Bak, Christen Kjeldahl

Kofoed, Bent

Pedersen, Niels Falsig

Særmark, Knud

Experimental evidence for subharmonic, parametric excitation of plasma oscillations in Josephson tunnel junctions is presented. The experiments described are performed by measuring the microwave power necessary to switch a Josephson tunnel junction biased in the zero voltage state to a finite voltage state

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Downloaded from orbit.dtu.dk on: Dec 17, 2017Experimental investigation on parametric excitation of plasma oscillations inJosephson tunnel junctionsBak, Christen Kjeldahl; Kofoed, Bent; Pedersen, Niels Falsig; Særmark, KnudPublished in:I E E E Transactions on MagneticsPublication date:1975Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Bak, C. K., Kofoed, B., Pedersen, N. F., & Særmark, K. (1975). Experimental investigation on parametricexcitation of plasma oscillations in Josephson tunnel junctions. I E E E Transactions on Magnetics, 11(2), 829-833.IEEE Transactions on Magnetics, vol. MAG-11, no. 2 ,  March 1975 EXPERIMENTAL INVESTIGATION ON PARAMETRIC EXCITATION OF PLASMA OSCILLATIONS IN JOSEPHSON TUNNEL JUNCTIONS C. K. Bak, B. Kofoed, N. F. ABSTRACT Experimental evidence for subharmonic, para- metric  excitation of plasma  oscillations  in  Josephson tunnel junctions is presented. The experiments des- cribed a re  performed  by  measuring  the  microwave power  necessary  to  switch  a  Josephson  tunnel  junction biased  in  the  zero  voltage  state  to  a  finite  voltage  state. I. INTRODUCTION The  use of a  Josephson  junction a s  a  parametric amplifier  has  been  investigated  previously  theoreti- cally" a s  well a s  experimentally. 4 a  '- In the Refs.  1,2;4,5  the  Josephson  frequency wo = 2eVo/h is used a s  the  pump frequency and an  external  cavity is used a s  the input circuit.  Here e i s  the  electron  charge, 2 ~ r h  is Planck's  constant, and Vo is the d. c.  voltage across  the junction. In Ref. 3 the  possibility of using the  plasma  frequency  in  a  Josephson  junction  as  the input circuit and an  external  signal a s  the pump has been  investigated  theoretically, and it was  suggested that  parametric  excitation of the  plasma  oscillations should  be  observable  in  a  Josephson  thin  film junction, but less  likely  in point contacts.  It is well known, that a  Josephson junction operating  in  the  zero  voltage  mode may be assigned  an  inductance  given by The plasma  resonance w is formed with the junction capacitance  C P w =-I  cos+ = ( w  max)  cos+o. (1) 2 2e max p -hC dc 0 P' 2 Using the  resistive shunt  model and neglecting  the cos$-term we may  calculate  the  &-factor Q = R/w L = RI max P dc h w COS+o P Q = ( w  /w )  COS^^, w = RIdc g P  g rnax 2" From Ref. 3 we know that  the  threshold  for  onset of plasma oscillations at w by applying wRF = 2w may be expressed  as P  P 2 1  V~~ ff c: -- ff=- Q W o '  f i w  Inserting Q = ( w  /a ) cos$o and 2w - wRF we obtain  the threshold  RF  vdftGe Manuscript received September 30, 1974. RF >x Physics  Laboratory I, The  Technical  University of Denmark, DK-2800 Lyngby, Denmark. Pedersen, and K. Saermark" From  measurements on a  Josephson  junction  analog we know, that  the  ampiitude of the  plasma  oscillations is of the  same  order of magnitude a s  the  threshold value of VRF. Thus, we obtain the available power at w P T 7  2 p=T--E--' 1 "RF Using the above expression  for VRF and - R ImaX = w we get 2e h dc  g P = - ( w  /w ) 2 Idc  (sin+,) . h 4 3 max -2 2e  P gA typical junction with I%= = 5 mA at f = 5 GHz and sin+, = 0.5 yields  P P' 0.5 . 10-13W corresponding  to - 1 0 3  dbm. This is just  the  sensitivity  limit  for  an  usual wide- band spectrum  analyzer  like  the  HP 8551B, so there is no margin  for  cable and mismatch  losses. It ex- plains why initial  attempts  to  directly  observe  the  ex- citation  failed. 11. EXPERIMENTAL  PROCEDURE According to the simple theory Idc 1s propor- max . tional  to  JO(2eVrf/ho ) where Jo is the  Bessel  function of order  zero.  Measurement of I%= a s  function of the square  root of the  applied  microwave  power  should give this dependence. In general a remarkable variety of singularities and hysteresis  effects have been  observed  for  example a s  reported  by Dahm et al. In tracing  the  IV-characteristic on an  oscillo- scope  certain  intervals of the  dc-Josephson  current showed instabilities with applied microwaves. Biasing the  junction  in these  intervals  for  definite  power settings was impossible. It i s  claimed that two of these  instabilities  are due to  the  plasma  resonance and a.parametric  excitation of the  plasma  resonance respectively. In order to make the measurements in a  reproducible way the  junction  was  biased with a fixed dc-current, Idc, at  zero voltage without any microwaves present. The microwave power was then gradually  increased  until  the  junction  switched  to  a voltage  different  from  zero. An example of measure- ments performed in this way is shown in Fig. 1. Here the  db-reading of the  calibrated  attenuator when the junction  switched is plotted a s  function of the  dc-bias current, Idc, the microwave frequency being kept constant during the measurements. Since it i s  the db-reading of the  inserted  attenuator which is plotted 829 a maximum point in  the  curve in Fig. 1 represents a point where  the  junction  demands  minimal  microwave power for switching to a voltage state. The values of the  dc-Josephson  current, I& at the  maximum  points are used  in  the  analysis. In order  to  compare  the measurements  to  similar  measurements  performed on a  Josephson junction analog the  square  root of the 9 applied microwave  power as function of the  dc- Josephson current  has  also  been plotted. An example is shown in  Fig. 2a. In the following we shall  call  a curve of this type for a "switching curve". Recently Balkashin  et al. Io have  reported on a similar  curve measured  in  a  different way  by keeping the  microwave power constant and increase  the  dc-current  until  the junction  switched. Curves  like  the  ones which have  been shown in Fig. 1 and in  Fig.  2a have  been measured  for a  number of microwave  frequencies  in  the  intervals 2 - 4 GHz and 8.5 - 11 GHz. Measurements  as  described have  been  performed on  several  thin-film  Josephson  junctions of the type Sn-S%O -Sn and Nb-Nb 0 -Pb. All the junctions behavedTn the  same  manner in  full  agreement with the X Y  discussion  in  section 111. 111. DISCUSSION OF EXPERIMENTAL RESULTS Central  to  the  discussion is the  Josephson  plasma frequency ( 1). In the junction experiments we assume  the applied  microwaves  to  be  a  current  source. When the applied  microwave  frequency is equal  to  the  plasma frequency w w the junction r. f. voltage is enhanced, and the junctiot?will require  comparatively  lower microwave  power  for switching than  for w # w . Hence, minima  in  the switching curve  may be  expectgd when the applied frequency is equal  to  the  plasma  frequency and, possibly,  to  harmonics and subharmonics of w p' I Figure 2a shows  a  typical  experimental switching curve obtained the way described above. The curve shows  the  square  root of the r. f. power a s  a  function o f  the dc-bias current, Idc. The applied frequency is 10.897 GHz and  the  junction has I%= = 6.11 mA and  a normal state resistance R = 0.1 ohm. Three character- istic  structures  are  observed  in Fig. 2a, and labelled w / w  = 2, 312, and 1 respectively. This labelling will be Zescribed in detail below. Figure 2b is a similar switching curve obtained for a  Josephson junction ana10g;~  again  the analog is biased  in  the  zero  voltage mode and an,r .  f. signal is applied  until it switches  to a voltage state. The analog parameters  are given in the caption for Fig. 2b. A careful investigation of the analog  voltage  waveform on an oscilloscope shows that the  observed  structures  are  related .to a large  signal plasma  resonance--subject  to  the condition w = w -- and a parametric,  subharmonic  excitation of the plasma resonance3 subject to the condition w = w 1 / 2 .  In addition the analog experiments show the  usual  har- monic  resonances--subject  to  the  conditiin nw = w P P P' In order to  unambigously  identify the  resonances in  the real junctions two methods  were employed. One method was to  obtain switching curves  for a wide frequency  range  covering both harmonic and subhar- monic  generation and then determine  the indexing that would f i t  all of the  observed  structures. An example 830 of this method is shown in  Fig. 3, which shows  a  plot of three  frequencies in  the 8.5 - 11 GHz range and two frequencies in the 2 - 4 GHz range. For each frequency  the  dc-current, Idc,  R corresponding  to  the pronounced structures  (minima  in the  switching curves) is read and the  quantity wo(proportional  to  the plasma  frequency, Eq. ( I ) )  is calculated a s  This  plot  gives  a  maximum  plasma  frequency of 12.6 GHz and the series o /wP = 2, 312, 1, 112, 113, and 1 /4 can  be  identified. The other  method  was  to  determine  independently the  magnitude of the  plasma  frequency  by  measuring the capacitance and inserting  in Eq. ( 1). For the Nb-Nb 0 -Pb junction ( R  = 0.05 ohm, I%= = 3.3 mA) the  capacltance x x  was  determined by measuring  the capacitance of a  high resistance  (R = 100 ohm)  junction from  the  same  batch  directly and extrapolating a s  done for example in Ref. 11. The results of the two methods agreed within  a few percent. In any case  an  improper indexing would give  a  factor of 4 in  the  capacitance-- far beyond the experimental uncertainty. Figure 4 shows the  results  for  the  three  samples  that  were  most extensively studied. The ordinate is the frequency normalized to the plasma frequency. The straight lines correspond to w / w  = 2, 312, 1, 112, 113, and 114, and are  not fitted t% the  data  points. We add that  in one case  the  plasma  frequency  was changed by applying a magnetic field. The structure in  the switching curve  shifted  in  qualitative  agreement with the  m  netic  field dependence of the  plasma frequency. % The excitation of the  plasma  resonance  by  har- monics of the applied microwave  signal is well under- stood and have  been  reported  earlier. 8~ l2 What is new in  the  present  experiments is the  excitation of the plasma  resonance by means of subharmonic  generation, which has been  theoretically  predicted  earlier, 3 .  The proposed  mechanism is a parametric  excitation of the plasma  resonance when the  applied microwave  have  a frequency w = 2%. For o 5 2 w  this parametric, sub- harmonic  generation  does  not  increase  gradually with junction nonlinearity as  harmonic  generation does,  but appears suddenly with a large amplitude when the microwave  power  level  exceeds  a  certain  threshold value depending on  the  junction losses  whereas  for w ,> 2 0  the  amplitude  grows up continuously  from  zero. The detailed  calculations will not be reproduced  here, but may be found in Ref. 3. P P From analog measurements where  the  waveform of the  rf-voltage  can be observed on an oscilloscope we  know that  the  threshold  value  for  subharmonic generation  does not  in general coincide with the r. f. voltage necessary  for switching. Thus the theory of Ref. 3 is not directly applicable for a  quantitative comparison,  particularly with respect to the amplitude of the rf voltage and the power threshold  curve.  For this  reason we have  not tried  to  determine  the  magni- tude and sign of the  cosbo-termi2, 13 although  some information  may be  contained in  the  experimental curves . A  comment  should be made  to  the  appearance of the structure at w / w  = 312. This structure does not correspond  to  a higl?e:erorder solution of the  Mathieu equation (3), but once the  threshold  curve  corres- ponding to the excitation at  w 2% has been reached, it is known that r. f. voltage contains frequency corn- ponents at w / 2 ,  3w/2, 5w/2, . . . . where the higher harmonics diminish rapidly in amplitude (Ref. 3 con- tains information about relative  magnitudes  for analog measurements). An interesting observation is that  for a junction very  similar to  the one in  Fig.  2a  but  contain- ing a  short ( circles  in  Fig.  4)  the  3 12 harmonics dis- appeared,  whereas  the  other  harmonics  were  essen- tially  similar  to  the junction in  Fig. 2a. This behavior may be expected if the Q of the junction is lowered because of the  short. IV. EXPERIMENTAL DETAILS It is felt appropriate  to shQw some  details of the measuring  setup. If the junction is biased 0.5% from the maximum supercurrent  great  care should  be taken that  the junction is switched by the applied rf voltage rather than by accidental  transients.  Transient  voltage distribution and frequency will, of course, depend on the  local  mains supply,  but the  occurrance of numerous 1 kV pulses  per  hour will not be atypical  (switching  a 60-W lamp  may  cause  a 1-kV transient). Since in  general  measuring  setups  are  firmly grounded via extended metal  systems,  large  transient currents will result  in  the  loop  thus  formed if no pre- cautions are taken (Fig. 5). The capacitors shown around  the  mains  transformer  are made up of winding capacitance,  stray  capacitance and now and then filter capacitors  purposely applied by.the  equipment manu- facturer. The  floating  input/floating  output  amplifier shown in  Fig. 5 reduces  transient  currents through  the  signal cable by a  factor 10-100, depending on transient voltage rise-time. Furthermore, hum problems are largely eliminated. Figure 6 shows schematically  a  metal body (heavy  lines) containing bias  current supply, input amplifier,  stabilized power supply and (not shown) a temperature measuring circuit. Note, that no lead from  the junction is brought  outside  the  top flange. This  ensures  that junction leads and the above men- tioned  ground  loop  will  have no impedance  in  common except for the  impedance of the  metal body itself. The braid of the  interconnecting  cable (Fig. 5) is connected  to  the metal body (and  chassis of the  control section)  through 18 pins  equally  spaced along the  peri- phery of a 38-pole connector  to  maintain  a  certain degree of symmetry.  This will to some extent reduce the  mutual  inductance between the  signal  path and the ground  loop. The microwaves  were  introduced  into  the  cryo- stat through  a  low temperature  coaxial  cable and coupled  to the junction by a  loop surrounding  the junc- tion, with the junction placed  in  the  middle of the loop. V. CONCLUSION By measuring switching curves  for  Jospe tunnel junctions, that is,  the microwave  power  neces- ary to switch  the junction to a finite  voltage as a  func- tion of the dc-current in  the zero voltage  mode and analyze  the  position of the pronounced structure in  the curves, it has been  possible  to  identify  the  structure a s  belonging to  subharmonic  generation of the  plasma frequency. This identification is further supported by similar  measurements on a  Josephson  junction analog where  the  waveform of the r. f. voltage has been  ob- served. Therefore, our conclusion is that we have demonstrated  experimentally  that  the  plasma  resonance may be  excited  by parametric,  subharmonic  generation a s  predicted in Ref. 3. This motivates attempts at using a zero-voltage, i. e.,  dc-current  biased, mode of a  Josephson junction a s  the  nonlinear  element  in  a parametric  amplifier. At this point it should be emphasized,  however, that  the  applicability  may be limited by the power levels obtainable. In astronomical observations, where in general  very ,weak signals containing no strong, coherent  sources  are  investigated,  a junction may operate quite satisfactory. In communication systems, however,  the  dynamic  range  may be  a serious  limitation. Let  us  consider  a  microwave  receiver  operating at 5 GHz with the antenna looking into  a 300-K source. For a  system bandwidth of only 1 0  MHz thermal  noise will be -104 dbm,  roughly  equal to  saturated output from the junction. This indicates, that a Josephson junction will be  applicable  in  microwave systems only, if  the  operating  frequency is very high bearing  in mind the  strong  frequency dependence of saturated output power. VI.  ACKNOWLEDGMENT We wish to  express  our  sincere  thanks  to Professor T. Stubb, Helsinki University of Technology, for placing the Nb junctions at  our  disposal. REFERENCES 'P. Russer, Arch. Elek. Ubertragung 23, 417 (1969). 2A. N. Vystavkin et al., Cornel1 Conference on High 3( unpublished). 4H. Zimmer, A p z  Phys. Letters 10,  193 (1967). 5H. Kanter and A. H. Silver, Appl.Phys. Letters 19 515 (1971). R. Graeffe and T. Wiik, J. Appl. Phys. 42, 2146 7(1971).  S. Shapiro, Phys. Rev. Letters 11, 80 (1963). 8A. J. Dahm, A. Denenstein,  T. F. Finnegan, D. N. Langenberg, and D. J. Scalapino, Phys. Rev. Letter& 20, 859 ( 19 68). 9C. K. Bakand N. F. Pedersen, Appl. Phys. Letters Frequency  Generation and Amplification 1971 N. F. Pedersen, M. R. Samuelsen, and K. Saermark, J. Appl. Phys. 44, 5120 (1973). 6--' -" -  Phys. of the Condensed State No. 28, 3 Khar'kov (1973). Phys. Rev. B - 4, 3003 (1971) .  "P. K. Hansma, G. I. Rochlin, and J. N. Sweet, 83 1 "N. F. Pederse.n, T. F. Finnegan, D. N. Langenberg, Phys. Rev. B 2, 4151 (1972). 13C. M. Falco, W. H. Parker, and S. E. Trullinger, Phys. Rev. Letters 2, 933 (1973); D. A. Vincent and B. S. Deaver, Jr., Phys. Rev. Letters 32, 212 (1974). Fig. 1 Inserted  attenuation  in db of the applied micro- wave power necessary  for switching the junction as a  function of the  dc-bias  current Idq at  zero voltage  for  a  Sn-SSO -Sn tunnel  junctlon. Y o ~ ' l ' l ' " l ' ' l '  a2 0.4 a 6  as 1.0 Idc (mA) -- Fig. 2 The  square  root of the microwave power, i. e . ,  a.  the r.f. current  in  arbitrary  units  necessary for switching the junction a s  function of the  dc- bias current I at zero voltage for the same junction as in  Flg. 1. . dc. b. Similar curve as in a, but measured on  a Josephson junction  analog ( I  = 1.1 mA, Ro = 500 n, C = 100 nF, f =?v2 kHz). Fig. 3 Fig. 4 The points  in  the  diagram are the applied microwave  frequency a s  a  function of which,is  calculated  from Eq. ( 2 )  using  the  dc- current Ifc corresponding  to  the pronounced structure m the switching curves. The extra- polated plasma  frequency is f p , m ~  = 12.6 GHz. Note that wo = 0.3 correspon s to  an  Idc- current of 99.5% of the  maximum  dc-current, ,Max I& . x Sn-SnO-Sn fp,mox=12.6 GHz 15 Experimental  points  for  three  different  tunnel junctions  plotted  in  the same way as in  Fig. 3, but the  microwave  frequency is here  normalized to,  the  plasma  frequency found for each  tunnel junction. 83 2 Fig. 5 Floating input/floating output amplifiers are used  to  break  ground  loops  thus  reducing transients  from  the  mains supply  to  a safe level. Fig. 6 Amplifier systems connected to the junction a re  housed  in  a metal  enclosure  directly on the top of the  dewar. 833 

Experimental investigation on parametric excitation of plasma oscillations in Josephson tunnel junctions

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Experimental investigation on parametric excitation of plasma oscillations in Josephson tunnel junctions

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