1. Arian Lalezari 22 September 2004 Modeling in Applied Math
SQUIDs
Arian Lalezari
22 September 2004
Modeling in Applied Math

2. Arian Lalezari: SQUIDS
Overview
History
Physics: Components
Fabrication
Implementation
MEG
Other Applications
Future
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Arian Lalezari: SQUIDS

3. Arian Lalezari: SQUIDS
History
Brian David Josephson
Born 4 January 1940
Graduate work with superconductors and quantum tunneling at Cambridge in 1962
Verification of “Josephson Junction” in 1963
Nobel Prize in 1973
First commercial sales in 1974
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Arian Lalezari: SQUIDS

4. Arian Lalezari: SQUIDS
What is a SQUID?
A SQUID is a Superconducting Quantum Interference Device
Construction is two Josephson Junctions in parallel, creating a loop through which one measures magnetic flux
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Arian Lalezari: SQUIDS

5. Arian Lalezari: SQUIDS
Physics
“Josephson Junction”
Analogy: water pipe
Superconductor: water pipe
Insulating barrier: pinch
DC current: water flow
Voltage: water pressure
If the material is not superconducting, no current flows until there is adequate voltage
Like a blockage
Not useful for this application
hose
pinch
superconductor
thin insulating barrier
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Arian Lalezari: SQUIDS

6. Arian Lalezari: SQUIDS
Physics
If the material is superconducting, small amounts of current can flow without generating voltage at the resistive barrier
This violates Ohm’s Law from classical physics: V = IR
Phenomenon is called “quantum tunneling”
If currents get too big, tunneling cannot take place, and the barrier becomes resistive
So where is this all going?
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Arian Lalezari: SQUIDS

7. Arian Lalezari: SQUIDS
Physics
Key Ideas:
Magnetic flux can only be produced in quanta (F0)
Flux through a loop may be a fractional part of a generated quantum
By Faraday’s Law, a loop in a changing magnetic field experiences an induced current
In SQUIDs, the barriers of the Josephson Junction are designed not to fail (become resistive) until the the induced current change is equal to what is generated by one quantum change in flux (DF=F0)
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Arian Lalezari: SQUIDS

8. Arian Lalezari: SQUIDS
Physics: Large Fields
Each flux quantum that is let through “resets” the system when the quantum is allowed to pass through the loop
This returns the setup to equilibrium
Systems to track the number of times this occurs can measure magnetic flux at the quantum level
Reset counting means no dependence on the presence of a DC magnetic field
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Arian Lalezari: SQUIDS

9. Arian Lalezari: SQUIDS
Physics: Small Fields
If DF is less than one quantum, the flux cannot pass
Around the SQUID loop, current must stay in phase (Df = n*2p)
Used alone, SQUIDs can “trap” magnetic flux
If we supply and measure a supplemental current so that the phase quantum requirement is met, we can estimate the percentage of a flux quantum through the loop
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Arian Lalezari: SQUIDS

10. Arian Lalezari: SQUIDS
Sensitivity
This means SQUIDs can theoretically be made more precise than a flux quantum!
In practice, this requires amplification of the signal obtained from the SQUID
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Arian Lalezari: SQUIDS

11. Arian Lalezari: SQUIDS
Fabrication Concerns
SQUIDs have edge lengths on the order of 10 – 100mm (1e-5m – 1e-4m)
Challenging, but not impossible
Traditional SQUIDs must be kept at about 4°K (-269°C) to stay superconductive
Much more challenging: liquid Helium
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Arian Lalezari: SQUIDS

12. Arian Lalezari: SQUIDS
Implementation: MEG
Helmet with dozens of SQUIDs
To bathe each SQUID in liquid Helium, the majority of the heavily insulated helmet enclosure is filled with liquid Helium
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Arian Lalezari: SQUIDS

13. Arian Lalezari: SQUIDS
Implementation: MEG
Each SQUID returns a time-domain signal reflecting changes in magnetic flux
This visualization maps the head to a circle, and shows short time samples from each SQUID
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Arian Lalezari: SQUIDS

14. Implementation: Microscope
Large flux application
Scanning SQUID Microscope scan of a small region of a floppy disk, and a diagonal cross-section
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Arian Lalezari: SQUIDS

15. Arian Lalezari: SQUIDS
Future
High-Temperature Semiconductors
Semiconducting behavior at much higher temperatures (e.g. above 77°K boiling point of liquid Nitrogen)
Fetal heartbeats
Better back-mapping techniques for data
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Arian Lalezari: SQUIDS

16. Arian Lalezari: SQUIDS
Questions?
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Arian Lalezari: SQUIDS

17. Arian Lalezari: SQUIDS
References
Fundamentals of superconductors:
Basic Introduction to SQUIDs:
Fancy cross-referenced site for Josephson Junctions/Josephson:
SQUID sensitivity and other ramifications of Josephson’s work:
Understanding a SQUID magnetometer:
Some exciting applications of SQUIDs:
Relative strengths of pertinent magnetic fields
The 1973 Nobel Prize in physics
Critical overview of SQUIDs
Research Applications
Technical overview of SQUIDs:
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Arian Lalezari: SQUIDS