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
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摘要
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.
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.
引文
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[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.111 412
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[5]Makhlin Y,Sch?n G,Shnirman A 2001 Rev.Mod.Phys.73357
[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 210503
[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 508 369
[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 WD 2016 Nat.Commun.7 12964
[10]Cosmelli C,Carelli P,Castellano M G,Chiarello F,Diambrini Palazzi G,Leoni R,Torrioli G 1999 Phys.Rev.Lett.82 5357
[11]Han S,Rouse R 2001 Phys.Rev.Lett.86 4191
[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.B70 140502
[13]Han S,Yu Y,Chu X,Chu S,Wang Z 2001 Science 293 1457
[14]McCumber D E 1968 J.Appl.Phys.39 3113
[15]Stewart W C 1968 Appl.Phys.Lett.12 277
[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 098301
[18]Martinis J M,Nam S,Aumentado J 2002 Phys.Rev.Lett.89117901
[19]Devoret M H,Esteve D,Martinis J M,Cleland A,Clarke J1987 Phys.Rev.B 36 58
[20]Manucharyan V E,Boaknin E,Metcalfe M,Vijay R,Siddiqi I,Devoret M 2007 Phys.Rev.B 76 014524
[21]Mao B,Han S 2007 IEEE Trans.Appl.Supercond.17 94
[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 082516
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