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Noise is one of the main factors affecting the performance index of weak signal detection devices, and the optimal filtering algorithm is an effective method to adaptively extract various useful weak signals from the white noise background. In order to improve the performance of single photon detector (especially the photon number resolution ability), one mainly focuses on the optimization of detector hardware such as the optimization of photosensitive materials and the technology of device fabrication. However, in this paper the performance of microwave kinetic Inductance detector (MKID) in the way of data processing is improved. Considering the fact that the template of light pulse signal in the optimal filtering algorithm is obtained by taking the average, we replace the noise model in the original optimal filtering algorithm with the white noise model and the whitening noise model. Then we process the photon response data that are detected by the MKID in an extremely low temperature environment. The results show that the energy resolution (one of the main performance indexes of single photon detector) of MKID is improved by about 15%, and we achieve an infrared single photon energy resolution of 0.26 eV. In this paper, the application and development trends of superconducting single photon detector are briefed. Then, how the MKID responds to weak coherent optical signal in low temperature environment, and the process of signal conversion, acquisition and output are explained in detail. According to the optimal filtering algorithm, we use different noise models to analyze the results of the signals detected by MKID. After that, we count the optimal amplitude multiple, perform the Gaussian fitting analysis on the statistical graph, and compare the energy resolution with the photon number resolution of the optimal filtering algorithm under different noise models. As a result, we find that under the white noise model, the optimal filtering algorithm is used to obtain the best result for MKID processing, and high energy resolution can be achieved.
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Keywords:
- optimal filtering /
- microwave kinetic inductance detector /
- energy resolution /
- noise model
[1] Hiskett P A, Lita A E, Hughes R J, Rosenberg D, Miller A J, Nordholt J E, Peterson C G, Nam S 2006 New J. Phys. 8 193Google Scholar
[2] Knill E, Laflamme R, Milburn G J 2001 Nature 409 46Google Scholar
[3] Zwinkels J C, Ikonen E, Fox N P, Ulm G, Rastello ML 2010 Metrologia 47 R15Google Scholar
[4] 周品嘉 2014 博士学位论文 (成都: 西南交通大学)
Zhou P J 2014 Ph. D. Dissertation (ChengDu: Southwest Jiaotong University) (in Chinese)
[5] Enss C 2005 Cryogenic Particle Detection 1 (Berlin: Springer-Verlag) pp417−452
[6] Zheng F, Xu R, Zhu G, Jin B, Kang L, Xu W, Chen J, Wu P 2016 Sci. Rep. 6 22710Google Scholar
[7] 张青雅, 董文慧, 何根芳, 李铁夫, 刘建设, 陈炜 2014 物理学报 63 200303Google Scholar
Zhang Q Y, Dong W H, He G F, Li T F, Liu J S, Chen W 2014 Acta Phys. Sin. 63 200303Google Scholar
[8] Day P K, Leduc H G, Mazin B A, Vayonakis A, Zmuidzinas J 2003 Nature 425 817Google Scholar
[9] 李春光, 王佳, 吴云, 王旭, 孙亮, 董慧, 高波, 李浩, 尤立星, 林志荣, 任洁, 李婧, 张文, 贺青, 王轶文, 韦联福, 孙汉聪, 王华兵, 李劲劲, 屈继峰 2021 物理学报 70 018501Google Scholar
Li C G, Wang J, Wu Y, Wang X, Sun L, Dong H, Gao B, Li H, You L X, Lin Z R, Ren J, Li J, Zhang W, He Q, Wang Y W, Wei L F, Sun H C, Wang H B, Li J J, Qu J F 2021 Acta Phys. Sin. 70 018501Google Scholar
[10] 周品嘉, 王轶文, 韦联福 2014 物理学报 63 070701Google Scholar
Zhou P J, Wang Y W, Wei L F 2014 Acta Phys. Sin. 63 070701Google Scholar
[11] Lita A E, Miller A J, Nam S W 2008 Opt. Express 16 3032Google Scholar
[12] Lolli L, Taralli E, Portesi C, Monticone E, Rajteri M 2013 Appl. Phys. Lett. 103 041107Google Scholar
[13] Yang X Y, Li H, Zhang W J, You L X, Zhang L, L iu, X Y, Wang Z, Peng W, Xie X M, Jiang M H 2014 Opt. Express 22 16267Google Scholar
[14] Li X, Tan J R, Zheng K M, Zhang L B, Zhang J L, He W J, Huang P W, Li H C, Zhang B, Chen Q, Ge R, Guo S Y, Huang T, Jia X Q, Zhao Q Y, Tu X C, Kang L, Chen J, Wu P H 2020 Photonics Research 8 637Google Scholar
[15] Geng Y, Zhang W, Li P Z, Zhong J Q, Wang Z, Miao W, Ren Y, Wang J F, Yao Q J, Shi S C 2020 J. Low Temp. Phys. 199 556Google Scholar
[16] Guo W, Liu X, Wang Y, Wei Q, Wei L F, Hubmayr J, Fowler J, Ullom J, Vale L, Vissers M R, Gao J 2017 Appl. Phys. Lett. 110 212601Google Scholar
[17] Liu X, Guo W, Wang Y, Dai M, Wei L F, Dober B, McKenney C M, Hilton G C, Hubmay J, Austermann J E, Ullom J N, Gao J, Ullom J N 2017 Appl. Phys. Lett. 111 252601Google Scholar
[18] Szymkowiak A E, Kelley R L, Moseley S H, Stahle C K 1993 J. Low Temp. Phys. 93 281Google Scholar
[19] Lindeman M A 2000 Ph. D. Dissertation (Davis, California: University of California at Davis)
[20] Anderson B D O, Moore J B 1979 Optimal Filtering (Upper Saddle River: Prentice Hall) pp417−421
[21] Walls D F, Milburn G 2008 Quantum Optics (2nd Ed.) (Berlin: Springer-Verlag) pp46−48
[22] Irwin K D 1995 Ph. D. Dissertation (Palo Alto, California: Stanford University)
[23] Wang L L, Li J, Yang N, Li X 2019 New J. Phys. 21 043005Google Scholar
[24] 张贤达 2013 矩阵分析与应用 (第2版) (北京: 清华大学出版社) 第502−508页
Zhang X D 2013 Matrix analysis and Application (2nd Ed.) (Beijing: Tsinghua University Press) pp502−508 (in Chinese)
[25] Alpert B K, Horansky R D, Bennett D A, Doriese W B, Fowler J W, Hoover A S, Rabin M W, Ullom J N 2013 Rev. Sci. Instrum. 84 056107Google Scholar
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表 1 光学衰减17 dB和20 dB下探测器的能量分辨
Table 1. Energy resolution of detector under optical attenuation of 17 dB and 20 dB.
能量分辨 $ \Delta E_{{0}}{/{\rm{eV}}} $ $ \Delta E_{{1}}{/{\rm{eV}}} $ $ \Delta E_{2}{/{\rm{eV}}} $ $ \Delta E_{3}{/{\rm{eV}}} $ $ \Delta E_{4}{/{\rm{eV}}} $ 衰减17 dB
的信号0.1015 0.3526 0.4360 0.4691 0.6140 衰减20 dB
的信号0.0955 0.3200 0.4199 0.4758 — 表 2 光学衰减17 dB下使用实测噪声和白噪声模型处理后探测器能量分辨对比
Table 2. Comparison of detector energy resolutions after processing with measured noise and white noise model under optical attenuation of 17 dB.
能量分辨 $ \Delta E_{{0}}{/{\rm{eV}}} $ $ \Delta E_{{1}}{/{\rm{eV}}} $ $ \Delta E_{2}{/{\rm{eV}}} $ $ \Delta E_{3}{/{\rm{eV}}} $ $ \Delta E_{4}{/{\rm{eV}}} $ $ \Delta E_{5}{/{\rm{eV}}} $ 实测噪声 0.1015 0.3526 0.4360 0.4691 0.6140 — 白噪声模型 0.1489 0.2992 0.3772 0.4382 0.4448 0.5113 提高 –31.83% +17.85% +15.59% +7.05% +38.04% — 表 3 光学衰减20 dB下使用实测噪声和白噪声模型处理后探测器能量分辨对比
Table 3. Comparison of detector energy resolutions after processing with measured noise and white noise model under optical attenuation of 20 dB.
能量分辨 $ \Delta E_{{0}}{/{\rm{eV}}} $ $ \Delta E_{{1}}{/{\rm{eV}}} $ $ \Delta E_{2}{/{\rm{eV}}} $ $ \Delta E_{3}{/{\rm{eV}}} $ 实测噪声 0.0955 0.3200 0.4199 0.4758 白噪声模型 0.1553 0.2650 0.3748 0.4032 提高/% –62.61 +17.19 +10.74 +15.26 表 4 光学衰减17 dB下实测噪声和噪声白化后处理得到的探测器能量分辨对比
Table 4. Comparison of energy resolutions for the experimental noises and the whitening ones, where the optical pulse is attenuated 17 dB.
能量分辨 $ \Delta {{E}}_{{0}}{/{\rm{eV}}} $ $ \Delta {{E}}_{{1}}{/{\rm{eV}}} $ $ \Delta {{E}}_{2}{/{\rm{eV}}} $ $ \Delta {{E}}_{3}{/{\rm{eV}}} $ $ \Delta {{E}}_{4}{/{\rm{eV}}} $ $ \Delta {{E}}_{5}{/{\rm{eV}}} $ 实测噪声 0.1015 0.3526 0.4360 0.4691 0.6140 — 噪声白化 0.1469 0.3274 0.4263 0.4897 0.5009 0.6216 提高/% –44.73 +7.15 +2.22 –4.39 +18.42 — 表 5 光学衰减20 dB下实测噪声和噪声白化后处理得到的探测器能量分辨对比
Table 5. Comparison of energy resolutions for the experimental noises and the whitening ones, where the optical pulse is attenuated 20 dB.
能量分辨 $ \Delta {{E}}_{{0}}{/{\rm{eV}}} $ $ \Delta {{E}}_{{1}}{/{\rm{eV}}} $ $ \Delta {{E}}_{2}{/{\rm{eV}}} $ $ \Delta {{E}}_{3}{/{\rm{eV}}} $ 实测噪声 0.0955 0.3200 0.4199 0.4758 噪声白化 0.1932 0.2855 0.39649 0.4196 提高/% –100.02 +10.78 +5.60 +11.81 表 6 光学衰减20 dB下原始滤波和改进噪声模型后探测器能量分辨对比(括号中是改进后相对于实测噪声处理所得到的能量分辨的提高百分比)
Table 6. Comparison of energy resolutions of the detector for the experimental noise, white noise and withened noise, respectively. The improvemence is relative to the those for the experimental noise. Here, the optical pulse is attenuated 20 dB.
能量分辨 $ \Delta {{E}}_{1}{/{\rm{eV}}} $ $ \Delta {{E}}_{{2}}{/{\rm{eV}}} $ $ \Delta {{E}}_{3}{/{\rm{eV}}} $ 实测噪声 0.3200 0.4199 0.4758 白噪声模型 0.2650
(+17.19%)0.3748
(+10.74%)0.4032
(+15.26%)噪声白化 0.2855
(+10.78%)0.39649
(+5.60%)0.4196
(+11.81%) -
[1] Hiskett P A, Lita A E, Hughes R J, Rosenberg D, Miller A J, Nordholt J E, Peterson C G, Nam S 2006 New J. Phys. 8 193Google Scholar
[2] Knill E, Laflamme R, Milburn G J 2001 Nature 409 46Google Scholar
[3] Zwinkels J C, Ikonen E, Fox N P, Ulm G, Rastello ML 2010 Metrologia 47 R15Google Scholar
[4] 周品嘉 2014 博士学位论文 (成都: 西南交通大学)
Zhou P J 2014 Ph. D. Dissertation (ChengDu: Southwest Jiaotong University) (in Chinese)
[5] Enss C 2005 Cryogenic Particle Detection 1 (Berlin: Springer-Verlag) pp417−452
[6] Zheng F, Xu R, Zhu G, Jin B, Kang L, Xu W, Chen J, Wu P 2016 Sci. Rep. 6 22710Google Scholar
[7] 张青雅, 董文慧, 何根芳, 李铁夫, 刘建设, 陈炜 2014 物理学报 63 200303Google Scholar
Zhang Q Y, Dong W H, He G F, Li T F, Liu J S, Chen W 2014 Acta Phys. Sin. 63 200303Google Scholar
[8] Day P K, Leduc H G, Mazin B A, Vayonakis A, Zmuidzinas J 2003 Nature 425 817Google Scholar
[9] 李春光, 王佳, 吴云, 王旭, 孙亮, 董慧, 高波, 李浩, 尤立星, 林志荣, 任洁, 李婧, 张文, 贺青, 王轶文, 韦联福, 孙汉聪, 王华兵, 李劲劲, 屈继峰 2021 物理学报 70 018501Google Scholar
Li C G, Wang J, Wu Y, Wang X, Sun L, Dong H, Gao B, Li H, You L X, Lin Z R, Ren J, Li J, Zhang W, He Q, Wang Y W, Wei L F, Sun H C, Wang H B, Li J J, Qu J F 2021 Acta Phys. Sin. 70 018501Google Scholar
[10] 周品嘉, 王轶文, 韦联福 2014 物理学报 63 070701Google Scholar
Zhou P J, Wang Y W, Wei L F 2014 Acta Phys. Sin. 63 070701Google Scholar
[11] Lita A E, Miller A J, Nam S W 2008 Opt. Express 16 3032Google Scholar
[12] Lolli L, Taralli E, Portesi C, Monticone E, Rajteri M 2013 Appl. Phys. Lett. 103 041107Google Scholar
[13] Yang X Y, Li H, Zhang W J, You L X, Zhang L, L iu, X Y, Wang Z, Peng W, Xie X M, Jiang M H 2014 Opt. Express 22 16267Google Scholar
[14] Li X, Tan J R, Zheng K M, Zhang L B, Zhang J L, He W J, Huang P W, Li H C, Zhang B, Chen Q, Ge R, Guo S Y, Huang T, Jia X Q, Zhao Q Y, Tu X C, Kang L, Chen J, Wu P H 2020 Photonics Research 8 637Google Scholar
[15] Geng Y, Zhang W, Li P Z, Zhong J Q, Wang Z, Miao W, Ren Y, Wang J F, Yao Q J, Shi S C 2020 J. Low Temp. Phys. 199 556Google Scholar
[16] Guo W, Liu X, Wang Y, Wei Q, Wei L F, Hubmayr J, Fowler J, Ullom J, Vale L, Vissers M R, Gao J 2017 Appl. Phys. Lett. 110 212601Google Scholar
[17] Liu X, Guo W, Wang Y, Dai M, Wei L F, Dober B, McKenney C M, Hilton G C, Hubmay J, Austermann J E, Ullom J N, Gao J, Ullom J N 2017 Appl. Phys. Lett. 111 252601Google Scholar
[18] Szymkowiak A E, Kelley R L, Moseley S H, Stahle C K 1993 J. Low Temp. Phys. 93 281Google Scholar
[19] Lindeman M A 2000 Ph. D. Dissertation (Davis, California: University of California at Davis)
[20] Anderson B D O, Moore J B 1979 Optimal Filtering (Upper Saddle River: Prentice Hall) pp417−421
[21] Walls D F, Milburn G 2008 Quantum Optics (2nd Ed.) (Berlin: Springer-Verlag) pp46−48
[22] Irwin K D 1995 Ph. D. Dissertation (Palo Alto, California: Stanford University)
[23] Wang L L, Li J, Yang N, Li X 2019 New J. Phys. 21 043005Google Scholar
[24] 张贤达 2013 矩阵分析与应用 (第2版) (北京: 清华大学出版社) 第502−508页
Zhang X D 2013 Matrix analysis and Application (2nd Ed.) (Beijing: Tsinghua University Press) pp502−508 (in Chinese)
[25] Alpert B K, Horansky R D, Bennett D A, Doriese W B, Fowler J W, Hoover A S, Rabin M W, Ullom J N 2013 Rev. Sci. Instrum. 84 056107Google Scholar
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