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SQUIDs: Then and Now 151

Brian Pippard wandered into our lab to see how things were going, and Paul

and I proudly showed him one of our new gadgets. Brian contemplated it

thoughtfully for a while, and then — with a smile — said, “It looks as though

a slug crawled through the window overnight and expired on your desk!”

I tried hard to make a SQUID by freezing a solder blob on a piece of

niobium wire doubled back on itself so that there were two junctions. I ap-

plied a magnetic ﬁeld to the loop of wire sticking out of the solder blob. This

never worked, in retrospect because the inductance of the loop was too high.

One day, I decided instead to pass a current along the wire, and immediately

saw oscillations in the critical current when I changed the current. It did

not take me very long to discover that the loop was irrelevant — I needed

to pass the wire through the solder only once, and apply a current to the

wire [Fig. 3(a)]. How did it work? Apparently, there were typically just two

or three dominant junctions between the wire and the solder. The current

in the wire generated a magnetic ﬁeld in the penetration depths of the wire

and solder, so that the area of the “SQUID” was given by the sum of the

penetration depths times the separation of the junctions. The periodicity

in current ranged randomly from about 0.2 to 1 mA. However unlikely, the

majority of these devices showed interference between two or three junctions,

and they generally survived at least scores of thermal cyclings. It is inter-

esting to note that, as I increased the current through the niobium wire,

I could generally observe thousands of oscillations in critical current with

no evident diminution in amplitude. This lack of a discernible Fraunhofer

pattern suggested that the junctions were essentially points.

The name for this new device had already been unwittingly provided by

Brian Pippard and we simply had to work out what it stood for. And so the

“Superconducting Low-inductance Undulatory Galvanometer” (SLUG) was

born.

Brian’s original concept was a digital voltmeter, but I soon realized that

one could readily measure changes in ﬂux that were much less than one ﬂux

quantum. I applied a static current and a sinusoidal current through the

SLUG [leads “I” in Fig. 3(a)] so that voltage pulses appeared across the

voltage leads [leads “V ” in Fig. 3(a)]. The area under these pulses depended

on the critical current of the SLUG, enabling me to determine the critical

current, and hence the current in the niobium wire [leads “I

” in Fig. 3(a)]

to about ±1 µA, using simple electronics. Once I had this worked out, I

immediately put the SLUG together as a voltmeter. A postdoctoral fellow

in the Mond, Steve Lipson, was interested in measuring the resistance of a

single crystal of copper (to be used for measurements of magnetoresistance)

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152 J. Clarke

Current I

in niobium wire

Voltage

(a) (b)

Fig. 3. The SLUG. (a) Photograph showing attachment of current (I), voltage (V)

and ﬂux bias (I

) leads. (b) Voltage V versus I

that he estimated to be about 10

−8

Ω. We made a voltmeter by connecting

the Cu block in series with a manganin wire, with a measured resistance of

about 10

−5

Ω, and the niobium wire through the SLUG. The idea was to

make a potentiometer, adjusting the currents in the two resistors to produce

zero current in the SLUG. After Steve and I cooled down our potentiometer,

I was chastened to observe that the output from the SLUG was horribly

noisy. Further inspection showed that the “noise” was in fact due to cur-

rents induced in the loop by 50-Hz magnetic ﬁelds. For the next run, Steve

soldered up some lead foil to make a box that enclosed the circuit, and our

pickup problem was solved. This was an invaluable lesson for me: if you

have a sensitive magnetometer or voltmeter, you have to protect it from the

real world, which is a very noisy place.

I used the SLUG as a voltmeter for the rest of my graduate career, mostly

to investigate SNS Josephson junctions.

With a typical circuit resistance

of 10

−8

Ω, I could measure a voltage of about 10

−14

V in a second. Other

members of the Mond subsequently used the SLUG, notably Eric Rumbo

for measuring thermoelectric voltages and Pippard, Shepherd and Tindall

for measuring the resistance of the SN interference — my original thesis

topic.

I moved to the Physics Department at the University of California, Berke-

ley in January 1968 as a postdoctoral scholar, and used SLUGs in various

measurements. I devised an experiment to test the accuracy of the Josephson

voltage-frequency relation in junctions made from diﬀerent superconductors.

I irradiated two SNS junctions with the same radiofrequency magnetic ﬁeld,

and measured the voltage diﬀerence between steps of a given order induced

on the two I-V characteristics. I found that the voltages were the same to

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SQUIDs: Then and Now 153

000-120 SCREW

AND NUT

Fig. 4. Point contact dc SQUID. (Reproduced with permission from Ref. 25.)

an accuracy better than 1 part in 10

, corresponding to a voltage diﬀerence

of less than 2 × 10

−17

V, regardless of the nature of the superconductor.

This result helped to establish the Josephson junction as a means of main-

taining the standard volt in terms of a frequency.

Much later, Shen Tsai

and co-workers

repeated the experiment to the remarkable accuracy of two

parts in 10

Subsequently, I used a SLUG voltmeter to measure the pair-quasiparticle

potential diﬀerence in nonequilibrium superconductors.

Single electrons

tunneling from a normal electrode into a superconducting ﬁlm generate

an imbalance between the electron-like and hole-like quasiparticles. This

“charge imbalance” is detected by a normal electrode in tunneling con-

tact with the reverse side of the superconductor: a voltage is induced on

the normal electrode relative to the chemical potential of the Cooper pairs

measured some distance away from the nonequilibrium region of the super-

conductor. Shortly after I had completed this experiment, in early 1972 I

returned to the Mond Laboratory on sabbatical leave. Mike Tinkham was

also there on leave, writing his celebrated book on superconductivity, and he

worked out the theory of charge imbalance.

Subsequently, charge imbal-

ance was investigated in a variety of other nonequilibrium superconducting

conﬁgurations.

During the time I was working on the SLUG, Zimmerman and Silver

were busily developing the “point contact” dc SQUID, shown in Fig. 4. The

body was machined from niobium, and the two halves were clamped together

with a thin insulator separating them. The junctions were formed by two

sharpened niobium screws that could be adjusted from outside the cryo-

stat to provide optimal current-voltage characteristics. This simple means

September 8, 2010 10:53 World Scientiﬁc Review Volume - 9.75in x 6.5in ch9

154 J. Clarke

Am-

plifier

Lock-in

detector

Inte-

grator

Oscillator

Fig. 5. dc SQUID in ﬂux-locked loop.

of making a Josephson junction or SQUID was emulated in many laborato-

ries. Single-junction versions were used by undergraduates

to demonstrate

constant-current steps induced by microwaves on the current-voltage charac-

teristics at voltages nhf/2e (n is an integer, f is the microwave frequency),

and thus verify the Josephson ac relation to an accuracy of 1% or better.

The observation of oscillations in voltage as the ﬂux was varied was a

beautiful piece of physics, but for practical applications, one needs a linear

response. I built and operated a version of the ﬂux-locked loop,

but a better

one — that is still used today — was developed by Robert Forgacs and Alan

Warnick

at the Ford Laboratory. Feedback serves several purposes: it

makes the response linear in the applied ﬂux, it allows one to track changes

in ﬂux corresponding to many ﬂux quanta, and it enables one to detect

ﬂux changes of a tiny fraction of a ﬂux quantum. As illustrated in Fig. 5,

a sinusoidal magnetic ﬂux with a peak-to-peak amplitude of Φ

/2 and a

frequency f

of 100 kHz is applied to the SQUID. When the static ﬂux in

the SQUID is nΦ

, the resulting oscillating voltage across it is a “rectiﬁed”

sine wave, with no component at f

. When this signal is coupled to a

lock-in detector referenced to the same oscillator, the output is zero. When,

on the other hand, the static ﬂux in the SQUID is increased from nΦ

(n + 1/4)Ω

, there is a steady increase in the amplitude of the component

at f

, and an increasing (say) voltage out of the lock-in. If instead, we

decrease the static ﬂux from nΩ

, the voltage out of the lock-in is negative.

The output from the lock-in detector is smoothed, and fed back via a resistor

into a coil inductively coupled to the SQUID. The action of the ﬂux-locked

loop is to maintain the sum of the applied and fed-back ﬂuxes in the SQUID

at a constant value. A ﬂux δΦ

applied to the SQUID is canceled by an

opposing ﬂux −δΦ

from the ﬂux-locked loop. The output voltage V

across

the feedback resistor is proportional to δΦ

. In the early days, a typical

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SQUIDs: Then and Now 155

ﬂux noise was of the order of 10

−3

−1/2

(“per root Hz”) — meaning

an integration time of 0.25 s — at frequencies where the noise is white. At

lower frequencies, f, the noise spectral density scales approximately as 1/f.

This ubiquitous “1/f noise” or “ﬂicker noise” is still actively investigated

today. Virtually all SQUIDs — except those used at high frequencies — are

operated in a ﬂux-locked loop. There are several other schemes, at least one

of which does not involve ﬂux modulation.

3. Early rf SQUIDs

Shortly afterwards, in 1967, the rf SQUID

appeared. This device involved

only a single Josephson junction, and the ﬁrst version was based on the

machined niobium dc SQUID (Fig. 4), with one junction shorted. The rf

SQUID was coupled to the inductor of a resonant circuit [Fig. 6(a)]. When

the tank circuit was driven with a radio-frequency current at the resonant

frequency, typically 30 MHz, the behavior shown in Fig. 6(b) was observed.

Here, the voltage across the tank circuit has been ampliﬁed, rectiﬁed with

a diode and smoothed, so that one observes the amplitude of the rf signals.

When the ﬂux in the SQUID is nΦ

, one sees a series of “steps and risers”

as the rf drive is increased. At (n + 1/2)Φ

, the steps split into a half-step

above and below the steps. Thus, when the SQUID is biased at the midpoint

of one of the steps the voltage is periodic in the applied ﬂux, as shown in

Fig. 6(c); needless to say, the period is Φ

. From this point of view, the

rf SQUID behaves operationally as a dc SQUID. Particularly in those early

days, when making a Josephson junction was a challenge, the fact that the

(b)

(c)

(a)

Fig. 6. The rf SQUID. (a) Schematic of rf SQUID and its readout circuit. (b) Steps

and risers: Amplitude of rf signal across the tank circuit versus rf drive current for

two values of applied ﬂux. (c) Amplitude of rf signal across the tank circuit versus

applied ﬂux for four values of drive current. [(b) and (c) reproduced with permission

from Ref. 31.]

September 8, 2010 10:53 World Scientiﬁc Review Volume - 9.75in x 6.5in ch9

156 J. Clarke

rf SQUID required only a single junction gave it an edge over the dc SQUID.

The rf SQUID is actually misnamed, however, as no interference takes place!

4. Tunnel Junctions Revisited

During the early 1970s, there was a general shift towards using the rf SQUID.

SQUIDs made of thin ﬁlms deposited on cylindrical substrates,

32,33

with a

narrow microbridge as the single junction, achieved a white ﬂux noise of

about 2 × 10

−4

−1/2

. The strong dependence of the critical current

of the microbridge on temperature, however, limited the operating temper-

ature range. Such devices, as well as machined niobium devices, became

commercially available.

While on sabbatical leave in the Mond in 1972, I wrote a review article

on SQUIDs.

At the time, there was no theory for ﬂux noise in either the

dc or rf SQUID, but I made a simple estimate for the dc SQUID assuming

that the noise arose from Nyquist noise in the junction resistances. This led

me to conclude that the ﬂux noise should be a few µΦ

−1/2

, far lower

than anything that had been achieved. I concluded that the ﬂux noise was

dominated by voltage noise in the preampliﬁer connected to the SQUID,

and that an appropriate matching network might signiﬁcantly improve the

performance.

After I returned to Berkeley, a new postdoctoral scholar, Wolf Goubau,

and a new graduate student, Mark Ketchen, and I set to work. We bor-

rowed three ideas from the rf SQUID: a cylindrical geometry (which gives

a large area for a low inductance), a tank circuit readout and thin ﬁlms.

I had wanted to move away from microbridge junctions because of their

narrow temperature range of operation. Fortunately, Paul Hansma, at the

University of California, Santa Barbara, had achieved good reproducibility

and longevity with Nb-NbOx-Pb tunnel junctions.

We decided to copy this

technique, and acquired a sputtering system to deposit niobium. Figure 7(a)

shows the geometry of our SQUID, grown on a 3-mm-diameter quartz tube.

We used shadow masks to pattern the various ﬁlms, which had a minimum

linewidth of 75 µm. We ﬁrst deposited the PbIn cylinder, followed by the

gold ﬁlm that formed the resistive shunt for each junction (to eliminate hys-

teresis on the current-voltage characteristic). We next sputtered the Nb

ﬁlm, which we oxidized in air in a closed oven (12 min at 130

◦

C was the

recipe). Immediately afterwards, we deposited the PbIn “T” that completed

the junctions. We scribed a slit in the PbIn cylinder with a razor blade.

Subsequently, we submerged the SQUID in a solution of Duco cement

September 8, 2010 10:53 World Scientiﬁc Review Volume - 9.75in x 6.5in ch9

SQUIDs: Then and Now 157

QUARTZ TUBE

LEAD BAND

LEAD T

GOLD SHUNT

INDIUM

CONTACT

FREQUENCY (Hz)

(b)(a)

−4

−12

−10

−8

−6

−2

JOSEPHSON

JUNCTIONS

NIOBIUM FILMS

INDIUM

CONTACT

(BACK SIDE)

75 m WIDE

Pb FILM

150 m WIDE

Nb FILM

SQUID NOISE (φ

/Hz)

Fig. 7. Cylindrical dc SQUID. (a) Schematic. (b) Representative power spectrum

of ﬂux noise in a ﬂux-locked loop.

dissolved in acetone — this was our favorite insulator, and it proved to

be very tough. The last step was to deposit a PbIn ﬁlm over the slit and

the various metal strips to reduce their inductances. We attached leads with

pressed indium beads. We wound the input coil from Nb wire on a Teﬂon

rod, potted it in Duco cement, and removed the coil by dipping the whole

thing in liquid nitrogen and slipping it oﬀ. The potted input coil would slide

neatly over the cylindrical SQUID, giving a high coupling eﬃciency. We po-

sitioned the Nb modulation-feedback coil, wound on an insulating rod, inside

the SQUID. This entire process sounds extraordinarily primitive by today’s

standards, but we could cool these devices to liquid helium temperature

many times with no degradation.

To test the SQUIDs, we built a ﬂux-locked loop with ﬂux modulation.

We boosted the resistance of the SQUID (∼0.5 Ω) to the optimum noise

impedance of our preampliﬁer (a few kΩ) with a cold resonant circuit: the

SQUID was shunted with an inductor and capacitor in series, and the pream-

pliﬁer was connected across the capacitor. The result was a substantially

enhanced signal into the preampliﬁer, and a correspondingly reduced ﬂux

noise. A representative power spectrum,

(f) versus f, is shown in

Fig. 7(b). The white noise, 3.5 × 10

−5

−1/2

, was a good deal lower

than that achieved previously, and the large loop area yielded a magnetic

ﬁeld noise of about 10 fTHz

−1/2

. It is also noteworthy that the 1/f noise

“knee” — about 2 ×10

−2

Hz — is substantially lower than that achieved in

today’s SQUID magnetometers.

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158 J. Clarke

We used our cylindrical SQUIDs in a variety of experiments. For example,

Wolf Goubau, Tom Gamble and I used two, three-axis SQUID magnetome-

ters for magnetotellurics. In this technique, one measures the impedance

of the Earth at depths down to 50 km using low-frequency electromagnetic

waves (10

−4

–100 Hz) propagating to the Earth’s surfaces from the mag-

netosphere and ionosphere. The low magnetic ﬁeld noise of our SQUIDs

ultimately led us to invent “remote reference magnetotellurics,” a technique

that eliminates noise induced by vibrational motion of magnetometers in

the Earth’s ﬁeld by cross-correlating the signals from two distant (∼5 km)

magnetometers.

37,38

I think the cylindrical SQUID played a role in turning the attention of

the community back to the dc SQUID. In fact, to my knowledge, no other

group adopted this design. One reason may have been the realization that

higher performance required tunnel junctions with smaller areas. Nobody

was excited about using photolithography — just being imported from the

semiconductor industry — on a cylindrical surface!

Mark Ketchen moved to IBM, Yorktown Heights to work in the Joseph-

son computer project. He and Jeﬀrey Jaycox developed the square washer

SQUID,

shown schematically in Fig. 8(a), which is the basis of virtually all

SQUIDs used today. Mark described this device as “The result of putting

your thumb on one end of the cylindrical SQUID and squashing it ﬂat,

transforming it into a washer with a spiral input coil.” The SQUID itself is

a thin-ﬁlm square washer, typically 1 mm across, with a hole in the middle

and a slit that runs to the outer edge where two tunnel junctions are grown.

The junctions are completed with an upper ﬁlm that connects them, thus

(a)

TO JUNCTIONS

MODULATION

COIL (L

)

INPUT

COIL(L

)

(b)

Fig. 8. Square washer dc SQUIDs. (a) Schematic of original design. (reproduced

with permission from Ref. 39.) (b) Typical practical device. The two resistively

shunted Josephson tunnel junctions are at the right-hand edge, one on each side of

the slit. The Nb washer (light blue) is 1 mm across.

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SQUIDs: Then and Now 159

closing the SQUID loop. An insulating layer is deposited over the square

washer, followed by a thin-ﬁlm, spiral coil. A current passed through the

coil generates a magnetic ﬂux that the washer focuses into the hole, giving

eﬃcient coupling between the coil and the washer.

These SQUIDs were fabricated on silicon wafers using the photolitho-

graphic patterning techniques developed by the semiconductor industry. Al-

though the stage was set for today’s SQUIDs, one obstacle remained. The

Ketchen-Jaycox SQUIDs were made from the PbInAu alloy used in the IBM

computer project, and not as robust as one would have liked. Fortunately,

in the early 1980s John Rowell and coworkers

and subsequently Gurvitch

et al.

developed the niobium-based junction technology that is univer-

sally used today. One ﬁrst deposits a Nb ﬁlm on a silicon wafer, followed

immediately by an Al ﬁlm that is a few nanometers thick. The Al ﬁlm is

subsequently oxidized in an O

(or sometimes an ArO

mixture) atmosphere

with a controlled pressure for a prescribed time. The gas is pumped out and

the upper Nb electrode is deposited. Subsequently, the “trilayer” is pat-

terned to form Josephson junctions. The thickness of the Al ﬁlm is chosen

so that some metal remains after the upper surface has been oxidized; this

oxidation process is highly controllable.

The technology for the Nb-based, square washer dc SQUID — the

workhorse of today’s SQUID applications — was essentially in place by the

mid ’80s. Today, these SQUIDs are typically made in batches of several

hundred on silicon wafers that are diced to produce individual devices. These

devices are virtually indestructible, and can be cycled between room and

cryogenic temperatures indeﬁnitely. At 4.2 K, the ﬂux noise is typically 1–2

µΦ

−1/2

at frequencies above the 1/f knee of roughly 1 Hz. The corre-

sponding (white) noise energy, S

(f)/2L, is ∼10

−32

JHz

−1

(∼100~). As we

shall see, much lower noise is achieved at millikelvin temperatures.

5. The Flux Transformer

Our story of the development of SQUIDs would not be complete without

mentioning the superconducting ﬂux transformer, illustrated in Fig. 9. Flux

transformers can increase the magnetic ﬁeld sensitivity of SQUIDs substan-

tially and enable one to make magnetic ﬁeld gradiometers. The magne-

tometer [Fig. 9(a)] consists of a superconducting pickup loop coupled to the

input coil of a SQUID — for example, the square washer SQUID (Fig. 8)

— to form a closed superconducting circuit. A magnetic ﬁeld applied to

the pickup loop induces a supercurrent in the transformer — because of ﬂux

September 8, 2010 10:53 World Scientiﬁc Review Volume - 9.75in x 6.5in ch9

160 J. Clarke

(a)

(b)

Fig. 9. Flux transformers. (a) Magnetometer and (b) ﬁrst-derivative axial

gradiometer, wound from niobium wire. Typical diameter of pickup loops is 50 mm.

quantization — and thus a ﬂux in the SQUID. The transformer operates

at frequencies down to zero. The transformer is optimized when the induc-

tances of the pickup and input coils are equal. For a pickup loop diameter

of 50 mm, a magnetic ﬁeld noise of 10

−15

THz

−1/2

is typical. Figure 9(b)

shows a ﬁrst-derivative, axial gradiometer in which the two pickup loops,

nominally equal in area, are wound in opposite senses. Application of a

uniform magnetic ﬁeld along the axis of the loops produces no net ﬂux in the

transformer and no output from the SQUID. An applied gradient ∂B

/∂z,

on the other hand, produces a current in the ﬂux transformer and an output

from the SQUID. Second-derivative axial gradiometers measuring ∂

/∂z

and oﬀ-diagonal gradiometers sensitive to, for example, ∂B

/∂x are also

commonly used. Gradiometers are mostly used to discriminate against

distant noise sources in favor of nearby signal sources: noise from a dipole

falls oﬀ with distance r as 1/r

and 1/r

for ﬁrst- and second-derivative

gradiometers. Gradiometers are commonly used to measure signals from the

brain (Sec. 8).

6. A Little Theory

The early development of both dc and rf SQUIDs was largely a “seat of

the pants” aﬀair, without any detailed theory to guide their optimization.