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Development of a Silicon Semiconductor Quantum Dot Qubit with Dispersive Microwave Readout by Edward Trowbridge Henry

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Development of a Silicon Semiconductor Quantum Dot Qubit with Dispersive Microwave Readout by Edward Trowbridge Henry Development of a Silicon Semiconductor Quantum Dot Qubit with Dispersive Microwave Readout by Edward Trowbridge Henry A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor I. Siddiqi, Chair Professor Hartmut Haeffner Professor K. Whaley Fall 2013 Development of a Silicon Semiconductor Quantum Dot Qubit with Dispersive Microwave Readout Copyright 2013 by Edward Trowbridge Henry 1 Abstract Development of a Silicon Semiconductor Quantum Dot Qubit with Dispersive Microwave Readout by Edward Trowbridge Henry Doctor of Philosophy in Physics University of California, Berkeley Professor I. Siddiqi, Chair Semiconductor quantum dots in silicon demonstrate exceptionally long spin lifetimes as qubits and are therefore promising candidates for quantum information processing. How- ever, control and readout techniques for these devices have thus far employed low frequency electrons, in contrast to high speed temperature readout techniques used in other qubit ar- chitectures, and coupling between multiple quantum dot qubits has not been satisfactorily addressed. This dissertation presents the design and characterization of a semiconductor charge qubit based on double quantum dot in silicon with an integrated microwave res- onator for control and readout. The 6 GHz resonator is designed to achieve strong coupling with the quantum dot qubit, allowing the use of circuit QED control and readout techniques which have not previously been applicable to semiconductor qubits. To achieve this cou- pling, this document demonstrates successful operation of a novel silicon double quantum dot design with a single active metallic layer and a coplanar stripline resonator with a bias tee for dc excitation. Experiments presented here demonstrate quantum localization and measurement of both electrons on the quantum dot and photons in the resonator. Further, it is shown that the resonator-qubit coupling in these devices is sufficient to reach the strong coupling regime of circuit QED. The details of a measurement setup capable of performing simultaneous low noise measurements of the resonator and quantum dot structure are also presented here. The ultimate aim of this research is to integrate the long coherence times observed in electron spins in silicon with the sophisticated readout architectures available in circuit QED based quantum information systems. This would allow superconducting qubits to be coupled directly to semiconductor qubits to create hybrid quantum systems with separate quantum memory and processing components. i For my mother. ii Contents List of Figures vi I Introduction 1 0.1StructureofthisThesis............................. 2 1 Background 3 1.1 Reduced Dimensional Conductivity in Semiconductors ............ 3 1.1.1 2-DChargeLocalizationandtheExtremeQuantumLimit...... 4 1.1.2 1-D Conductance Constrictions and Quantum Point Contacts .... 5 1.1.3 QuantumDots.............................. 6 1.2ModelingQuantumDotBehavior........................ 7 1.2.1 TheConstantInteractionApproximation............... 8 1.2.2 ACircuitModelofaDoubleQuantumDot.............. 9 1.2.3 Stability Diagrams ............................ 9 1.2.4 HamiltonianofaDoubleQuantumDot................ 10 1.3 Overview of Quantum Dot Research ...................... 12 1.3.1 2DEGHeterostructuresUsedforQuantumDots........... 12 1.3.2 ChargeSensing.............................. 14 1.3.3 Microwaves and Photon Assisted Tunneling .............. 15 1.4QuantumDotsasQubits............................ 16 1.4.1 ChargeandSpinQubits......................... 16 1.4.2 DecoherenceMechanisms........................ 17 1.4.3 Existing Semiconductor Qubit Readout and Control Techniques . 18 1.5CircuitQED................................... 20 1.5.1 Fast,QNDreadout............................ 22 1.5.2 Benchmarks from the Superconducting Qubit Community...... 22 1.5.3 InterfacewithotherQubitArchitectures................ 23 1.6Quantumdotscoupledtoresonators...................... 23 2 Overview of our experiment 25 2.1CircuitQEDReadoutofaSiDoubleQuantumDotChargeQubit..... 25 2.2 Confining Photons: A 6 GHz Coplanar Stripline Resonator . ........ 27 2.3 Confining Electrons: A Novel Accumulation Mode Si Double Quantum Dot 28 iii 2.4CouplingPhotonstotheElectricDipoleMomentoftheDQD........ 30 2.5PotentialforFutureCouplingtoElectronSpin................ 33 II A Novel Quantum Dot Design 35 3 Silicon Double Quantum Dot Design and Simulation 36 3.1DotDimensions.................................. 37 3.2UCLADotLayout................................ 38 3.3BerkeleyDotLayout............................... 39 3.4CalculatingthePotentialLandscape...................... 40 3.5 Simulations of Ground and Excited State Wavefunctions . ........ 41 4 Silicon Double Quantum Dot Low Frequency Measurement and Charac- terization 43 4.1SingleDotTransport-CoulombDiamonds.................. 43 4.2TransportMeasurements:HoneycombsandDiamonds............ 45 4.2.1 UCLAdot................................. 46 4.2.2 BerkeleyDot............................... 48 4.3NarrowConstriction/ExtraDotIssue..................... 49 4.4QuantumPointContactMeasurements..................... 49 III Integrated Microwave Resonator for cQED Readout 53 5 Resonator design 54 5.1ResonatorGeometry............................... 54 5.2ModelingtheResonator............................. 55 5.3ResonatorDesignParameters.......................... 56 5.4RFshortandbiastee.............................. 57 5.5CouplingCapacitors............................... 58 5.6SourcesofLoss.................................. 59 5.6.1 Oxide layers ................................ 59 5.6.2 Ohmiccontacts.............................. 61 5.6.3 2DEG................................... 61 6 Resonator Measurement and Fitting 62 6.1ResonatorPerformanceWithoutCoupledQuantumDotStructure..... 62 6.2ResonatorPerformancewithCoupledQuantumDotStructure....... 65 6.3FittingResonatorData............................. 67 6.4ResonatorResponseto2DEGCoupling.................... 69 6.4.1 DipolePolarization............................ 69 6.4.2 Charge Trap Submersion ........................ 69 6.4.3 2DEGresistiveloss............................ 71 6.4.4 Screening................................. 71 iv 6.4.5 Inter-Subbandtransitions........................ 71 IV Technical Details of Fabrication and Measurement 73 7 Measurement Setup 74 7.1SampleConnectionandMounting....................... 74 7.1.1 Fridge-agnosticSampleHolder..................... 75 7.1.2 Superconducting Sample box with Controlled Microwave Environment 78 7.1.3 4KLHeDipProbeforDCSampleTriage............... 80 7.2 Low Frequency Conductance Measurements .................. 81 7.2.1 WiringandCrosstalk.......................... 81 7.2.2 Filtering of DC Control Signals ..................... 83 7.2.3 Conductance Measurement Setup .................... 83 7.2.4 VoltageAddition............................. 85 7.2.5 Grounding ................................ 89 7.3QuantumDotEvaluationandCharacterizationProcedure.......... 90 7.3.1 RoomTemperatureTests........................ 90 7.3.2 4.2KTests................................. 90 7.3.3 ColdTests................................. 91 7.4RFReadoutandControlElectronics...................... 94 7.4.1 180DegreeHybrid............................ 94 7.4.2 Amplification, Attenuation, and Filtering ............... 97 7.4.3 Spectroscopy............................... 98 7.4.4 TimeDomainManipulationandHeterodyneDetection........ 98 8 Fabrication Details 100 8.1 Fabrication Process Overview .......................... 100 8.2 Fabrication Process for Berkeley Quantum Dot Devices ........... 100 8.2.1 OhmicContactPreparation....................... 101 8.2.2 Gate Oxidation .............................. 101 8.2.3 Metallayer1:OhmicContactPads.................. 101 8.2.4 Metallayer2:Quantumdotandresonator.............. 102 8.2.5 Metallayer3:ShuntCapacitor..................... 103 8.3FailureModes................................... 103 8.3.1 Lithography&Liftoff.......................... 103 8.3.2 ElectrostaticDischarge.......................... 103 8.3.3 Oxide Shorts ............................... 104 8.4EvaluatingDevicePerformancethroughImaging............... 104 9 Conclusion and Future Outlook 108 9.1NovelDesignforHybridQuantumSystems.................. 108 9.2ChargeTrapping................................. 108 9.3ResonatorCapableofStrongCoupling..................... 108 9.4 Future Research Directions ........................... 109 v 9.4.1 ObserveRabiSplittinginaChargeQubit............... 109 9.4.2 DecreaseResonatorLossforImprovedReadout............ 109 9.4.3 DepositNanomagnettoCoupletoSpinDegreeofFreedom..... 109 Bibliography 110 vi List of Figures 1.1 Confinement of electrons at the Si/SiO2 interface. Top: conduction band energy through the semiconductor heterostructure, as it crosses the Fermi level at the interface. The fermi level of silicon is raised by eVg by an exter- nally applied electric field. Bottom: the first few energy levels of electrons in the 2DEG conduction band ........................... 4 1.2 Schematic showing transport through a double quantum dot. Electric field lines are shown to emphasize the effect of metallic gates on quantum dot structure. Red regions are metal, light blue regions are insulating oxide, and grey regions are semiconductor. Green regions are semiconductor in which conductance has been induced by externally applied field from the metal gates.
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