Quantum and thermal phase escape in extended Josephson systems [Elektronische Ressource] / vorgelegt von Alexander Kemp

QuantumandThermalPhaseEscapeinExtendedJosephsonSystemsDenNaturwissenschaftlichenFakultaten¨ derFriedrich Alexander Universit at¨ Erlangen N urnber¨ gzurErlangungdesDoktorgradesvorgelegtvonAlexanderKempausMontreal(Kanada)AlsDissertationgenehmigtvondenNaturwissenschaftlichenFakultaten¨ derUniversitat¨ Erlangen N urnber¨ gTagdermundlichen¨ Prufung:¨ 12.7.2006VorsitzenderderPromotionskommission: Prof.Dr.D. P.H ader¨Erstberichterstatter: Prof.Dr.A.V.UstinovZweitberichterstatter: Prof.Dr.N.PederseniiiContentsPreface vii1 IntroductionandTheory 11.1 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 SmallJosephsonJunctions . . . . . . . . . . . . . . . . . . . . 41.3 QuasiparticlesandtheGap . . . . . . . . . . . . . . . . . . . . 61.4 TheRCSJModel . . . . . . . . . . . . . . . . . . . . . . . . . 81.5 TheTwo DimensionalSine GordonEquation . . . . . . . . . . 101.6 LongJosephsonJunctions . . . . . . . . . . . . . . . . . . . . 121.6.1 SolitonSolutions . . . . . . . . . . . . . . . . . . . . . 151.6.2 SmallWaveExcitations . . . . . . . . . . . . . . . . . 151.6.3 IdleRegionEffects . . . . . . . . . . . . . . . . . . . . 171.7 AnnularJunctions . . . . . . . . . . . . . . . . . . . . . . . . . 181.7.1 PerturbationTheory: VortexEffectivePotentials . . . . 221.7.2 VortexDynamics . . . . . . . . . . . . . . . . . . . . . 232 ExperimentalTechniqueanddataevaluation 272.1 MeasurementScheme . . . . . . . . . . . . . . . . . . . . . . .
Publié le : lundi 1 janvier 2007
Lecture(s) : 18
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Source : WWW.OPUS.UB.UNI-ERLANGEN.DE/OPUS/VOLLTEXTE/2007/485/PDF/MAIN.PDF
Nombre de pages : 170
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QuantumandThermalPhase
EscapeinExtendedJosephson
Systems
DenNaturwissenschaftlichenFakultaten¨ der
Friedrich Alexander Universit at¨ Erlangen N urnber¨ g
zur
ErlangungdesDoktorgrades
vorgelegtvon
AlexanderKemp
ausMontreal(Kanada)AlsDissertationgenehmigtvondenNaturwissenschaftlichenFakultaten¨ der
Universitat¨ Erlangen N urnber¨ g
Tagdermundlichen¨ Prufung:¨ 12.7.2006
VorsitzenderderPromotionskommission: Prof.Dr.D. P.H ader¨
Erstberichterstatter: Prof.Dr.A.V.Ustinov
Zweitberichterstatter: Prof.Dr.N.PederseniiiContents
Preface vii
1 IntroductionandTheory 1
1.1 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 SmallJosephsonJunctions . . . . . . . . . . . . . . . . . . . . 4
1.3 QuasiparticlesandtheGap . . . . . . . . . . . . . . . . . . . . 6
1.4 TheRCSJModel . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 TheTwo DimensionalSine GordonEquation . . . . . . . . . . 10
1.6 LongJosephsonJunctions . . . . . . . . . . . . . . . . . . . . 12
1.6.1 SolitonSolutions . . . . . . . . . . . . . . . . . . . . . 15
1.6.2 SmallWaveExcitations . . . . . . . . . . . . . . . . . 15
1.6.3 IdleRegionEffects . . . . . . . . . . . . . . . . . . . . 17
1.7 AnnularJunctions . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.7.1 PerturbationTheory: VortexEffectivePotentials . . . . 22
1.7.2 VortexDynamics . . . . . . . . . . . . . . . . . . . . . 23
2 ExperimentalTechniqueanddataevaluation 27
2.1 MeasurementScheme . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 VortexInjection . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3 EscapeFieldDistributions . . . . . . . . . . . . . . . . . . . . 32
2.4 ThermalEscapeinaWashboardPotential . . . . . . . . . . . . 37
2.5 DampingRegimes . . . . . . . . . . . . . . . . . . . . . . . . 38
2.6 ParameterEstimation . . . . . . . . . . . . . . . . . . . . . . . 41
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3 MetastableVortexStates 45
3.1 MetastableVortexStates . . . . . . . . . . . . . . . . . . . . . 45
iii3.2 SpectroscopyonanAnnularJunction . . . . . . . . . . . . . . 47
3.3 OnClassicalResonancesandQuantumTransitions . . . . . . . 50
3.4 ThermalActivationofaVortex . . . . . . . . . . . . . . . . . . 54
3.5 FromtheLowDampingRegimetotheQuantumRegime . . . . 57
3.6 CrossovertotheSmallJunctionCase. . . . . . . . . . . . . . . 61
3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 PhaseEscapeInExtendedSystems 71
4.1 HarmonicApproximation . . . . . . . . . . . . . . . . . . . . . 72
4.2 VAVDissociation . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3 RFInducedDecay . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4 ThermalActivationandQuantumRegime . . . . . . . . . . . . 82
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Double WellPotentials 87
5.1 ParasiticPotentials . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2 LithographicMicroshorts . . . . . . . . . . . . . . . . . . . . . 95
5.2.1 BistableStatesinMicroshortJunctions . . . . . . . . . 99
5.2.2 Readout . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2.3 StatePreparation . . . . . . . . . . . . . . . . . . . . . 104
5.2.4 ExperimentalTestofStatePreparationandReadout . . 104
5.2.5 SymmetryofthePatterns . . . . . . . . . . . . . . . . . 108
5.2.6 ThermalActivationoveraSuppressedBarrier . . . . . . 109
5.2.7 SecondOrderPerturbation . . . . . . . . . . . . . . . . 114
5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6 Discussion,conclusionsandoutlook 119
Summary 121
Zusammenfassung 123
A Biasing 125
A.1 BiasingScheme . . . . . . . . . . . . . . . . . . . . . . . . . . 126
A.2 PowerDissipationoftheBiasingSystem . . . . . . . . . . . . . 127
B Electronics 131
B.1 ComputerControl . . . . . . . . . . . . . . . . . . . . . . . . . 131
B.2 NoiseEstimationoftheRamp TypeExperiments . . . . . . . . 132
ivC TableofSamplesandMeasurements 137
C.1 SamplesUsed . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
C.2 TableofMeasurements . . . . . . . . . . . . . . . . . . . . . . 137
D Tableofvariables 141
Bibliography 147
Acknowledgements 155
CurriculumVitae 159
vviPreface
SincethedescriptionofthephenomenaoncoupledsuperconductorsbyJoseph
son[1],thedynamicsofthequantummechanicalphaseacrossaJosephsonjunc
tion(JJ)hasbeenstudiedextensively. Awellknownapplicationoftheseeffects
is the superconducting quantum interferometer, which is a sensitive measure
ment device. The JJ in a SQUID is completely described by this single macro
scopicvariable,whichbehavesasasingledegreeoffreedom. Intheresistively
capacitively shunted junction model, a resistance acts as a damping element on
this degree of freedom, while the capacitive part represents an effective mass.
Because of the nonlinearity of the Josephson element, metastable states can ex
ist. Fluctuations by thermal noise current in the resistive state of the junction
weredescribedbyDahmetal. [2]Duetothisnoisecurrentmetastablestatesina
smalljunctionhaveafinitelifetime,examinedbyFultonetal. [3]andKukijarvi¨
et al. [4]. Recently, Josephson junctions received attention in the context of
quantumcomputation. Thebasisforthiswassetlongago[5,6,7]byobserving
macroscopicquantumbehaviourofthesuperconductingphasedifference.
In long Josephson junctions the soliton solution of the governing sine
Gordon equation corresponds to a circulating vortex of supercurrent. In this
workthermal,quantumlimitedandRFinducedactivationfrommetastablestates
inlong,annularJosephsonjunctionsarepresented. Itisacontinuationofthere
searchonfluctuationinducedactivationinannularJosephsonjunctionsdoneby
A. Wallraff [8] which resulted in the experimental observation of macroscopic
quantumtunnelingofavortexinsub μmjunctions,describedinRef.[9]. Atthis
stage,aclassicaltwo statesystem,formedbyheart shapedJosephsonjunctions
was demonstrated [10, 11, 12], the use of which as a quantum bit was proposed
in Ref. [13]. Hence another direction of research was open at the beginning of
theworkonthisthesis.
Quantum tunneling in reproducibleμm scale annular junctions is observed,
similartotheresultsgiveninRef.[9]. Thesamplesusedwereoflowcriticalcur-
viirent density, and therefore physically shorter, and may behave as short Joseph
sonjunctions. Themeasurementspresentedhereanswerthefollowingquestion:
May the phase variable in a long Josephson junction tunnel homogeneously,
evenifitistwistedbyatrappedquantumofmagneticflux? Dependingontem
peratureandmagneticfieldarangeofbehaviours,likethermalvortexactivation
[14],thermalsmalljunctionactivation[3],andquantumtunneling[5,6,7,9]is
observed. I interpret the results using a newly developed approximation of the
phase distribution in the junction, derived from the one given in Ref. [15], but
adapted to a single flux quantum trapped in a short annular Josephson junction
limit. FromtheactivatedescapeofthephaseIproceedtoanothertypeofactiva
tionfromametastablestate. Thevortex antivortexnucleationprocess,discussed
by Fistul et al. [16], is another approximation of what is described for a short
junctioninRef.[15].
Of major importance for applications, the parasitic barrier created by the
two dimensional design of the heart shaped Josephson junctions was to be de
termined by the means of thermal activation between bistable states. Only the
calculationsgiveninRef.[17]explainthefailuretoobserveanythermalactiva
tion. Achangedvortexrestmass,aparasiticeffectatstronglycurvedregionsin
thesamplesused,prohibitedanysystematicobservationofthermalactivationin
heart shapedJosephsonjunctions.
Although this leaves some perspective for an enhanced design of heart
shapedJosephsonjunctions,anotherbistablesystem,namelyamicroshortjunc
tion, seems more attractive. This kind of junction was examined before theo
retically in Ref. [18]. The realization was prevented by the trilayer technology
generallyusedfortheproductionofthejunctions,whichallowsforonlyasingle
critical current density. As a conclusion and a way ahead, we propose a novel
production technique for microshorts, namely a width modulated junction. The
use of this mechanism for potential engineering was discussed by Goldobin et
al. [19]. The concept of this approach is that a small longitudinal region of the
junctionrepelsthevortexbecauseofitsenhancedwidth. Theadvantagesofthis
approach are, besides the simplicity of the concept, the steepness of the poten
tialsgenerated. Furthermore,itdoesnotrequiresub μmsampleproduction,but
onlysub μmlevelsizecontrol,whichiswithinthelimitsofvisiblelightphoto
lithography. Results, including state preparation and readout protocol, will be
published elsewhere in Ref. [20] and form the last experimental chapter of this
thesis. MeasurementsdoneincollaborationwithA.Priceleadtotheobservation
of quantum tunneling of a vortex through a barrier in a photo lithographically
2kAproduced1 /cm sample,whichwillbepublishedelsewhere[21].
viii

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