搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一种通过约瑟夫森结非线性频率响应确定微波耗散的方法

陈恒杰 薛航 李邵雄 王镇

引用本文:
Citation:

一种通过约瑟夫森结非线性频率响应确定微波耗散的方法

陈恒杰, 薛航, 李邵雄, 王镇

A method of determining microwave dissipation of Josephson junctions with non-linear frequency response

Chen Heng-Jie, Xue Hang, Li Shao-Xiong, Wang Zhen
PDF
HTML
导出引用
  • 通过对电流偏置超导约瑟夫森结的微波驱动行为的研究, 提出了一个确定约瑟夫森结微波耗散的方法. 结的微波耗散由它的品质因子描述. 微波耗散严重影响约瑟夫森器件如参量放大器、超导量子比特等的性能. 对电流偏置的约瑟夫森结势阱采用四阶近似后, 可以得到在较强微波驱动下约瑟夫森结非线性微波响应方程. 该方程定量描述了非线性共振频率随外加微波功率变化关系: 非线性共振频率与结等离子频率的差别依赖于约瑟夫森结的微波品质因子. 对电流偏置的约瑟夫森结的微波运动行为进行了数值模拟. 模拟结果确证了微波品质因子与非线性共振频率-等离子频率差别的定量关系可以应用于约瑟夫森结中. 用这种非线性频率响应方法来确定约瑟夫森结的微波耗散没有严格的温度要求, 可在单个电流偏置的结中完成, 实验上具有简单可靠性.
    Based on Josephson junction (JJ), superconducting quantum bit (qubit) is operated at frequencies of several GHz. Dissipation of JJs in this frequency range can cause energy relaxation in qubits, and limit coherence time, therefore it is highly concerned and needs to be determined quantitatively. The dissipation of JJs can be quantified by microwave quality factor. It is usually done at very low temperature (~mK) to determine whether a JJ is suitable for qubit devices by measuring the quality factor. In this paper, a method based on nonlinear frequency response of JJs is proposed to determine the quality factor. This method can be used in thermal activation regime, which may bring great conveniences to experiments. To analyze high frequency properties of JJs, the dynamic equation of a current-biased JJ, which describes high frequency oscillation of the JJ, is introduced. A fourth-order potential approximation is used to obtain the analytical equation of non-linear response. The dependence on quality factor, as well as on amplitude, of difference between JJ’s plasma frequency and resonant frequency, is derived from the equation. The approximate treatment is quantitatively validated by our numerical simulations with practical JJ parameters including different environment influences. Thus, based on nonlinear frequency response of JJs, a reliable and simple method to determine quality factor of JJ is proposed, which is desirable for exploring JJ based microwave devices such as parametric amplifier, superconducting qubit. Being driven well into the nonlinear microwave response regime, due to frequency-amplitude interaction, the resonant frequency of a current bias JJ deviates from the JJ’s plasma frequency. The deviation is directly related to the microwave quality factor. Hence, the quality factor can be deducted from the experimental measurement of the resonant frequency deviation, with different microwave power values applied. In comparison with linear resonance experiment, the nonlinear resonance used by the proposed method produces stronger signal. Therefore it is more robust against external noise. When being conducted at high temperature, the proposed method is more reliable. The accuracy of the measured quality factor primarily depends on those of the JJ’s parameters such as critical current and capacitance, while those parameters can be experimentally determined with high precision.
      通信作者: 李邵雄, sxli@mail.sim.ac.cn
    • 基金项目: 国家自然科学基金(批准号: 61771459)资助的课题.
      Corresponding author: Li Shao-Xiong, sxli@mail.sim.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61771459).
    [1]

    Devoret M H Schoelkopf R J 2013 Science 339 1169Google Scholar

    [2]

    van Theodore D, Charles W T 1998 Principles of Superconductive Devices and Circuits Second Edition (Upper Saddle River: Prentice Hall) p194

    [3]

    Mattis D C, Bardeen J 1958 Phys. Rev. 111 412Google Scholar

    [4]

    Leggett A J, Chakravarty S, Dorsey A T, Fisher M P A, Garg A, Zwerger W 1987 Rev. Mod. Phys. 59 1Google Scholar

    [5]

    Makhlin Y, Schön G, Shnirman A 2001 Rev. Mod. Phys. 73 357Google Scholar

    [6]

    Martinis J M, Cooper K B, McDermott R, Steffen M, Ansmann M, Osborn K D, Cicak K, Oh S, Pappas D P, Simmonds R W, Yu C C 2005 Phys. Rev. Lett. 95 210503Google Scholar

    [7]

    Tinkham M 2004 Introduction to Superconductivity (2nd Ed.) (Dover) p76

    [8]

    Pop I M, Geerlings K, Catelani G, Schoelkopf R J, Glazman L I, Devoret M H 2014 Nature 508 369Google Scholar

    [9]

    Yan F, Gustavsson S, Kamal A, Birenbaum J, Sears A P, Hover D, Gudmundsen T J, RosenBerg D, Samach G, Weber S, Yoder J L, Orlando T P, Clarke J, Kerman A J, Oliver W D 2016 Nat. Commun. 7 12964Google Scholar

    [10]

    Cosmelli C, Carelli P, Castellano M G, Chiarello F, Diambrini Palazzi G, Leoni R, Torrioli G 1999 Phys. Rev. Lett. 82 5357Google Scholar

    [11]

    Han S, Rouse R 2001 Phys. Rev. Lett. 86 4191Google Scholar

    [12]

    Dutta S K, Xu H, Berkley A J, Ramos R C, Gubrud M A, Anderson J R, Lobb C J, Wellstood F C 2004 Phys. Rev. B 70 140502Google Scholar

    [13]

    Han S, Yu Y, Chu X, Chu S, Wang Z 2001 Science 293 1457Google Scholar

    [14]

    McCumber D E 1968 J. Appl. Phys. 39 3113Google Scholar

    [15]

    Stewart W C 1968 Appl. Phys. Lett. 12 277Google Scholar

    [16]

    Landau L D, Lifshitz E M 2007 Mechanics Third Edition (Beijing: World Publishing Corporation) p88

    [17]

    Li S X, Yu Y, Zhang Y, Qiu W, Han S, Wang Z 2002 Phys. Rev. Lett. 89 098301Google Scholar

    [18]

    Martinis J M, Nam S, Aumentado J 2002 Phys. Rev. Lett. 89 117901Google Scholar

    [19]

    Devoret M H, Esteve D, Martinis J M, Cleland A, Clarke J 1987 Phys. Rev. B 36 58Google Scholar

    [20]

    Manucharyan V E, Boaknin E, Metcalfe M, Vijay R, Siddiqi I, Devoret M 2007 Phys. Rev. B 76 014524Google Scholar

    [21]

    Mao B, Han S 2007 IEEE Trans. Appl. Supercond. 17 94Google Scholar

    [22]

    Sun G, Chen J, Ji Z, Xu W, Kang L, Wu P, Dong N, Mao G, Yu Y, Xing D 2006 App. Phys. Lett. 89 082516Google Scholar

  • 图 1  计算得到的相位粒子在相空间中的运动轨迹 纵坐标$ v = {{{\rm{d}}\phi } / {{\mathop{\scriptsize\rm d}\nolimits} \tau }}$, 计算采用的实验参数为${i_{{\rm{dc}}}} = {\rm 0.473},{i_{{\rm{rf}}}} =$$ {\rm 5.5} \times {\rm 10^{ - 4}}$, γ = 0.9306

    Fig. 1.  Calculated trajectory of phase particle with experiment parameters for junction 3: ${i_{{\rm{dc}}}} = 0.473$, ${i_{{\rm{rf}}}} = 5.5 \times $10–4, γ = 0.9306. Vertical axis $v = {{{\rm{d}}\phi } / {{\rm{d}}\tau }}$.

    图 2  结(${I_{\rm{C}}} = 8$ μA, Q = 515.7)在不同的微波驱动下, (5)式(曲线)和模拟(误差棒)得到的响应振幅b随归一直流偏置${i_{\rm{dc}}}$的函数变化关系, 响应曲线按其最大振幅从小到大顺序对应的外加微波强度分别为${i_{{\rm{rf}}}}={\rm{ 1}}.{\rm{63}} \times {\rm{1}}{{\rm{0}}^{ - 4}},{\rm{ 2}}.{\rm{44}} \times $${\rm{1}}{{\rm{0}}^{ - 4}},{\rm{ 3}}.{\rm{67}} \times {\rm{1}}{{\rm{0}}^{ - 4}}$$ {\rm{5}}.{\rm{50}} \times {\rm{1}}{{\rm{0}}^{ - 4}}$, 点划线显示了最大振幅对应的${i_{{\rm{dc}}}}$随外加微波强度的变化

    Fig. 2.  Microwave response curves obtained by Eq. (5) (curves) and numerical simulation (error bars), for junction (${I_{\rm{C}}} = 8$ μA, Q = 515.7) with applied microwave ${i_{{\rm{rf}}}}=$${\rm{ 1}}.{\rm{63}} \times {\rm{1}}{{\rm{0}}^{ - 4}},{\rm{ 2}}.{\rm{44}} \times {\rm{1}}{{\rm{0}}^{ - 4}},{\rm{ 3}}.{\rm{67}} \times {\rm{1}}{{\rm{0}}^{ - 4}}\;{\rm{ and }}\;5.{\rm{50}} \times {\rm{1}}{{\rm{0}}^{ - 4}}$ for the curves with the maximum amplitude from small to large respectively. Dot-dash line shows the dependence of ${i_{{\rm{dc}}}}$ where corresponding to the maximum oscillation amplitude on the power of the applied microwave.

    图 3  表1中三个样品结的$ \tilde v = \sqrt {{{\Delta \omega }}/{k}} {\omega _{\rm{p}}}$$ {i_{{\rm{rf}}}}$的变化关系图, 线是(7)式的结果, 误差棒是$\tilde v $的数值模拟结果, 图中直线斜率从小到大分别对应Q值163.0(结1), 508.6(结2), 1549.1(结3)

    Fig. 3.  $\tilde v = \sqrt {{{\Delta \omega }}/{k}} {\omega _{\rm{p}}}$ as a function of ${i_{{\rm{rf}}}}$ for different parameters of sample Josephson junctions in Table 1. Lines are results of Eq. (7). Error bars are numerical simulation results of $\tilde v$. The lines of slops from small to large corresponding to Q values: 163.0 (junction 1), 508.6 (junction 2), 1549.1 (junction 3).

    图 4  结2在不同的电路环境下, 导致不同的品质因子Q (51.6, 257.8, 515.7, 1533.0, 对应直线斜率从小到大)时, $\tilde v$${i_{{\rm{rf}}}}$的变化关系, 直线是(7)式的结果, 误差棒是$\tilde v$的数值模拟结果

    Fig. 4.  $\tilde v$ as a function of ${i_{{\rm{rf}}}}$ for different quality factors. Lines are Eq. (7)’s results. Error bars are numerical simulation results of $\tilde v$. The lines of slops from small to large corresponding to Q values: 51.6, 257.8, 515.7, 1533.0 accounting for junction 2 with different environment influences.

    表 1  数值模拟采用的结参数

    Table 1.  Parameters of Josephson junctions used in numerical simulations.

    结参数结1结2结3
    临界电流密度jc/A·cm–2100150200
    比电容Cs/fF·μm–242.946.450.5
    品质因子Q163.0508.61459.1
    下载: 导出CSV

    表 2  数值模拟采用的实验参数

    Table 2.  Experiment settings used in numerical simulations.

    实验参数表示符号取值
    归一直流偏置idc0.46—0.52
    归一微波电流irf1.6 × 10–4—5.5 × 10–4
    归一微波频率γ0.9306
    下载: 导出CSV
  • [1]

    Devoret M H Schoelkopf R J 2013 Science 339 1169Google Scholar

    [2]

    van Theodore D, Charles W T 1998 Principles of Superconductive Devices and Circuits Second Edition (Upper Saddle River: Prentice Hall) p194

    [3]

    Mattis D C, Bardeen J 1958 Phys. Rev. 111 412Google Scholar

    [4]

    Leggett A J, Chakravarty S, Dorsey A T, Fisher M P A, Garg A, Zwerger W 1987 Rev. Mod. Phys. 59 1Google Scholar

    [5]

    Makhlin Y, Schön G, Shnirman A 2001 Rev. Mod. Phys. 73 357Google Scholar

    [6]

    Martinis J M, Cooper K B, McDermott R, Steffen M, Ansmann M, Osborn K D, Cicak K, Oh S, Pappas D P, Simmonds R W, Yu C C 2005 Phys. Rev. Lett. 95 210503Google Scholar

    [7]

    Tinkham M 2004 Introduction to Superconductivity (2nd Ed.) (Dover) p76

    [8]

    Pop I M, Geerlings K, Catelani G, Schoelkopf R J, Glazman L I, Devoret M H 2014 Nature 508 369Google Scholar

    [9]

    Yan F, Gustavsson S, Kamal A, Birenbaum J, Sears A P, Hover D, Gudmundsen T J, RosenBerg D, Samach G, Weber S, Yoder J L, Orlando T P, Clarke J, Kerman A J, Oliver W D 2016 Nat. Commun. 7 12964Google Scholar

    [10]

    Cosmelli C, Carelli P, Castellano M G, Chiarello F, Diambrini Palazzi G, Leoni R, Torrioli G 1999 Phys. Rev. Lett. 82 5357Google Scholar

    [11]

    Han S, Rouse R 2001 Phys. Rev. Lett. 86 4191Google Scholar

    [12]

    Dutta S K, Xu H, Berkley A J, Ramos R C, Gubrud M A, Anderson J R, Lobb C J, Wellstood F C 2004 Phys. Rev. B 70 140502Google Scholar

    [13]

    Han S, Yu Y, Chu X, Chu S, Wang Z 2001 Science 293 1457Google Scholar

    [14]

    McCumber D E 1968 J. Appl. Phys. 39 3113Google Scholar

    [15]

    Stewart W C 1968 Appl. Phys. Lett. 12 277Google Scholar

    [16]

    Landau L D, Lifshitz E M 2007 Mechanics Third Edition (Beijing: World Publishing Corporation) p88

    [17]

    Li S X, Yu Y, Zhang Y, Qiu W, Han S, Wang Z 2002 Phys. Rev. Lett. 89 098301Google Scholar

    [18]

    Martinis J M, Nam S, Aumentado J 2002 Phys. Rev. Lett. 89 117901Google Scholar

    [19]

    Devoret M H, Esteve D, Martinis J M, Cleland A, Clarke J 1987 Phys. Rev. B 36 58Google Scholar

    [20]

    Manucharyan V E, Boaknin E, Metcalfe M, Vijay R, Siddiqi I, Devoret M 2007 Phys. Rev. B 76 014524Google Scholar

    [21]

    Mao B, Han S 2007 IEEE Trans. Appl. Supercond. 17 94Google Scholar

    [22]

    Sun G, Chen J, Ji Z, Xu W, Kang L, Wu P, Dong N, Mao G, Yu Y, Xing D 2006 App. Phys. Lett. 89 082516Google Scholar

  • [1] 李中祥, 王淑亚, 黄自强, 王晨, 穆清. 原子级控制的约瑟夫森结中Al2O3势垒层制备工艺. 物理学报, 2022, 71(21): 218102. doi: 10.7498/aps.71.20220820
    [2] 宿非凡, 杨钊华, 赵寿宽, 严海生, 田野, 赵士平. 铌基超导量子比特及辅助器件的制备. 物理学报, 2022, 71(5): 050303. doi: 10.7498/aps.71.20211865
    [3] 熊磊, 丁洪伟, 李光元. 银纳米粒子阵列中衍射诱导高品质因子的四偶极晶格等离子体模式. 物理学报, 2022, 71(4): 047802. doi: 10.7498/aps.71.20211629
    [4] 徐达, 王逸璞, 李铁夫, 游建强. 微波驱动下超导量子比特与磁振子的相干耦合. 物理学报, 2022, 71(15): 150302. doi: 10.7498/aps.71.20220260
    [5] 熊磊. 银纳米粒子阵列中衍射诱导高品质因子的四偶极晶格等离子体共振. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211629
    [6] 韩金舸, 欧阳鹏辉, 李恩平, 王轶文, 韦联福. 超导约瑟夫森结物理参数的实验推算. 物理学报, 2021, 70(17): 170304. doi: 10.7498/aps.70.20210393
    [7] 赵士平, 刘玉玺, 郑东宁. 新型超导量子比特及量子物理问题的研究. 物理学报, 2018, 67(22): 228501. doi: 10.7498/aps.67.20180845
    [8] 王松, 王星云, 周章渝, 杨发顺, 杨健, 傅兴华. 硼膜制备工艺、微观结构及其在硼化镁超导约瑟夫森结中的应用. 物理学报, 2016, 65(1): 017401. doi: 10.7498/aps.65.017401
    [9] 赵娜, 刘建设, 李铁夫, 陈炜. 超导量子比特的耦合研究进展. 物理学报, 2013, 62(1): 010301. doi: 10.7498/aps.62.010301
    [10] 曹文会, 李劲劲, 钟青, 郭小玮, 贺青, 迟宗涛. 用于电压基准的Nb/NbxSi1-x/Nb约瑟夫森单结的研制. 物理学报, 2012, 61(17): 170304. doi: 10.7498/aps.61.170304
    [11] 张立森, 蔡理, 冯朝文. 约瑟夫森结中周期解及其稳定性的解析分析. 物理学报, 2011, 60(3): 030308. doi: 10.7498/aps.60.030308
    [12] 张立森, 蔡理, 冯朝文. 线性延时反馈Josephson结的Hopf分岔和混沌化. 物理学报, 2011, 60(6): 060306. doi: 10.7498/aps.60.060306
    [13] 岳宏卫, 阎少林, 周铁戈, 谢清连, 游峰, 王争, 何明, 赵新杰, 方兰, 杨扬, 王福音, 陶薇薇. 嵌入Fabry-Perot谐振腔的高温超导双晶约瑟夫森结的毫米波辐照特性研究. 物理学报, 2010, 59(2): 1282-1287. doi: 10.7498/aps.59.1282
    [14] 岳宏卫, 王争, 樊彬, 宋凤斌, 游峰, 赵新杰, 何明, 方兰, 阎少林. 高温超导双晶约瑟夫森结阵列毫米波相干辐射. 物理学报, 2010, 59(8): 5755-5758. doi: 10.7498/aps.59.5755
    [15] 崔大健, 林德华, 于海峰, 彭智慧, 朱晓波, 郑东宁, 景秀年, 吕 力, 赵士平. 本征约瑟夫森结跳变电流分布的量子修正. 物理学报, 2008, 57(9): 5933-5936. doi: 10.7498/aps.57.5933
    [16] 李照鑫, 邹 健, 蔡金芳, 邵 彬. 电荷量子比特与量子化光场之间的纠缠. 物理学报, 2006, 55(4): 1580-1584. doi: 10.7498/aps.55.1580
    [17] 侯璐景, 王友年. 尘埃颗粒在射频等离子体鞘层中的非线性共振现象的理论研究. 物理学报, 2003, 52(2): 434-441. doi: 10.7498/aps.52.434
    [18] 杜启振, 杨慧珠. 线性黏弹性各向异性介质速度频散和衰减特征研究. 物理学报, 2002, 51(9): 2101-2108. doi: 10.7498/aps.51.2101
    [19] 王震宇, 廖红印, 周世平. 直流偏置的与RLC谐振器耦合的约瑟夫森结动力学行为的数值模拟. 物理学报, 2001, 50(10): 1996-2000. doi: 10.7498/aps.50.1996
    [20] 王丹翎, 龚旗煌, 汪凯戈, 杨国健. 光学简并参量振荡中的量子非破坏性测量. 物理学报, 2000, 49(8): 1484-1489. doi: 10.7498/aps.49.1484
计量
  • 文章访问数:  5371
  • PDF下载量:  53
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-01-28
  • 修回日期:  2019-03-21
  • 上网日期:  2019-06-01
  • 刊出日期:  2019-06-05

/

返回文章
返回