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SQUID and Josephson DevicesSQUID and Josephson Devices

By :By :

Yatin SinghalYatin Singhal


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OverviewOverview

What is SQUID?What is SQUID?

TheoryTheory SQUID.SQUID.

Josephson effect :Josephson effect :DC effectDC effect

AC effectAC effect

Inverse AC effect.Inverse AC effect. Cooper pairs.Cooper pairs.

Applications of SQUID and Josephson devices.Applications of SQUID and Josephson devices.


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Facts about SQUIDFacts about SQUID

Superconducting quantum interference device is aSuperconducting quantum interference device is amechanism used to measure extremely week signals.mechanism used to measure extremely week signals.

Detect change of 100 billion times weaker signal than thatDetect change of 100 billion times weaker signal than that

moves a compass needle.moves a compass needle.

Have been used to measure the magnetic field in mouseHave been used to measure the magnetic field in mousebrain to test whether there might be enough magnetism tobrain to test whether there might be enough magnetism toattribute their navigational ability to an compass.attribute their navigational ability to an compass.

Threshold for SQUID: 10Threshold for SQUID: 10--1414 TT Magnetic field of heart:10Magnetic field of heart:10--1010 TT Magnetic field of brain: 10Magnetic field of brain: 10--1313 TT


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SQUIDSQUID


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Material used for construction ofMaterial used for construction ofSQUIDSQUID

SQUIDs are usually fabricated from either a leadSQUIDs are usually fabricated from either a leadalloy (with 10% gold or indium) and/or niobium.alloy (with 10% gold or indium) and/or niobium.

often consisting of the tunnel barrier sandwichedoften consisting of the tunnel barrier sandwichedbetween a base electrode of niobium and the topbetween a base electrode of niobium and the topelectrode of lead alloy.electrode of lead alloy.

More recently developed "High Temperature"More recently developed "High Temperature"SQUIDS are made of a substance calledSQUIDS are made of a substance called YBCOYBCO(chemical formula YBa2Cu3O7(chemical formula YBa2Cu3O7--x),x),


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SQUID devicesSQUID devices

The great sensitivity of the SQUID devices isThe great sensitivity of the SQUID devices isassociated with measuring changes in magneticassociated with measuring changes in magneticfield associated with one flux quantum.field associated with one flux quantum.

One of the discoveries associated with JosephsonOne of the discoveries associated with Josephsonjunctions was the flux is quantized in unitsjunctions was the flux is quantized in units


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Josephson JunctionJosephson Junction

A Josephson junction is a type of electronicA Josephson junction is a type of electroniccircuit capable of switching at very highcircuit capable of switching at very high

speeds when operated at temperaturesspeeds when operated at temperaturesapproaching absolute zero.approaching absolute zero.

The ability of certain materials to conductThe ability of certain materials to conductelectric current with practicallyelectric current with practically zerozeroresistanceresistance..


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Operation of junctionOperation of junction

Assume Hamiltonian for the system can be written as a sum of twoAssume Hamiltonian for the system can be written as a sum of twoHamiltoniansHamiltonians

H = H0+ HTH = H0+ HTwhere:where:

H0H0 = normal Hamiltonian for 2 isolated superconductors= normal Hamiltonian for 2 isolated superconductorsHTHT = tunneling Hamiltonian= tunneling Hamiltonian

So, this is "right" for tunneling links only.So, this is "right" for tunneling links only.


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Josephson EquationsJosephson Equations

Consider the very simpleConsider the very simpleexample of two, identicalexample of two, identicalsuperconductors separated by asuperconductors separated by athin insulator.thin insulator.

(Typically about 1nm is(Typically about 1nm issufficiently thin).sufficiently thin).

Assume junction is sufficientlyAssume junction is sufficientlylarge in thelarge in the xx andand yy direction todirection toignore edge/boundary effects,ignore edge/boundary effects,and thick enough inand thick enough in zz..

The governing equations are:The governing equations are:


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DC Josephson EffectDC Josephson Effect

No Magnetic field:No Magnetic field:

A current flows, nut noA current flows, nut novoltage drop, up untilvoltage drop, up until

the critical current.the critical current. Past the critical current,Past the critical current,

normal single electronnormal single electrontunneling is dominant.tunneling is dominant.

With magnetic field:With magnetic field:

Current is:Current is:


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With no magnetic field, static potential:With no magnetic field, static potential:

Integrating equation forIntegrating equation for ::

We can substitute into our other equation andWe can substitute into our other equation andget :get :

From this, we get a time varying current withFrom this, we get a time varying current withfrequencyfrequency

AC Josephson EffectAC Josephson Effect


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AC Josephson EffectAC Josephson Effect

With varying potential:With varying potential:

Do similar analysis as static potential case.Do similar analysis as static potential case.

It turns out that this has dc componentIt turns out that this has dc componentbut when qVo/w = n (where n= integer)but when qVo/w = n (where n= integer)

Dc current has spikes atDc current has spikes at

regularly values of Voregularly values of Vo

Total current has steps at theseTotal current has steps at these

points.points.


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If the phase takes the formIf the phase takes the form

((tt) =) =0 +0 + nntt ++ aasin(sin(tt),),

the voltage and current will bethe voltage and current will be

The DC components will then beThe DC components will then be

Inverse AC Josephson EffectInverse AC Josephson Effect


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Electron pairs coupling over range ofElectron pairs coupling over range ofhundreds of nanometers are called cooperhundreds of nanometers are called cooperpair.pair.

These coupledThese coupledelectron can take character of boson andelectron can take character of boson andcondense into ground state.condense into ground state.

Cooper pairCooper pair


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ApplicationsApplications

Magneto encephalography (MEG)Magneto encephalography (MEG)

Applications of MEG include mapping SomatosensoryApplications of MEG include mapping Somatosensoryand motor cortices.and motor cortices.

Foetal Examination: SQUID are used to measure theFoetal Examination: SQUID are used to measure theminute magnetic fields generated by babys heartminute magnetic fields generated by babys heart


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ApplicationsApplications

Further Applications of Josephson DevicesFurther Applications of Josephson Devices

Magnetic SensorsMagnetic Sensors GradiometersGradiometersOscilloscopesOscilloscopes

DecodersDecoders Analogue to Digital convertersAnalogue to Digital converters SamplersSamplers OscillatorsOscillators Microwave amplifiersMicrowave amplifiers Sensors for biomedical, scientific and defense purposesSensors for biomedical, scientific and defense purposes Digital circuit development for Integrated circuitsDigital circuit development for Integrated circuits MicroprocessorsMicroprocessors Random Access Memories (RAMRandom Access Memories (RAMs)s)


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