Contribution of thermal noise to line width of Josephson radiation from superconducting point contact

Kamper, R. A.

Silver, R. H.

Zimmerman, J. E.

English

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Vdume 11. Number 6 A P P L I E D  PHYSICS LETTERS 15 !?kpemkr 1967 - 
ClONTRIgUTiON OF THERMAL NOISE TO THE LINEWIDTH OF 
JO6EPHSQN RADIATION FROM SUPERCONDUCTING 
POINT WNTACIS 
A. H. Silivr nnd J. E .  Zirnmtrmnn 
Scitnlihr laboratory. Ford M ~ U K  Company 
Dearborn. Michigan 
R. A. (h'nm/& 
N.B.S. Institute for Materials Research 
&nrl&r. Colorado 
(Rccciwd I 4  J d y  IF167) 
The line-width of the Josephson cscilhtions o l  ;I voltapr-biased superc.olLduc-tiiig point contact has been measured 
k r w t c n  I .4*K and IPK, with bias resistors H bctwnn I .7 X 10"' f l  and 2.6 x IO-f n. Within the experimental 
accuracy the line-width is pruponicwral t o  HT. and is coiisi*ttnl with the estimated theoretical value 8kTRPPI. 
where 4 b Boltzmann's constant and 4% is the Hux quantum. lim-widths below 0.1 l i z  have been obscrvd at 
4.PK for R = 1.7 x iO-" 0. pnwiding an experimental upper iimit io other noise sources and indicating that 
his is useful as a voltmeter and thermometer k k ; w  I t P  V and IO-+'K. 
It has been proposed' that a voluphiased super- 
conducting point contactza might be used as a low 
temperature thermometer. This p r o p 1  was based 
on the assumption that the main contribution to 
the he-width of the Josephson radiation fmrn a 
superconducting point contact comes from the 
thermal noise voltage on the shunt mistor supply- 
*Suppod in part by NASA. 
ing the bias voltage. A simple argument t k n  p- 
dicts that the iine-width should be proportional to 
the shunt resistance R and absolute temperature 
T of this resistance. We report here an experimental 
verification of these predictions for values of T 
betwee9 1.4"K and 8°K and of R between 1.7 x 
IO-'' fl and 2.6 X 10-' 0. 
The experimental arrangement follows that pre- 
viotisly dcscribcd'-' and is  s h w n  in Fig. 1. Because 
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A P P L I E D  P H Y S I C S  LETTERS 15 Septc~nbnS lq67 - Volume 11, Number 6 
of its sinall resistance the shunt appears t o  the point 
contact as a voltage source' 
I' = vfi + I'.% ( 1 )  
where 1'(, = I 8  and V S  is the random fliictuaing 
component due to thermal noise. We employed two 
different methods IO measure the line-width, re- 
ferred t o  as the direct and parametric methods. The 
direct method consisted of measuring the power 
output from the point conkct with a 27-MHz re- 
ceiver whose bandwidth was limited to about I 
kHr by a quartz crystal filter as shown in Fig. 1. 
The bias current lo was scarified slowly thrGugh 
the value @,,j"/R (where @of,, = 2.07 X I ()-I5 X 27 x 
10'' V = 0.56 yV) and !he receiver output was re- 
corded as a function of /,,. Since this method is 
limited to line-widths greater than 1 kHz by the 
crystal hlter and will ultimately h limited by the 
stability of 1" upon further reducing the bandwidth 
by coriventional hoterodyning, we also employed a 
novel parametric method as shown in Fig. 1. This 
method, which will be fully described in a separate 
publication, is related to the oscillating detector 
mode4J previously employed and requires a 27- 
MHr signal to be weakly coupled into the Joseph- 
son ciscill~tor io addition to the dc bias I,. Mixing 
of the .Josephson frequency, 1; =. and the 
receiver frequency. /r, =1 27 MHz, by the nonlinear 
behavior of the point contact produces signal at 
I,, 2 /I. F o r b  less than the receiver bandwidth ( I50 
kVz) the demodu!ated signal acciirdtel! repro- 
duced fi. which is  then filtered via a (vaiiable) 
narrow-band audio amplifier. Again as in the direct 
method above, thi. filtered signal is rectified and 
recorded as a function of fl,. The obvioiis advantage 
of the parametric over the direct method is that it 
permits observation of J I  in the audio frequency 
region and below, where it is relatively easy to meas- 
ure line-widths of the urder of 1 Hr without 
stringent stability conditions for 1,) and the rf- 
frequencydctermining corn pnents .  
Some results of the measured iine-widths 4 are 
given in Table 1. The accuracy of these data is 
+IO%. Some inconsistency is anticipated since the 
observed line-shapes . m y  with the operating p i n t  
of the rf detectors. ALw the signal-to-roise ratio 
was not sufficient to permit an accurace line-width 
determination and a time-averaging method would 
be desirable. However, in the case of largs Af the 
direct and parametric measurements give the 
same resiilt showing that both methods measure 
the same quantity. 
The observed temperature dependence is shown 
in Fig. 2 for the 26-@ resistance using the para- 
metric method. In Fig. 2(tt) a IO-khr narrow-band 
amplifier with a Q = 25 was used at nomina! tem- 
peratures of 2. 4. and 8'K. tn order tu directly 
compare the line-widths, Fig. 36) shows the re- 
sponse where both the rrequency scale and the 
narrow-band amplifier f: equency are varied pro- 
portional to T. The Josephson line-width from 
voltage-biased point contacts is shown to be linear 
in both T and H ove h e  range  investigated. No 
evidence of line brcvdening b! other noise sr)urces. 
e.y.. mapetic field tiuctuatio;.,. --ceiver input noise 
&ding back into the cryostat, or shot noise in the 
.jiiiictioii. has heen oberved in this study. 
Wc can c ) h t ; l i n  a Icimple physical interpretation 
of these rewlts by mnsidering the nndom frr- 
q i i e rq  rnodi iLi~ici~i  of the Iosephson oscillation 
Vdume 11, Nrrkr 6 APPLIED PHYSXCS LETTERS 15 1967 
auscd by thermal noise on the bias resistor. We 
start with Nyquh's formuk 
(W) = UTRf, (2) 
w h  ( V a )  is the mean q u a r e  noisc voltage and 
f. in thc width of thc hand of mise to which the 
mystem is d t i v e .  This extends from zero frc- 
qucncy up to a cutoff which we estimatc tq CoIWidcr- 
ing a miqk component of the noise spectrum at 
Tbc spectrum of a sine wave which is f q u c n e y  
moddad over a range qabaut a center frequency 
A at a i~.qdulation frcqucrrcrf, consists of an a m y  
ofcauaY, spofcd aide bands at interval],,. All thc 
s ick bands of significant amplitude m r  in a range 
(f,-lJj') to (f,,+ tJf), so that iffrn > Ythere are no 
fqucracrf- 
la:-gc side bands and a normal receiver would not 
detect the modulation. This limit corresponds 
physically to the variation of phase due to the modu- 
laiion. This limit cornsponds physically to the 
variation of p h a  due to the modulation becoming 
less than one cycle. 
Using thc Josephson relationship between vdtage 
and frequency m find 
af- (W)'"l@. (3) 
where = U2e. Applying the condition thatf, 
must not exceed 8fwe find chat thc cutoff frequency 
f. in Eq. (2) is of thc same order of magnitude as 
8Jin Eq. (3). Equating& and 3f( combining Eqs. (2) 
and (3). and ddining the full Sine-width 4= 2yD 
we have 
4 = 8&TR/a,' = 1.57 X 10' RT. (0 
Equation (4) is consistent with much mom rip. 
ous calcuhtionr by Sw~&pmP and by Burgess.' It 
p d i  correctly the o&r of magnitud~ of thc 
ObQCtved line-width as well as its linear depcrince 
o n R a n d T .  
A codhry of the above discwsion is that the 
lim-width is independent of the fregucncy in a p -  
mcnt with thc obemtions. In the ditca method 
the J e x e p b n  oscillator was operated at 47 MHz, 
whik in the parameuic method it mopcrated at 
audio frequencies and below. The data g;ven in the 
last tine of the table were obtained by operating 
the Josephson clarillamr at a frequency kss than 1 
Hz.atabiasvolcagekssthan lW'V.Suchadevice 
may be used as a vdtmeter. with sensitivity com- 
parable to that m p o d  for other quantum intcr- 
ference tcchnques.' 


Contribution of thermal noise to the line width of Josephson radiation from superconducting point contacts

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