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Superconducting quantum interference devices

Zheng Dong-Ning

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Superconducting quantum interference devices

Zheng Dong-Ning
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  • Superconductivity is a macroscopic quantum phenomenon. Flux quantization and the Josephson effect are two physical phenomena which can best reflect the macroscopic quantum properties. Superconducting quantum interference device (SQUID) is one type of superconducting devices which uses these two characteristics. SQUID devices are widely used in the sensitive detection of magnetic signals. This paper briefly introduces the background and recent developments of low temperature superconductor and high temperature superconductor SQUID devices.
      Corresponding author: Zheng Dong-Ning, dzheng@iphy.ac.cn
    • Funds: Project supported by the National Basic Research Program of China (Grant Nos. 2016YFA0300600, 2017YFA0304300) and the Strategic Priority Research Program of Chinese Academy of Sciences, China (Grant No. XDB28000000)
    [1]

    London F 1950 Superfluids (New York: Wiley)

    [2]

    Deaver B S, Fairbank W M 1961 Phys. Rev. Lett. 7 43Google Scholar

    [3]

    Doll R, Näbauer M 1961 Phys. Rev. Lett. 7 51Google Scholar

    [4]

    Gough C E, Colclough M S, Forgan E M, Jordan R G, Keene M, Muirhead C M, Rae A I M, Thomas N, Abell J S, Sutton S 1987 Nature 326 855Google Scholar

    [5]

    Josephson B D 1962 Phys. Lett. 1 251Google Scholar

    [6]

    Anderson P W, Rowell J M 1963 Phys. Rev. Lett. 10 230Google Scholar

    [7]

    Clarke J, Braginski A I 2004 The SQUID Handbook (Vol. 1) (New Jersey: John Wiley & Sons)

    [8]

    Clarke J, Braginski A I 2004 The SQUID Handbook (Vol. 2) (New Jersey: John Wiley & Sons)

    [9]

    Fagaly R 2006 Rev. Sci. Instrum 77 101101Google Scholar

    [10]

    Anders S, Blamire M G, Buchholz F Im, Crété D G, Cristianoe R, Febvref P, Fritzsch L, Herr A, Ilichev E, Kohlmann J, Kunert J, Meyer H G, Niemeyer J, Ortlepp T, Rogalla H, Schurig T, Siegel M, Stolz R,Tarte E, Brake H J M ter, Toepfer H, Villegier J C, Zagoskin A M, Zorin A B 2010 Physica C 470 2079Google Scholar

    [11]

    Körber R, Storm J H, Seton H 2016 Supercond. Sci. Technol. 29 113001Google Scholar

    [12]

    Clarke J, Lee Y H, Schneiderman J 2018 Supercond. Sci. Technol. 31 080201Google Scholar

    [13]

    Pulizzi F 2011 Nature Materials 10 262Google Scholar

    [14]

    Zhang Y, Dong H, Krause H J, Zhang G F, Xie X M 2020 SQUID Readout Electronics and Magnetometric Systems for Practical Applications (New York: Wiley)

    [15]

    Jaklevic R C, Lambe J, Silver A H, Mercereau J E 1964 Phys. Rev. Lett. 12 159

    [16]

    Caputo P, Oppenläder J, Hässler Ch, Tomes J, Friesch A, Träble T, Schopohl N 2004 Appl. Phys. Lett. 85 1389Google Scholar

    [17]

    Drung D 2003 Supercond. Sci. Technol. 16 1320Google Scholar

    [18]

    Dantsker E, Tanaka S, Clarke J 1997 Appl. Phys. Lett. 70 2037Google Scholar

    [19]

    Tesche C D, Clarke J 1977 J. Low Temp. Phys. 27 301

    [20]

    Faley M I, Pratt K, Reineman R, Schurig D, Gott S, Atwood C G, Sarwinski R E, Paulson D N, Starr T N, Fagaly R L 2017 Supercond. Sci. Technol. 30 083001Google Scholar

    [21]

    Gurvitch M, Washington M, Higgins H 1983 Appl. Phys. Lett. 42 472Google Scholar

    [22]

    Koelle D, Kleiner R, Ludwig F, Dantsker E, Clarke J 1999 Rev. Mod. Phys. 71 631Google Scholar

    [23]

    Tafuri F, Kirtley J R 2005 Rep. Prog. Phys. 68 2573Google Scholar

    [24]

    Dimos D, Chaudhari P, Mannhart J, LeGoues F K 1988 Phys. Rev. Lett. 61 219Google Scholar

    [25]

    Du J, Lazar J Y, Lam S K H, Mitchell E E, Foley C P 2014 Supercond. Sci. Technol. 27 095005Google Scholar

    [26]

    Wakana H, Adachi S, Kamitani A, Nakayama K, Ishimaru Y, Tarutani Y, Tanabe K 2005 IEICE Trans. Electron. E88-C 208Google Scholar

    [27]

    Bergeal N, Lesueur J, Faini G, Aprili M, Contour J 2006 Appl. Phys. Lett. 89 112515Google Scholar

    [28]

    Trabaldo E, Ruffieux S, Andersson E, Arpaia R, Montemurro D, Schneiderman J F, Kalaboukhov A, Winkler D, Lombardi F, Bauch T 2020 Appl. Phys. Lett. 116 132601Google Scholar

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    Cybart S A, Cho E, Wong T, Wehlin B H, Ma M K, Huynh C, Dynes R 2015 Nat. Nanotechnol. 10 598Google Scholar

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    Cho E Y, Li H, LeFebvre J C, Zhou Y W, Dynes R, Cybart S A 2018 Appl. Phys. Lett. 113 162602Google Scholar

    [31]

    Hari R, Salmelin R 2012 NeuroImage 61 386Google Scholar

    [32]

    Hämäläinen M, Hari R, Ilmoniemi R J, Knuutila J, Lounasmaa O V 1993 Rev. Mod. Phys. 65 413

    [33]

    Mäkelä J P, Forss N, Jääskeläinen J, Kirveskari E, Korvenoja A, Paetau R 2006 Neurosurgery 59 493Google Scholar

    [34]

    Lee Y H, Kwon H, Yu K K, Kim J M, Lee S K, Kim M Y, Kim K 2017 Supercond. Sci. Technol. 30 084003Google Scholar

    [35]

    Öisjöen F, Schneiderman J F, Figueras G A, Chukharkin M L, Kalabukhov A, Hedström A, Elam M, Winkler D 2012 Appl. Phys. Lett. 100 132601Google Scholar

    [36]

    Sander T H, Preusser J, Mhaskar R, Kitching J, Trahms L, Knappe S 2012 Opt. Express 3 981Google Scholar

    [37]

    Boto E, Holmes N, Leggett J, Roberts G, Shah V, Meyer S S, Muñoz L D, Mullinger K J, Tierney T M, Bestmann S, Barnes G R, Bowtell R, Brookes M J 2018 Nature 555 657Google Scholar

    [38]

    Inaba T, Nakazawa Y, Yoshida K, Kato Y, Hattori A, Kimura T, Hoshi T, Ishizu T, Seo Y, Sato A, Sekiguchi Y, Nogami A, Watanabe S, Horigome H, Kawakami Y, Aonuma K 2017 Supercond. Sci. Technol. 30 114003Google Scholar

    [39]

    Enpuku K, Tsujita Y, Nakamura K, Sasayama T, Yoshida T 2017 Supercond. Sci. Technol. 30 053002Google Scholar

    [40]

    Yang S Y, Chieh J J, Yang C C, Liao S H, Chen H H, Horng H E, Yang H C, Hong C Y, Chiu M J, Chen T F, Huang K W, Wu C C 2013 IEEE Trans. Appl. Supercond. 23 1600604Google Scholar

    [41]

    Clarke J, Hatridge M, Möβle M 2007 Annu. Rev. Biomed. Eng. 9 389Google Scholar

    [42]

    Dong H, Hwang S M, Wendland M, You L, Clarke J, Inglis B 2017 Magn. Reson. Med. 78 2342Google Scholar

    [43]

    Buckenmaier K, Pedersen A, SanGiorgio P, Scheffler K, Clarke J, Inglis B 2019 Neuroimage. 186 185Google Scholar

    [44]

    Busch S E, Hatridge M, Mößle M, Myers W, Wong T, Mück M, Chew K, Kuchinsky K, Simko J, Clarke J 2012 Magn. Reson. Med. 67 1138Google Scholar

    [45]

    Magnelind P E, Gomez J J, Matlashov A N, Owens T, Sandin J H, Volegov P L, Espy M A 2011 IEEE Trans. Appl. Supercond. 21 456Google Scholar

    [46]

    Leslie K E, Binks R A, Lam S K H, Sullivan P A, Tilbrook D L, Thorn R G, Foley C P 2008 Leading Edge 27 70Google Scholar

    [47]

    Hato T, Tsukamoto A, Adachi S, Oshikubo Y, Watanabe H, Ishikawa H, Sugisaki M, Arai E, Tanabe K 2013 Supercond. Sci. Technol. 26 115003Google Scholar

    [48]

    Chwala A, Stolz R, Schmelz M, Zakosarenko V, Meyer M, Meyer H G 2015 IEICE Trans. Electron. E98.C 167Google Scholar

    [49]

    Supracon A Ghttp://www.supracon.de/

    [50]

    Song Z, Dai H, Rong L, et al. 2019 IEEE Trans. Appl. Supercond. 29 1600205

    [51]

    Rong L, Bao S, Wu J, et al. 2019 IEEE Trans. Appl. Supercond. 29 1601704

    [52]

    Stolz R, Zakosarenko V, Schulz M, Chwala A, Fritzsch L, Meyer H G, Kötlin E O 2006 Leading Edge 25 178Google Scholar

    [53]

    Halperin W P 2014 Nat. Phys. 10 467Google Scholar

    [54]

    Yang C, Si M T, You L X 2020 Sci. China Inf. Sci. 63 180502Google Scholar

    [55]

    Irwin K D, Cho H M, Doriese W B, Fowler J W, Hilton G C, Niemack M D, Reintsema C D, Schmidt D R, Ullom J N, Vale L R 2012 J. Low Temp. Phys. 167 588Google Scholar

    [56]

    Sloan J V, Hotz M, Boutan C, et al. 2016 Phys. Dark Universe 14 95Google Scholar

    [57]

    Asztalos S J, Carosi G, Hagmann C, et al. 2010 Phys. Rev. Lett. 104 041301Google Scholar

    [58]

    Tsuei C C, Kirtley J R 2000 Rev. Mod. Phys. 72 969Google Scholar

    [59]

    Embon L, Anahory Y, Jelić Ž L, Lachman E O, Myasoedov Y, Huber M E, Mikitik G P, Silhanek A V, Milošević M V, Gurevich A, Zeldov E 2017 Nat. Commun. 8 85Google Scholar

    [60]

    Halbertal D, Cuppens J, M. Ben Shalom Shalom M. B, Embon L, Shadmi N, Anahory Y, Naren H R, Sarkar J, Uri A, Ronen Y, Myasoedov Y, Levitov L S, Joselevich E, Geim A K, Zeldov E 2016 Nature 539 407Google Scholar

    [61]

    Hatsukade Y, Inaba T, Maruno Y, Tanaka S 2005 IEEE Trans. Appl. Supercond. 15 723Google Scholar

    [62]

    Krause H J, Michael M M, Tanaka S 2015 SQUlDs in Nondestructive Evaluation. In Applied Superconductivity: Handbook on Devices and Applications (Vol. 2) (Weinheim: Wiley)

    [63]

    Faley M, Kostyurina E, Kalashnikov K, Maslennikov Y, Koshelets V, Dunin-Borkowski R 2017 Sensors 17 2798Google Scholar

    [64]

    Clarke J, Wilhelm F K 2008 Nature 453 1031Google Scholar

    [65]

    Krantz J P, Kjaergaard M, Yan F, Orlando T P, Gustavsson S, Oliver W D 2019 Appl. Phys. Rev. 6 021318Google Scholar

    [66]

    Kwon S, Tomonaga A, Gopika L B, Devitt S J, Tsai J S 2020 arXiv:2009.08021 [quant-ph]

    [67]

    Kjaergaard M, Schwartz M E, Braumuller J, Krantz P, Wang J I J, Gustavsson S, Oliver W D 2020 Annu. Rev. Condens. Matter Phys. 11 369Google Scholar

  • 图 1  DC-SQUID示意图[7]

    Figure 1.  Schematic drawing of the DC-SQUID configuration[7].

    图 2  不同屏蔽参数βL对应的磁通对DC-SQUID器件临界电流调制的情况[7]

    Figure 2.  Critical current of the DC-SQUID vs. applied flux for 3 values of the screening parameter βL. Junction parameters are assumed to be identical[7].

    图 3  DC-SQUID (a)等效电路示意图; (b)磁通分别为整数个和半整数个Φ0时的I-V曲线; (c)电压-磁通曲线[7]

    Figure 3.  The DC-SQUID: (a) Schematic electric circuit; (b) current-voltage characteristics at integer and half-integer values of applied flux; the operation point is set by the bias current Ib; (c) voltage vs. flux Φa/Φ0 for constant bias current[7].

    图 4  DC-SQUID的直接读出FLL读出电路(左)和磁通调制的FFL读出电路(右)[17]

    Figure 4.  DC-SQUID readout FLL circuit. Basic FLL circuit with direct readout (left) and with flux modulation (right)[17].

    图 5  RF-SQUID和用于读出的谐振电路以及前置放大器的等效电路示意图[7]

    Figure 5.  Schematic representation of the RF-SQUID, with tank circuit and preamplifier[7].

    图 6  几种常见的高温超导约瑟夫森结 (a)双晶结; (b)台阶结; (c)台阶SNS结; (d)斜边结[22]

    Figure 6.  Schematic drawing of four types of HTS Josephson junctions used in SQUIDs: (a)[21]

    图 7  MgO衬底上45°台阶上生长的YBCO薄膜的扫描电镜(SEM)图像(左图)和高分辨透射电镜HRTEM图像(中图). 右图: 一个16 mm大小、采用台阶结的高温超导DC-SQUID磁强计在超导屏蔽环境下测量的噪声谱[20]

    Figure 7.  SEM image (left) and HRTEM image (middle) of an YBCO film deposited on a double-layer-buffered 45° step on an MgO substrate. A 45° [100]-tilted GB is clearly shown. Right: Noise spectral density of a 16 mm high-Tc DC-SQUID magnetometer with step-edge junctions measured in a superconducting shield[20].

    图 8  (a)一个方形线圈DC-SQUID器件的显微镜照片, 上有15圈输入线圈(即磁通变换器); (b) 狭缝左侧末端的放大图. 从图中可以看见结区和并联电阻[7]

    Figure 8.  (a) Square-washer DC-SQUID with overlaid 15-turn input coil; (b) expanded view of the left-hand end of the slit showing the junction on each side of the slit, and the resistive shunts[7].

    图 9  左图: 利用MEG信号进行双稳视觉感知研究. 右图: 一个SQUID脑磁测量系统[11]

    Figure 9.  Left: MEG study of bistable visual perception using a frequency-tagged stimulus; Right:A SQUID MEG system[11].

    图 10  (a) 在MEG-MRI集成实验系统上测量的以及(b)同样刺激在最先进的MEG系统上得到的视觉诱发反应产生的等效偶极和磁场分布; (c)用另一个MEG-MRI集成实验系统在96 μT磁场下得到的超低磁场MRI切片图和记录的听觉反应脑磁信号对应的偶极子; (d)常规3 T磁场下同一个样本的切片图[11]

    Figure 10.  Equivalent dipoles and field patterns of the visually evoked responses using (a) the MEG–MRI system and (b) state-of-the-art MEG with the same stimulus protocol. MRI slices (c) at 96 μT, with the registered equivalent dipole of the auditory response overlaid, and (d) from an uncoregistered 3 T image acquired separately from the same subject[11].

    图 11  超导瞬变电磁探矿系统(左图), 与野外探测结果(右图)

    Figure 11.  SQUID TEM system (left) and field detection results (right).

    图 12  左图: 针尖Nano-SQUID探测Pb薄膜的磁通的示意图; 右图: 测量的Pb薄膜中静态和运动状态磁通线的图像[60]

    Figure 12.  Left: Pb thin film sample and the experimental set-up; Right: Magnetic imaging of stationary and fast moving vortices in Pb film at 4.2 K[60].

  • [1]

    London F 1950 Superfluids (New York: Wiley)

    [2]

    Deaver B S, Fairbank W M 1961 Phys. Rev. Lett. 7 43Google Scholar

    [3]

    Doll R, Näbauer M 1961 Phys. Rev. Lett. 7 51Google Scholar

    [4]

    Gough C E, Colclough M S, Forgan E M, Jordan R G, Keene M, Muirhead C M, Rae A I M, Thomas N, Abell J S, Sutton S 1987 Nature 326 855Google Scholar

    [5]

    Josephson B D 1962 Phys. Lett. 1 251Google Scholar

    [6]

    Anderson P W, Rowell J M 1963 Phys. Rev. Lett. 10 230Google Scholar

    [7]

    Clarke J, Braginski A I 2004 The SQUID Handbook (Vol. 1) (New Jersey: John Wiley & Sons)

    [8]

    Clarke J, Braginski A I 2004 The SQUID Handbook (Vol. 2) (New Jersey: John Wiley & Sons)

    [9]

    Fagaly R 2006 Rev. Sci. Instrum 77 101101Google Scholar

    [10]

    Anders S, Blamire M G, Buchholz F Im, Crété D G, Cristianoe R, Febvref P, Fritzsch L, Herr A, Ilichev E, Kohlmann J, Kunert J, Meyer H G, Niemeyer J, Ortlepp T, Rogalla H, Schurig T, Siegel M, Stolz R,Tarte E, Brake H J M ter, Toepfer H, Villegier J C, Zagoskin A M, Zorin A B 2010 Physica C 470 2079Google Scholar

    [11]

    Körber R, Storm J H, Seton H 2016 Supercond. Sci. Technol. 29 113001Google Scholar

    [12]

    Clarke J, Lee Y H, Schneiderman J 2018 Supercond. Sci. Technol. 31 080201Google Scholar

    [13]

    Pulizzi F 2011 Nature Materials 10 262Google Scholar

    [14]

    Zhang Y, Dong H, Krause H J, Zhang G F, Xie X M 2020 SQUID Readout Electronics and Magnetometric Systems for Practical Applications (New York: Wiley)

    [15]

    Jaklevic R C, Lambe J, Silver A H, Mercereau J E 1964 Phys. Rev. Lett. 12 159

    [16]

    Caputo P, Oppenläder J, Hässler Ch, Tomes J, Friesch A, Träble T, Schopohl N 2004 Appl. Phys. Lett. 85 1389Google Scholar

    [17]

    Drung D 2003 Supercond. Sci. Technol. 16 1320Google Scholar

    [18]

    Dantsker E, Tanaka S, Clarke J 1997 Appl. Phys. Lett. 70 2037Google Scholar

    [19]

    Tesche C D, Clarke J 1977 J. Low Temp. Phys. 27 301

    [20]

    Faley M I, Pratt K, Reineman R, Schurig D, Gott S, Atwood C G, Sarwinski R E, Paulson D N, Starr T N, Fagaly R L 2017 Supercond. Sci. Technol. 30 083001Google Scholar

    [21]

    Gurvitch M, Washington M, Higgins H 1983 Appl. Phys. Lett. 42 472Google Scholar

    [22]

    Koelle D, Kleiner R, Ludwig F, Dantsker E, Clarke J 1999 Rev. Mod. Phys. 71 631Google Scholar

    [23]

    Tafuri F, Kirtley J R 2005 Rep. Prog. Phys. 68 2573Google Scholar

    [24]

    Dimos D, Chaudhari P, Mannhart J, LeGoues F K 1988 Phys. Rev. Lett. 61 219Google Scholar

    [25]

    Du J, Lazar J Y, Lam S K H, Mitchell E E, Foley C P 2014 Supercond. Sci. Technol. 27 095005Google Scholar

    [26]

    Wakana H, Adachi S, Kamitani A, Nakayama K, Ishimaru Y, Tarutani Y, Tanabe K 2005 IEICE Trans. Electron. E88-C 208Google Scholar

    [27]

    Bergeal N, Lesueur J, Faini G, Aprili M, Contour J 2006 Appl. Phys. Lett. 89 112515Google Scholar

    [28]

    Trabaldo E, Ruffieux S, Andersson E, Arpaia R, Montemurro D, Schneiderman J F, Kalaboukhov A, Winkler D, Lombardi F, Bauch T 2020 Appl. Phys. Lett. 116 132601Google Scholar

    [29]

    Cybart S A, Cho E, Wong T, Wehlin B H, Ma M K, Huynh C, Dynes R 2015 Nat. Nanotechnol. 10 598Google Scholar

    [30]

    Cho E Y, Li H, LeFebvre J C, Zhou Y W, Dynes R, Cybart S A 2018 Appl. Phys. Lett. 113 162602Google Scholar

    [31]

    Hari R, Salmelin R 2012 NeuroImage 61 386Google Scholar

    [32]

    Hämäläinen M, Hari R, Ilmoniemi R J, Knuutila J, Lounasmaa O V 1993 Rev. Mod. Phys. 65 413

    [33]

    Mäkelä J P, Forss N, Jääskeläinen J, Kirveskari E, Korvenoja A, Paetau R 2006 Neurosurgery 59 493Google Scholar

    [34]

    Lee Y H, Kwon H, Yu K K, Kim J M, Lee S K, Kim M Y, Kim K 2017 Supercond. Sci. Technol. 30 084003Google Scholar

    [35]

    Öisjöen F, Schneiderman J F, Figueras G A, Chukharkin M L, Kalabukhov A, Hedström A, Elam M, Winkler D 2012 Appl. Phys. Lett. 100 132601Google Scholar

    [36]

    Sander T H, Preusser J, Mhaskar R, Kitching J, Trahms L, Knappe S 2012 Opt. Express 3 981Google Scholar

    [37]

    Boto E, Holmes N, Leggett J, Roberts G, Shah V, Meyer S S, Muñoz L D, Mullinger K J, Tierney T M, Bestmann S, Barnes G R, Bowtell R, Brookes M J 2018 Nature 555 657Google Scholar

    [38]

    Inaba T, Nakazawa Y, Yoshida K, Kato Y, Hattori A, Kimura T, Hoshi T, Ishizu T, Seo Y, Sato A, Sekiguchi Y, Nogami A, Watanabe S, Horigome H, Kawakami Y, Aonuma K 2017 Supercond. Sci. Technol. 30 114003Google Scholar

    [39]

    Enpuku K, Tsujita Y, Nakamura K, Sasayama T, Yoshida T 2017 Supercond. Sci. Technol. 30 053002Google Scholar

    [40]

    Yang S Y, Chieh J J, Yang C C, Liao S H, Chen H H, Horng H E, Yang H C, Hong C Y, Chiu M J, Chen T F, Huang K W, Wu C C 2013 IEEE Trans. Appl. Supercond. 23 1600604Google Scholar

    [41]

    Clarke J, Hatridge M, Möβle M 2007 Annu. Rev. Biomed. Eng. 9 389Google Scholar

    [42]

    Dong H, Hwang S M, Wendland M, You L, Clarke J, Inglis B 2017 Magn. Reson. Med. 78 2342Google Scholar

    [43]

    Buckenmaier K, Pedersen A, SanGiorgio P, Scheffler K, Clarke J, Inglis B 2019 Neuroimage. 186 185Google Scholar

    [44]

    Busch S E, Hatridge M, Mößle M, Myers W, Wong T, Mück M, Chew K, Kuchinsky K, Simko J, Clarke J 2012 Magn. Reson. Med. 67 1138Google Scholar

    [45]

    Magnelind P E, Gomez J J, Matlashov A N, Owens T, Sandin J H, Volegov P L, Espy M A 2011 IEEE Trans. Appl. Supercond. 21 456Google Scholar

    [46]

    Leslie K E, Binks R A, Lam S K H, Sullivan P A, Tilbrook D L, Thorn R G, Foley C P 2008 Leading Edge 27 70Google Scholar

    [47]

    Hato T, Tsukamoto A, Adachi S, Oshikubo Y, Watanabe H, Ishikawa H, Sugisaki M, Arai E, Tanabe K 2013 Supercond. Sci. Technol. 26 115003Google Scholar

    [48]

    Chwala A, Stolz R, Schmelz M, Zakosarenko V, Meyer M, Meyer H G 2015 IEICE Trans. Electron. E98.C 167Google Scholar

    [49]

    Supracon A Ghttp://www.supracon.de/

    [50]

    Song Z, Dai H, Rong L, et al. 2019 IEEE Trans. Appl. Supercond. 29 1600205

    [51]

    Rong L, Bao S, Wu J, et al. 2019 IEEE Trans. Appl. Supercond. 29 1601704

    [52]

    Stolz R, Zakosarenko V, Schulz M, Chwala A, Fritzsch L, Meyer H G, Kötlin E O 2006 Leading Edge 25 178Google Scholar

    [53]

    Halperin W P 2014 Nat. Phys. 10 467Google Scholar

    [54]

    Yang C, Si M T, You L X 2020 Sci. China Inf. Sci. 63 180502Google Scholar

    [55]

    Irwin K D, Cho H M, Doriese W B, Fowler J W, Hilton G C, Niemack M D, Reintsema C D, Schmidt D R, Ullom J N, Vale L R 2012 J. Low Temp. Phys. 167 588Google Scholar

    [56]

    Sloan J V, Hotz M, Boutan C, et al. 2016 Phys. Dark Universe 14 95Google Scholar

    [57]

    Asztalos S J, Carosi G, Hagmann C, et al. 2010 Phys. Rev. Lett. 104 041301Google Scholar

    [58]

    Tsuei C C, Kirtley J R 2000 Rev. Mod. Phys. 72 969Google Scholar

    [59]

    Embon L, Anahory Y, Jelić Ž L, Lachman E O, Myasoedov Y, Huber M E, Mikitik G P, Silhanek A V, Milošević M V, Gurevich A, Zeldov E 2017 Nat. Commun. 8 85Google Scholar

    [60]

    Halbertal D, Cuppens J, M. Ben Shalom Shalom M. B, Embon L, Shadmi N, Anahory Y, Naren H R, Sarkar J, Uri A, Ronen Y, Myasoedov Y, Levitov L S, Joselevich E, Geim A K, Zeldov E 2016 Nature 539 407Google Scholar

    [61]

    Hatsukade Y, Inaba T, Maruno Y, Tanaka S 2005 IEEE Trans. Appl. Supercond. 15 723Google Scholar

    [62]

    Krause H J, Michael M M, Tanaka S 2015 SQUlDs in Nondestructive Evaluation. In Applied Superconductivity: Handbook on Devices and Applications (Vol. 2) (Weinheim: Wiley)

    [63]

    Faley M, Kostyurina E, Kalashnikov K, Maslennikov Y, Koshelets V, Dunin-Borkowski R 2017 Sensors 17 2798Google Scholar

    [64]

    Clarke J, Wilhelm F K 2008 Nature 453 1031Google Scholar

    [65]

    Krantz J P, Kjaergaard M, Yan F, Orlando T P, Gustavsson S, Oliver W D 2019 Appl. Phys. Rev. 6 021318Google Scholar

    [66]

    Kwon S, Tomonaga A, Gopika L B, Devitt S J, Tsai J S 2020 arXiv:2009.08021 [quant-ph]

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Metrics
  • Abstract views:  19761
  • PDF Downloads:  1638
  • Cited By: 0
Publishing process
  • Received Date:  15 December 2020
  • Accepted Date:  29 December 2020
  • Available Online:  03 January 2021
  • Published Online:  05 January 2021

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