata K, Yamamoto T, Nakamura Y, Solano E, Marx A, Gross R 2012 Phys. Rev. Lett. 109 250502
Google Scholar
[5] Andersen U L, Neergaard-Nielsen J S, van Locck P, Furusawa A 2015 Nat. Phys. 11 713
Google Scholar
[6] Marshall K, Jacobsen C S, Schafermeier C, Gehring T, Weedbrook C, Andersen U L 2016 Nat. Commun. 7 13795
Google Scholar
[7] Sanz M, Las H U, Garcia R, Solano E, Di C R 2017 Phys. Rev. Lett. 118 070803
Google Scholar
[8] Xiong B, Li X, Wang X Y, Zhou L 2017 Ann. Phys. 385 757
Google Scholar
[9] Li X, Wu D W, Wei T L, Miao Q, Zhu H N, Yang C Y 2018 AIP Adv. 8 065217
Google Scholar
[10] Fedorov K G, Pogorzalek S, Las Heras U, Sanz M, Yard P, Eder P, Fische M R, Goetz, Xie J E, Inomata K, Nakamura Y, Candia D R, Solano E, Marx A, Deppe F, Gross R 2018 Sci. Rep. 8 6416
Google Scholar
[11] Beltran M A C 2010 Ph. D. Dissertation (Colorado: University of Colorado)
[12] Ku H S, Kindel W F, Mallet F 2015 Phys. Rev. A 91 042305
Google Scholar
[13] Eichler C, Bozyigit D, Lang C 2011 Phys. Rev. Lett. 107 113601
Google Scholar
[14] 朱浩男, 吴德伟, 李响, 苗强, 方冠 2018 67 040301
Google Scholar
Zhu H N, Wu D W, Li X, Wang X L, Miao Q, Fang G 2018 Acta Phys. Sin. 67 040301
Google Scholar
[15] Koshino K, Inomata K, Lin Z, Nakamura Y, Yamamoyo T 2015 Phys. Rev. A 91 43805
Google Scholar
[16] Sathyamoorthy S R, Stace T M, Johansson G 2016 C. R. Phys. 17 756
Google Scholar
[17] Koshino K, Lin Z, Inomata K, Yamamoyo T, Nakamura Y 2016 Phys. Rev. A 93 23824
Google Scholar
[18] Fan B, Johansson G, Combes J, Mibrun G J, Stace T M 2014 Phys. Rev. B 90 035132
Google Scholar
[19] 郭伟杰 2016 博士学位论文 (成都: 西南交通大学)
Guo W J 2016 Ph. D. Dissertation (Chengdu: Southwest Jiaotong University) (in Chinese)
[20] Chen K, Chen S X, Wu D W, Yang C Y, Miao Q 2017 Acta Photon. Sin. 46 0512003
Google Scholar
[21] Yurke B, Mccall S L, Klauder J R 1986 Phys. Rev. A 33 4033
Google Scholar
[22] Zyczkowski K, Horodecki P, Sanpera A, Lewenstein M 1998 Phys. Rev. A 58 883
Google Scholar
[23] Viasl G, Werner R F 2002 Phys. Rev. A 65 032314
Google Scholar
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