SQUIDs

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SQUIDs

• Why squids?
• Superconducting Quantum Interference Devices -
  the most sensitive detectors of magnetic flux BS

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Why SQUIDs?

• For a large number of applications extremely
  small magnetic signals have to be detected and
  accurately measured.
• Sensitivities of magnetic sensors
• Hall probes  mT
• Flux gate sensors  nT
• SQUIDs fT
• SQUIDs allow to detect and characterize the
  magnetic signals which are so small as to be
  virtually immeasurable by any other sensors.
• How sensitive? Allows to measure magnetic fields
  produced by the nerve currents associated with
  the physiological activity of the human heart
  (magnetocardiogram  MCG) or the human brain
  (magnetoencephalogram  MEG) these signals have
  a typical strength  pT.
• Best of the SQUID sensors have energy sensitivity
  approaching Plancks constant.
• The energy sensitivity is a figure of merit of
  SQUIDS and SETs device and refers to the minimum
  signal energy per unit bandwidth (J/Hz) which
  must be coupled to the device to generate an
  output just exceeding the noise.
• SQUIDs are the most sensitive detectors
• of extremely small changes in magnetic flux.
• Fluxes can be created by currents
• therefore the most sensitive current sensors
  as well

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SQUIDs - basic facts

• SQUIDs combine the physical phenomena of flux
  quantization in superconducting loops and
  Josephson tunneling.
• The Josephson effect refers to the ability of two
  weakly coupled superconductors to sustain at zero
  voltage a supercurrent associated with transport
  of Cooper pairs, whose magnitude depends on the
  phase difference between the two superconductors.
• The maximum current which a Josephson weak link
  can support without developing any voltage across
  it is known as its critical current Ic. When the
  current passed through a Josephson weak link
  exceeds Ic, a voltage appears across it
• If a closed loop made of superconductor magnetic
  field cannot enter the loop (ideal
  diamagnetism). But if there is a weak link flux
  enters the loop in quanta! Flux quantum

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SQUIDs - basic facts

• Types of SQUIDs
• The DC SQUID consists of a closed loop of
  superconductor interrupted by two Josephson
  junctions.
• AC SQUIDs have one junction.
• When a symmetric DC SQUID is biased with an
  external dc current I, a current I/2 flows
  through each of the two junctions the critical
  current of the SQUID, in the absence of any
  external magnetic fields, is thus 2Ic.
• When a magnetic flux Fext is applied
  perpendicular to the plane of the loop, the loop
  responds with a screening current J to satisfy
  the requirement of flux quantization
• Flux quantization requires that the magnetic flux
  enclosed by a superconducting loop be quantized
  in units of the flux quantum
• The screening current J is zero when the applied
  external flux is nF0 and is  (F0/2L) when the
  external flux is (n  1/2)F0, thus exhibiting a
  periodic variation with externally applied flux.
• The screening current J flowing around the SQUID
  loop leads to a reduction in the critical current
  of the SQUID from 2Ic to (2Ic2J).
• The critical current of the SQUID is a periodic
  function of externally applied flux. If the SQUID
  is biased with a current slightly larger than
  2Ic, the output voltage of the SQUID turns out to
  be a periodic function of the magnetic flux
  applied perpendicular to the plane of the SQUID
  loop.
• The SQUID device thus functions as a transducer
  for magnetic flux producing measurable voltage
  changes at its output for small changes in
  magnetic flux applied at the input.
• Since the response of the SQUID is periodic, it
  is necessary to linearize it using the flux
  locked loop electronics in order to build
  SQUID-based measuring instruments.

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RF and DC SQUIDS

• One junction (RF SQUID)
• consists of a single Josephson junction inserted
  into a superconducting loop.
• The loop is inductively coupled to the inductor
  of an LC-resonant circuit that is excited with a
  current at a frequency ranging from a few tens of
  megahertz to several gigahertz.
• The amplitude of the oscillating voltage across
  the resonant circuit is periodic in the applied
  flux, with a period , enabling one to detect
  changes in flux of the order of 10-5 F0 .
• RF SQUIDs were more popular in the past (easier
  to match impedances and a bit easier to make )
• Two Junctions (DC-SQUID)
• consists of two Josephson junctions connected in
  parallel on a superconducting loop and is
  operated in the voltage state with a current
  bias.
• When the flux in the loop is increased, the
  voltage oscillates with a period F0.
• By detecting a small change in the voltage one is
  able to detect a change in flux typically as low
  as 10-6F0 .

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SQUID designs how to couple it

• Need to couple SQUID to the input signal
• Need to increase the coupling but keep the
  inductance low

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DC SQUID tuning
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Flux locked Loop operation of SQUIDs

• In most applications, the signal from the SQUID
  is amplified and fed back as a flux to the SQUID
  loop.
• Two modes of operation with and without
  modulation
• Feedback linearizes the SQUID response, enabling
  one to detect small fractions of a flux quantum
  as well as to track many flux quanta.
• Flux-locked loop (FLL) with modulation involves
  flux modulation of the SQUID with a peak-to-peak
  amplitude of F0 /2 and a frequency of fm 0.110
  MHz (Fig. 4).
• The resulting oscillating voltage across the
  SQUID is coupled via a resonant matching circuit
  or transformer to a room-temperature preamplifier
  and then lock-in detected at frequency fm.
• After integration, the resulting signal is fed
  back as a current through a resistor to a coil,
  thus keeping the flux in the SQUID constant at an
  optimum working point on the V-F characteristic.
• NULL DETECTOR is a KEYWORD

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Another example of FLL with modulation

• An oscillator is used to modulate the flux
  coupled to the SQUID at a frequency of 100 kHz
  and an amplitude F0/4 by feeding appropriate
  current to the modulation coil.
• The signal appearing across the SQUID is phase
  sensitively detected at the modulation frequency
  after suitable amplification, and is fed back via
  a feedback resistor Rf, to the modulation coil.
• The voltage across the resistor Rf provides the
  SQUID read out. As long as the quasistatic flux
  threading through the SQUID loop remains on a
  peak or a trough of the periodic VF
  characteristic, there is no signal at the
  modulation frequency present at the output.
• In the presence of a quasistatic signal applied
  additionally at the input, however, the circuit
  produces an output voltage which is proportional
  to the signal flux while ensuring that the SQUID
  stays locked in the vicinity of a single
  operating point on the VF characteristic by
  generating a feedback flux which practically
  cancels the signal flux.
• This technique offers several distinct
  advantages the signal of interest is moved to
  frequencies above the 1/f noise threshold of the
  preamplifier and there is a greater immunity from
  dc drifts in the amplifiers and the biasing
  circuitry. The closed loop signal bandwidth of
  the system is, of course, much less than the
  modulation frequency however, a signal bandwidth
  of 1 to 10 kHz is considered adequate for a
  majority of applications

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FLL with modulation -1

• Amplitude of modulation fm f0/4
• In the peak (or in the valley) signal at 2f
• Resonant coupling to improve impedance matching

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FLL with modulation -2
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Frequency response in FLLwith modulation
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Direct FLL

• Old times problem 1 it is hard to match
  impedances, so SNR is poor
• Clever design idea to use additional positive
  feedback (APF)
• A small change of the magnetic flux in the SQUID
  produces the change of voltage, and the voltage
  produces an additional flux by the current
  through the APF coil, so that the flux-to-voltage
  transfer coefficient increases.
• For the FFL circuit with no modulation,
  increasing the flux-to-voltage transfer
  coefficient makes the system noise decrease and
  the sensitivity increase.
• The transfer function becomes asymmetric with a
  steeper slope on the portion for which the
  feedback is positive
• Transfer function enhances from 50mV/F0 to
  500mV /F0

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Design idea for noise reduction

• By using 4 opamps in parallel, the noise is
  reduced by a factor of 2

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APFadditional positive feedback
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SQUID applications picovoltmeter(!)

• Feedback provides high input impedance of the
  voltmater

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SQUIDs applications - Magnetoencephalography

• Magnetoencephalography (MEG)the detection
• of magnetic fields produced by the brain
• A typical helmet contains about 300 sensors,
  including a number of reference sensors for noise
  cancellation, cooled to 4.2 K. The sensors are
  generally configured as first-order gradiometers.
• The magnetic field sensitivity referred to one
  pickup loop is typically 35 fT Hz-1/2 .
• Each SQUID is operated in its own FLL, and the
  outputs from all the channels are recorded
  digitally for subsequent analysis.
• The biggest single challenge is the suppression
  of environmental magnetic noise. For example, a
  typical signal from the brain might be 50 fT,
  while urban noise may vary from 10 nT to 1 mT
  rms.
• Noise rejection of 108 (160 dB) is required.
• use gradiometers, which reject distant noise
  sources in favor of nearby signal sources.
• Signals from two first-order gradiometers can be
  subtracted in software to form a second
  derivative.
• The signals from more devices can be combined in
  software to form a third derivative. Why? Because
  the field from a magnetic dipole falls off with
  distance as 1/r3 , the first, second, and third
  derivatives fall off as 1/r4, 1/r5 and 1/r6.
• Shielding by a high-permeability material that
  further reducesambient fluctuations in magnetic
  field.
• When the brain is stimulated, by auditory,
  somatosensory, or visual means, a small region of
  the cortex responds by producing magnetic signals
  that are recorded by the array of SQUIDs
  surrounding the patients head. Each signal
  source can be modeled approximately as an
  equivalent current dipole, that is, as a tiny
  battery embedded in the conducting medium of the
  brain. By solving the inverse problem one can
  locate the source of a given dipole, typically to
  within about 2 mm
• Purpose brain tumor detection. Although a brain
  tumor can be located precisely by MRI, this image
  does not reveal the function of the surrounding
  brain tissue. MEG is used to map the function of
  the brain in the vicinity of the tumor.
• Purpose epilepsy source detection. The MEG
  system detects the magnetic signals generated by
  spontaneous interictal discharges in the
  epileptic source. In many cases, these sources
  can be modeled as equivalent current dipoles and
  can, thus, be localized. If surgery is
  appropriate, it is again guided by mapping the
  function of the surrounding tissue
• Purpose brain trauma detection, mapping and
  studies of patients suffering from schizophrenia
  or from Alzheimers or Parkinsons disease.

System for MEG with 275 sensor channels and 29
reference channels (courtesy CTF Systems, Inc.).
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SQUIDs applications - Magnetocardiography

• In MCG, an array of SQUID gradiometersanywhere
  from 9 to 64is placed just above the chest to
  record the magnetic fields produced by the heart.
• From these magnetocardiograms, one reconstructs
  the current flow in the heart, which varies
  greatly during the cardiac cycle.
• Alpplications
• Localization of accessory pathwaysessentially
  electrical short circuitsthat are a source of
  heart arrhythmia.
• Diagnosis of ischemiaoxygen starvation of the
  heart muscle due to narrowed arterieswhich can
  severely distort the magnetic dipole pattern
  characteristic of the healthy heart during the
  repolarization cycle.
• In hospital emergency roomsis the rapid
  diagnosis of a suspected heart attack.
• Fetal MCG.
• The general conclusion appears to be that the
  diagnostic ability of MCG is superior to that of
  electrocardiography (ECG) in at least some
  applications. However, the high cost of MCG
  compared to ECG has proven to be a significant
  barrier, and MCG is not yet adopted clinically.
  This reluctance may be due, in part, to the fact
  that the systems marketed so far have not
  incorporated cryocoolers and, thus, require
  regular transfers of liquid helium. This is an
  application for which high-SQUID gradiometers
  have sufficiently low noise, and the introduction
  of a cryocooled high- system might well result in
  a much more widespread use of this technique

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SQUIDs applications Rock magnetometry

• Superconducting Rock Magnetometer manufactured by
  2G Enterprises
• The magnetometer has a horizontal
  room-temperature access and is aimed specifically
  at determining the magnetic momentalong three
  axesof rock core samples up to 0.12 m in
  diameter and 1.5 m in length.
• With the aid of cryocooled thermal radiation
  shields, the system can run for a remarkable 1000
  days between liquid helium refills. Thus, the
  need for cryogenics is virtually invisible to the
  user, and this instrument has become the standard
  rock magnetometer of the geophysics community.
• One application is to measure the magnetic moment
  of sedimentary cores taken from the ocean basins
  to study the polarity reversal of the earths
  field over geologic time.

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SQUIDs applications - Magnetic Property
Measurement System (MPMS)

• The essential feature is the use of a gradiometer
  to measure the magnetic properties of a sample
  inserted into one of its pickup loops via a
  vertical tube with room-temperature access.
• The temperature of the sample can be varied from
  about 2 to 400 K, and the magnetic field can be
  varied from zero to 7 T.
• The system can be used to measure both the
  intrinsic magnetic moment of a sample in zero
  magnetic field and the magnetic susceptibility by
  applying a magnetic field.
• The original system operated in liquid helium,
  but a version equipped with a cryocooler is now
  available the latter is an excellent example of
  a turnkey system where the operator does not need
  to be aware that it contains a superconducting
  device. The MPMS has found a great variety of
  applications in physics, materials science,
  geology, electronics, and biology.
• Examples of its applications include high- and
  heavy fermion superconductors, antiferromagnets,
  fullerenes, spin glasses, magneticoptic
  materials, nanocomposites, amorphous alloys,
  ceramics, metalloproteins, sea-bed lava, and iron
  concentrations in chlorophyll.

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SQUIDs applications imaging currents in
semiconductor packages

• The SQUIDwhich is cooled by a cryocooleris
  mounted just above a thin window at the bottom of
  the vacuum enclosure. The package is scanned in a
  two-dimensional (2-D) raster below the window and
  the low-frequency oscillating current applied to
  the part of the circuit in question produces a
  magnetic field that is detected by the SQUID.
• An inversion algorithm produces an image of the
  current paths and even provides depth resolution.
• This instrument is used to locate faults in
  packages, for example, open lines, unintended
  shorts between metallic layers, and wire bond
  failures.
• A useful function is the ability to store the
  image of a functioning package from which the
  image of a defective package can be subtracted,
  thus giving a rapid diagnosis of the failure.
• Link Magma_Brochure

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SQUIDs applications - Biosensors

• In biosensors a SQUID detects the presence of
  antigens selectively labeled with magnetic
  markers.
• The superparamagnetic particles, which are
  commercially available and usually 20100 nm in
  diameter, typically consist of a cluster of Fe2O3
  subparticles each 10 nm in diameter.
• When a magnetic field is applied to immobilized
  particles, they become magnetized when the field
  is removed, the magnetization relaxes via Néel
  relaxation in a time which depends exponentially
  on the volume of an individual subparticle, and
  is typically 1 ms to 1 s.
• On the other hand, if the particleis freely
  suspended in a liquid, the application of the
  magnetic field aligns the particle removal of
  the field enables the particle to undergo
  Brownian relaxation, causing the magnetic moment
  of an ensemble of particles to decay in a time
  that is typically tens of microseconds.
• The distinction between fast Brownian rotation
  and slow Néel relaxation enables one to
  distinguish free and immobilized particles.
• The microscope (Fig. 9) sample at room
  temperature and atmospheric pressure distance
  from 100200 mm of a high- SQUID, which is at 77
  K in a vacuum. The SQUID is mounted on a sapphire
  rod, which is cooled by a reservoir of liquid
  nitrogen. The 20- mL liquid sample is contained
  in a nonmagnetic holder.
• The measurement involves pulsing a 0.4 mT field
  parallel to the SQUID on for 1 s and off for 1 s,
  and recording the magnetic decay while the field
  is off.
• The limit of detection was estimated to be about
  105 L. monocytogenes in the 20- mL sample volume.

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