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Superconducting Instrumentation
for Precision Measurement and Control
R.V. Duncan
Sandia National Laboratories, Albuquerque, NM 87185, USA
Abstract. The Josephson series-array voltage standard (JAVS) has
dramatically improved the level to which high-accuracy electrical
equipment may be monitored and stabilized.
For example, a small
pressure dependence in the output of some solid-state voltage standards
has been measured with the JAVS. The use of two such series-arrays
in a superconductive loop promises to be a new method of ultra-small
frequency
difference measurement.
The accuracy of these new
measurement configurations is set by the superconductive loop induct-
ance and the Josephson junction parameters.
1.
Introduction
Series-arrays
[1] of Josephson junctions,
all biased by a common
microwave source, are in use within approximately twenty laboratories
throughout the world as an intrinsic voltage standard.
At Sandia
National Laboratories (SNL), and similarly at many other laboratories,
this standard is routinely used to track the drift, accuracy, and linearity
of digital volt meters (DVM), voltage reference standards, and voltage
calibrators to an uncertainty better than 0.1 ppm.
In collaboration with
the National Institute of Standards and Technology (NIST, formerly
NBS) we have used
this technology
to
detect
small
systematic
variations in the output of some solid-state voltage standards with
elevation.
Such refinements in measurement technology would be
impossible without this wide-spread use of the JAVS.
Recently a
powerful new measurement technique utilizing these series- arrays of
Josephson junctions has been developed
[2],
Here two such arrays
have been placed in series-opposition in a superconductive measure-
ment loop which is inductively coupled to a SQUID. We
[3] have
analyzed
this interferometer circuit within the framework of the
Steward-McCumber model [4] to determine the measurement accuracy
[5].
This circuit, which we refer to as a macroscopic quantum circuit
(MQC) due to its superconductive coherence throughout the loop, may
prove useful as an ultra-accurate interferometric readout at millimeter
wavelengths for such applications as
gravity wave detection and
Sagnac-effect gyroscopes [6] . The full utilization of a MQC requires
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Springer Proceedings in Physics, Vol. 64
Superconducting Devices and Their Applications
Editors: II. Koch, H. Liibbig
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the development of a superconductive positioner to fine-tune cavity
oscillators used to bias the Josephson junctions and possibly to tune the
MQC frequency response directly.
The SNL Josephson voltage standard is similar to that used by NIST
[7] except that it incorporates cryogenic (rather than room-temperature)
passive filtering
[8], and
it is cooled continuously by a refrigerated
Dewar [9] which maintains the standard at 4K with no helium loss or
routine operator intervention.
In the near future this refrigerated Dewar
will be used to simultaneously support the Josephson array and to re-
liquify the ^He boil-off from a nearby quantum Hall effect resistance
standard.
2. Environmental
effects on
solid-state voltage standards
Solid-state voltage standards (SSVSs) utilizing Zener diode references
are in common use today for dc voltage metrology [10].
The JAVS
provides an extremely accurate measurement system against which
these SSVSs may be critically evaluated.
The thermal coefficient of
many SSVS have been measured against the JAVS and found to be
typically 17 ppm/K. Since the set temperature of the SSVS enclosure is
stable to better than 2 mK, and when intentionally over-heated it returns
to its set point to within 5 mK, thermal effects create inconsequential
errors in all the SSVSs observed to date. A systematic variation in
some SSVS with elevation (and hence pressure) has been detected.
One such SSVS, designated SSVS#1, was transported between four
locations within the United States during 1989.
This device was
operated at elevations ranging from sea-level to 1,500 meters and no
elevation or pressure dependence was observed in its output. SSVS#1
displayed excellent repeatability and stability as measured against the
JAVS from location to location (once
its drift rate was taken into
account, SSVS#1 typically deviated by no more than 0.1 ppm during
shipment).
No variation of the JAVS has been observed during
controlled temperature and pressure changes [11].
In August, 1990 another SSVS (called SSVS#2) was shipped round-
trip between SNL in Albuquerque and NIST in Gaithersburg. At each
location the device was measured against a Josephson voltage standard.
The
average of
its
four
1.018V
taps was 0.98 ppm higher
at
Gaithersburg than at Albuquerque - a factor of ten larger in variation
than the SSVS#1 result! A comparison of the value of SSVS#2 after its
return from NIST to its value before it was shipped agreed to within
0.15 ppm.
In order to check for a pressure dependence in the SSVS#2
output, both SSVS#1
and SSVS#2 were measured
in
a mobile
laboratory at an elevation of 3,260 meters (on the summit of Sandia
Crest, which is located 50 km from SNL) in collaboration with S. L.
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Kupferman.
These measurements were made against a high-accuracy
8.5-digit DVM which was calibrated against the JAVS immediately
before and immediately after the mountain measurements.
SSVS#2
experienced a -3.40 ppm deviation in the average of its four 1.018V
taps with the 1,760 meter elevation gain, while SSVS#1 displayed an
inconsequential +0.8 ppm deviation. Given the previous performance
of SSVS#1, this deviation was likely due to a systematic change in the
DVM gain with elevations. Only the 1.018V taps of SSVS#2 displayed
this variation with elevation, indicating that a resistive voltage divider
within SSVS#2 was most likely the source of this systematic error.
These results serve as a warning that all transportable voltage standards
used in critical metrology applications must be individually qualified
through their full range of environmental conditions against a JAVS.
In
the
future we
will
use our JAVS
and an
automated pressure/
temperature/ humidity-controlled chamber to make these
critical
environmental qualification measurements. Notice also that these very
small systematic effects could not have been detected without the JAVS.
3. Macroscopic Quantum Circuit Measurements
Consider two rf-biased series-arrays connected in series-opposition
with superconductive
wire, forming the MQC with
a
total
self-
inductance L.
The supercurrent is in the MQC which builds up over
time t due to the difference in electric potential AV between the two rf-
biased devices is given by
is(0 =
t
:
<J
AV dt’.
( 1 )
This supercurrent is then read out by a SQUID which is magnetically
coupled to the MQC.
This method of ultra-precise potentiometry was
developed by Clarke [12], and more recently used by Jain et al. [13] to
obtain measurements with a precision of AV/V ~ 3x10'^ using single
rf-biased junctions operating at about 300 pV.
Kautz and Lloyd [2]
have used this technique to compare the voltage output of two series-
arrays, each containing 2,076 Josephson junctions and biased to W~
volt, to a precision of AV/V ~ 2x1 0‘* 7.
in ap the above measurements
both Josephson devices were biased by the same rf source to check for
deviations from is = 0 when both Josephson devices were biased to the
same step (n). Other experiments! 14] have been performed which used
two different rf sources of known detuning (Aco) to bias the junctions
and thus to generate an increasing
i s consistent with Eq.
1 and the
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prediction that AV = AV0 = nhA(o/47te, where h is Planck’s constant,
and e is the magnitude of the charge of the electron.
This method of
measurement may provide a powerful new method of detecting very
tiny frequency differences generated in gravity wave detectors and
Sagnac-effect gyroscopes [6].
Referring to Eq.
1, it is clear that an arbitrarily precise measurement
of AV may be made by either decreasing L, increasing the length of the
measurement interval, or both. The value of the self-inductance (L) of
the MQC need not be limited by the SQUID's input inductance [13].
Due
to
the
interaction
of
the two Josephson
devices
via
the
superconductive loop, the measured AV is not simply equal to AV0 =
nhAco/47te.
Rather there exists a correction which depends on the value
of L, and which becomes
large
as L approaches
the Josephson
inductance Lj = h/2elc , where
Ic
is the junction's critical current.
These corrections, which have been calculated within the framework of
the Steward-McCumber model [4] in the absence of external noise, are
detailed in the proceedings of ISEC '91 [5].
These JAVS may be used as an ultra-stable voltage source provided
that the load is very quiet and that the compliance current never exceeds
the voltage state's critical current (which is on the order of 100 pA).
In
such
applications (which may
include
ultra-accurate
drift tube
measurements at cryogenic temperatures) the voltage resolution and
stability is directly determined by the linewidth and center-frequency
stability
of
the
biasing
oscillator.
Conventional
microwave
locker/counters can
servo
the
center frequency of Gunn diode
oscillators to within a few Hertz out of 75
- 95 GHz.
Superconductive
cavity oscillators have been developed which have Q > 10^ over their
full tuning range [15].
This cavity oscillator may be tuned with a
proposed ultra-stable superconductive positioner [16] in order to obtain
about a factor of one thousand improvement over conventional center-
frequency stability.
Acknowledgement
This work is supported by the U.S.A. Department of Energy under
Contract Number DE-AC04-76DP00789.
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References
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F. L. Lloyd, C. A. Hamilton, J. A. Beall, D. Go, R. H. Ono,
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4.
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R.V. Duncan, Physica B 165, 101 (1990).
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16.
R. V. Duncan, in preparation.
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