below millikelvin kai

8/6/2019 Below Millikelvin Kai

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HeadingHeading beyondbeyond thethe MillikelvinMillikelvin

SomeSome IssuesIssues of ultraof ultra lowlowtemperaturetemperature (ULT)(ULT) physicsphysics

Kai SchwarzwlderInstitut fr PhysikUniversitt BaselFebruary 5th 2007


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2Heading beyond the Millikelvin

OutlineOutline Motivation: AMotivation: A FerromagneticFerromagnetic PhasePhaseTransitionTransition

AchievingAchievinglowlowtemperaturestemperatures

HistoricalHistorical overwievoverwiev,, temperaturestemperatures reachedreached FromFrom RT toRT to thethe MillikelvinMillikelvin: Helium: Helium

BeyondBeyond thethe MillikelvinMillikelvin:: NuclearNuclear DemagnetisationDemagnetisation

ThermometryThermometry FromFrom RT toRT to thethe MillikelvinMillikelvin

ThermometryThermometrybeyondbeyond thethe MillikelvinMillikelvin HeatHeat Transport andTransport and CouplingCoupling

MetalMetal--metalmetal interfaceinterface

HeHe--SolidSolid interfaceinterface

HeatHeat LoadsLoads

PracticalPractical ConsiderationsConsiderations onon BuildingBuildingCoolingCoolingSetSet upsups Materials: Advantages andMaterials: Advantages and DisadvantagesDisadvantages

IsolationIsolation

RadiationRadiation ShieldingShielding


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AAFerromagneticFerromagnetic PhasePhaseTransitionTransition

Motivation


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State ofState ofSpinSpin--QuBitsQuBits onon DotsDots SpinSpin coherencecoherence time in GaAs:time in GaAs:

MethodsMethods toto extendextend Spin echoSpin echo techniquestechniques

ProjectionProjection ofofnuclearnuclear spinspin statesstates

Polarisation ofPolarisation ofnuclearnuclear spinsspins (so far 60%(so far 60% bybyopt.opt. PumpingPumping))

=>=> ferromagneticferromagnetic phasephase transitiontransition

6060 yearsyears agoago, Fr, Frhlich andhlich and NabarroNabarro:: predictedpredicted forfor 3D metals:3D metals:

TypicalTypical metal:metal:

2DEG in GaAs:2DEG in GaAs:

kBTC A2

8EF

TC . K

TC mK

t = 100ns (bulk) . . .s (dots)

t

Motivation


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NonNon--interactinginteracting TTCC

KondoKondo latticelattice HamiltonianHamiltonian

For 2DFor 2D--metal ametal a meanmean fieldfield theorietheorie predictspredicts inin

nonnon--interctinginterctingcasecase::

H = H0 +12

NPj=1

Ajcj~cj

~Ij

kBTC = I(I + 1)A2

12EF

= TC 1K for GaAs

Motivation


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InteractingInteracting TTCC ThermodynamicThermodynamic examinationexamination givesgives::

WithWith thethe BetheBethe--SalpeterSalpeter eqeq.. forfor and aand a shortshort--rangedranged interactioninteraction potentialpotential

oneone getsgets

ForFor typicaltypical 2DEG2DEG parametersparameters.. LFFA (LFFA (locallocal fieldfield factorfactor approxapprox.).) yieldsyields

TC =A2I2kB

q3Ins

s(q)q

q0s

TC 25K

TC =IA

2kB

r3I

A

( 1)2

g0V(a) 25mK (rs 5)

g0 1

2(1 + X1rS + X2r

2S + X3r

3S)e

X4rS rS =ECoul

Ekin

Motivation


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Experiment to TestExperiment to Test PorarisedPorarised spinsspins createcreate BB--fieldfield ofoffewfewTeslaTesla

=>=> ZeemanZeeman--splittingsplittingin 2DEGin 2DEG

=>Transport=>Transport measurementmeasurement in QPCin QPC

QuestionsQuestions:: DirectionDirection ofofpolarisationpolarisation

BB--fieldfield dependencedependence

MeanMean freefree pathpath,, scatteringscattering,, impuritiesimpurities

Motivation

2DEG


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HistoricalHistorical OverviewOverview

Liquid Helium (Liquid Helium (KammerlingKammerling--OnesOnes))19081908

DRP1250 KDRP1250 Klteerzeugungsmaschinelteerzeugungsmaschine (Linde)(Linde)18771877

Discovery of absoluteDiscovery of absolute zerozero (Thompson(Thompson))18481848

LiquificationLiquification ofofvariousvarious gasesgases19th19th centcent..

artificialartificial iceice bybyevaporatingevaporating((CullenCullen))17551755

22KK5050KK19561956NuclearNuclear magneticmagneticKKIIIIII

1mK1mK3mK3mK19341934ElectronicElectronic magneticmagnetic

2mK2mK3mK3mK19651965PomeranchukPomeranchuk

2mK2mK10mK10mK19651965DilutionDilutionmKmKIIII

0.25K0.25K0.3K0.3K19501950HeHe--33 evaporationevaporation

0.7K0.7K1.3K1.3K19081908HeHe--44 evaporationevaporationKKII

TTrecrecTTtyptypSinceSinceRefrigarationRefrigaration TechniqueTechniqueRangeRange

Achieving Low Temperatures


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PumpingPumping on LHeon LHe3/43/4

with

Clausius-Clapeyron-Equation

Pvap e

LRT

Sgas Sliq =LT

Vmol,gas Vmol,liqVgasP = RT

L 6= L(T)

The vapour pressure is

Resulting cooling power

Q = nL LPvap e

1

T

PTvap =

SgasSliqVmol,gasVmol,liq

From RT to the Millikelvin


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PrinciplesPrinciples of Heof He33

/He/He44

DilutionDilution



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AADilutionDilution RefridgeratorRefridgeratorMNK 126MNK 126--700700



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NuclearNuclear DemagnetisationDemagnetisation StepStep 1:1:

isothermalisothermal increaseincrease of Bof B

Step2:Step2:adiabaticadiabatic decreasedecrease of Bof B

EntropyEntropy::

adiabaticadiabatic//isentropicisentropic stepstep::

includingincludinginternalinternal fieldfield::

Cu:Cu:

Achieving Temperatures beyond the Millikelvin

b = 0.36mT

BiTi

=BfTf

Tf =TiBi

Bf

Tf =TiBi

qB2f + b

2

S = R ln(2I + 1) 2 BT2


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NuclearNuclear DemagnetisationDemagnetisation Set upSet up



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EquilibrationEquilibration SpinSpin--latticelattice relaxationrelaxation:: mutualmutual spinspin--flipflip (e(e--n)n)

KorringaKorringa lawlaw

Pt:Pt:

DifferentDifferent heatheat capacitancescapacitances::

SpinSpin--spinspin relaxationrelaxation:: mutualmutual spinspin--flipflip (n(n--n)n)

MuchMuch fasterfaster thanthan spinspin--latticelattice relaxationrelaxation


= 1T

b1 = 1

CeCe+Cn

Ce


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HeatHeat AbsorptionAbsorption Rate (Bloch)Rate (Bloch) equationsequations

andand nuclearnuclear heatheat capacitycapacity

yieldyield::


Te = Q+nB2nB2 Tn

dMdt

= 11

(MM0)

Cn =B2

T2n

QnB2

& ,


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GasGas PressurePressure ThermometryThermometry General gasGeneral gas thermometrythermometry

Ideal gasIdeal gas lawlaw

DeadDead volumesvolumes

Absorption/Absorption/ desorptiondesorption

HeHevapourvapour pressurepressure CallibrationCallibration ofofRR--thermometersthermometers at 0.5Kat 0.5K--4.2K4.2K

P V = nRT

Thermometry from RT to the Millikelvin


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ResistanceResistance ThermometryThermometry II OverallOverall problemsproblems::

ThermalThermal conductivityconductivity

ThermalThermal contactcontact

selfself--heatingheating

RFRF absorptionabsorption

Metals:Metals: Pt:Pt:

LinearLinear

DuctileDuctile

Down to 10KDown to 10K KondoKondo--alloysalloys ((e.ge.g.. RhFeRhFe))

KonoKono effecteffect



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ResistanceResistance ThermometryThermometry IIII SemiconductorsSemiconductors

EmpiricalEmpirical ResistanceResistance tootoo highhigh forfor ULTULT

WorkhorseWorkhorse 10mK10mK10K10K

Ge:Ge: Doping:Doping:As(nAs(n),), Ga(pGa(p))

0.3K0.3K40K (30mK40K (30mKspecialspecial dopingdoping)) StabilityStability

MagnetoresistanceMagnetoresistance

RuORuO22::

MetalMetal

--ceramicceramic

SmallSmall sizesize

ReproducibleReproducible

LowLowcostcost

EasyEasytoto overheatoverheat


R(T) = eE

2kBT

R(T) = R0e( T0T )

0.345


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MiscellaneousMiscellaneous ThermometryThermometry NoiseNoise thermometrythermometry::

NyquistNyquist lawlaw

SmallSmallvoltagesvoltages =>=> amplificationamplification => SQUIDS=> SQUIDS

ThermoelectricityThermoelectricity ThermoelectricThermoelectric powerpower

DielectricDielectric--constantconstant thermometrythermometry

CapacitanceCapacitance measurementmeasurement


S = UT

U2 = 4kBRT


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NMRNMR--ThermometryThermometry OnlyOnlyreliablereliable methodmethod forfor KK--regimeregime

TippingTippingangleangle

TemperatureTemperature dependencedependence

FitFit

Thermometry beyond the Millikelvin

= B1Bz

U = Mn sin 1Tn

Mxy(t) = Mne

t

2


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NMRNMR--ThermometryThermometry ee--temperaturetemperature bybymeasuringmeasuring andand applyingapplying

KorringaKorringa lawlaw::9090 -- spinspin--latticelattice--relaxationrelaxation -- check pulsecheck pulse

Problems:Problems: TippingTippingangleangle reducesreduces nuclearnuclear magnetisationmagnetisation

RFRF fieldfield inducesinduces eddyeddycurrentcurrent

Thermometry beyond the Millikelvin

1

Mz(t) = Mn(0)(1 e

t

1 )


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MetalMetal--metalmetal InterfaceInterface KapitzaKapitza resistanceresistance

MethodesMethodes toto decreasedecrease RRK,metK,met--metmet goldgold--platedplated surfacesurface

pressurepressure => larger=> larger contactcontact areaarea,, latticelattice bentbent

coldcold weldweld =>=> riprip offoffoxideoxide layerlayer

ManyManysolderssolders becomebecome superconductingsuperconducting:: SoftSoft solderssolders: T: Tcc~ a~ a fewfewKK

HardHard solderssolders::TTcc~a~a fewfewten mKten mK

ApplyApplyB toB to breakbreaksuperconductivitysuperconductivity(a(a fewfewmT)mT)

Heat Transport and Coupling

T = RKQ

A 1


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HeHe--solid Interfacesolid InterfaceTotalTotal reflectionreflection

SnellSnellss lawlaw

withwith

thethe criticalcritical angleangle isis 33

AcousticAcoustic mismatchmismatch

AcousticAcoustic transmissiontransmission andand reflectionreflection areare givengiven byby


Thermal isolation !

sin lsin s

= clcs

cHe = 200ms

cmet = 5000ms

tac =4ZlZs

(Zl+Zs)2 2 103

rac =(ZlZs)

2

(Zl+Zs)2

trfr 103

t = trfr tac 105


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HeHe--solid Interfacesolid Interface


NuclearNuclear spinsspins ofof33

HeHe couplecouple toto ee--spinsspins of metalof metal33HeHe phononsphonons couplecouple to softto softvibrationalvibrational modesmodes

>10mK>10mK

ExplainedExplained bybyacousticacoustic mismatchmismatch20mK20mK100mK100mK

NotNot yetyet understoodunderstood,,

order largerorder larger thanthan predictedpredicted bybyacousticacoustic mismatchmismatch

>1K>1K

RK 1

AT3

RK 1T2

RK 1T

Rliq Rsol

Improve contact by use of sintered metals!


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HeatHeat LoadsLoads ExternalExternal LeaksLeaks

ThermalThermal conductionconduction RadioactiveRadioactive backgroundbackground radiationradiation

VibrationsVibrations

EddyEddycurrentcurrent RFRF

InternalInternal leaksleaks HeatHeat buffersbuffers timetime depentdepent heatheat leakleak

RadioactiveRadioactive isotopesisotopes inin constructionconstruction materialmaterial


~0.5pW/cm3 forCu(1)


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Materials (Materials (forfor ND)ND)

NuclearNuclear spinspin

MetalMetal

NotNot superconductingsuperconducting

NoNo magneticalmagnetical orderorder NoNo quadrupolquadrupol momentmoment

Practical Considerations on Building Cooling Set ups

b

1

1

b


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Materials (Materials (forfor ND)ND)



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IsolationIsolation RadiationRadiation shieldingshielding

ThermalThermal isolationisolation GoodGoodvacuumvacuum

SuperconductersSuperconducters

VibrationVibration dampingdamping SandSand boxesboxes

FloatingFloatingtablestables

HeavyHeavyblocksblocks



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LiteratureLiterature(1)(1) G.R.G.R. PickettPickett,,MicrokelvinMicrokelvinphysicsphysics, Rep. Prog. Phys. 51, Rep. Prog. Phys. 51

(1988) 1295(1988) 1295--13401340(2)(2) P. Simon, D.P. Simon, D. LossLoss,,NuclearNuclearspinspinferromagneticferromagneticphasephase

transitiontransitionin anin aninteractinginteracting2D2D electronelectrongasgas,, CondCond--matmat/0611292 v2 12 Nov 2006/0611292 v2 12 Nov 2006

(3)(3) F.F. PobellPobell,,Matter andMatter andMethodsMethodsatatLowLowTemperaturesTemperatures22ndnd

Ed., Springer1996Ed., Springer1996

(4)(4) G.G. FrossatiFrossati,, ExperimentalExperimentalTechniquesTechniques::MethodsMethodsforforCoolingCoolingBelowBelow300mK300mK, J., J. LowLowTempTemp. Phys. 87 (1992) 595. Phys. 87 (1992) 595--633633


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Vielen DankVielen Dank

ffrrIhre Aufmerksamkeit !Ihre Aufmerksamkeit !

below millikelvin kai

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