1. Seung Hyun Park Hyperfine Mapping of Donor Wave Function Deformations in Si:P based Quantum Devices Seung Hyun Park Advisors: Prof. Gerhard Klimeck Prof. Lloyd Hollenberg

2. Seung Hyun Park Outline 1.Single Donor Physics - Basic single donor physics - Si:P based quantum device 2. Single donor wave function engineering - Hyperfine mapping of donor electron wave function deformations

3. Seung Hyun Park Basic Donor Physics Si P+P+ e-e- Quantum Picture CB EDED Donor QD Conventional Picture CB Donor EDED E D (P) = -45.6 meV E D (As) = -54 meV Donor Physics Donors provide 3D confinement to electrons Analogous to Quantum Dots Hydrogen-like system : 1s, 2s, 2p, … Six fold degeneracy corresponding to the valley structure of the Si CB Valley-orbit interaction contributes the splitting of Donor GS in multi-valley Si

4. Seung Hyun Park Si:P based Quantum Computing (QC) QC Idea: Encode information in quantum states. Manipulate information by controlled perturbation of states. Classical Computing: |0> or |1> Quantum Computing: a|0> + b|1> Nuclear Spin Qubit Device: Tunable Spin Qubit -Single Qubit: Hyperfine Interaction A(E) -Double Qubit: Exchange Interaction J(E) B. Kane, Nature.1998.p316 Nuclear spin qubit (Kane) Donor Charge Qubit (Hollenberg) L. Hollenberg, PRB 69, 113301 (2003) Donor Qubits Benefits: Vast experience in Si:P Long spin coherence time Scalability Problems: Precise donor placement Control is sensitive

5. Seung Hyun Park Outline 1.Single Donor Physics - Basic single donor physics 2. Single donor wave function engineering - Hyperfine mapping of donor electron wave function deformations - Usefulness of measurement for hyperfine coupling probing by 29Si

6. Seung Hyun Park 29 Si (S=1/2) 28 Si (S=0)Si isotopes: Wavefunction (wf) distortion by electric field Wavefunction (wf) distortion by electric field Impurity WF at an interface A: Probing the field induced distortions of the donor wavefunction by 29 Si atom using hyperfine interaction HF application: Experimentally mapping WF deformations Q: Possible to generate an experimentally detectable spatial map of a WF in the presence of E-field? Recently Accepted in PRL 103, 106802 (Sept. 2009) S.H. Park, R. Rahman, G. Klimeck, and L. Hollenberg Hyperfine Mapping of WF

7. Seung Hyun Park Hyperfine: Fermi contact hyperfine interaction  Directly proportional to WF Hyperfine Interaction Anisotropic hyperfine interaction (AHF)  (Magnetic dipolar interaction) Information about average WF about the 29Si site AHF : Hyperfine Interaction Usefulness of the study => Possible to WF Observables in QM:

8. Seung Hyun Park Possible to measure of deformed WF Measurement of deformed WF 29 Si atom act as a probe |Ψ| 2 E=0 MV/m Byy E=0 MV/m Y (nm) 0 15 0 10 0.12 0.02 E E -0.04 0 0 15 E=20 MV/m 0 10 0.16 0.02 0.01 -0.04 X (nm) -0.02 E=40 MV/m 0 10 0.4 0 0.015 Coulomb ConfinementHybridizationInterface Confinement A (Coulomb Confinement)B (Hybridization)C (Interface Confinement) E-field E=0 MV/mE=20 MV/mE=40 MV/m R. Rahman et al. [Orbital Stark Effect Theory Paper, PRB 80 165314 (2009)]

9. Seung Hyun Park Measurement of deformed WF |Ψ| 2 E=0 MV/m Byy E=0 MV/m Y (nm) 0 15 0 10 E E 0 15 E=20 MV/m 0 10 X (nm) E=40 MV/m 0 10 Coulomb ConfinementHybridizationInterface Confinement 0 15 Mapping deformed donor electron WF 29 Si atom act as a probe

10. Seung Hyun Park Outline 1.Single Donor Physics - Basic single donor physics 2. Single donor wave function engineering - Hyperfine mapping of donor electron wave function deformations - Feasibility and usefulness of the technique - Measurement of hyperfine resonance peak for experiments

11. Seung Hyun Park GateSiO 2 Si Proposed Experiments and Shell [100] axis Proposed experiments to measure hyperfine tensor for shells around donor Measure hyperfine frequencies at shells near the donor site What is shell? * Note: a 0 =0.543095 nm Dono r

12. Seung Hyun Park Relative change of Hyperfine coupling peak for various E-field at shells on the [100] axis Shell 1Shell 2 HF AHF Points in shell 1 are equidistant Peaks are NOT distinguishable at E=0 MV/m (Degeneracy at E=0 MV/m) (+/- a 0,0,0) and (0,0,+/-a 0 ) are perpendicular to E-field -> Produce a single resonance peak Curves start splitting with E-filed [100] axis E-field on [010] direction Measure of Hyperfine Resonance Peak

13. Seung Hyun Park Usefulness of the hyperfine peak curves Shell 1 Shell 2 HF AHF Relative change of Hyperfine coupling for various E-field at nearest neighbors on [100] axis,where Fit curves to Provide Table of hyperfine Stark coefficients η 2 and η 1 Answer) Yes! Be able to expect WF deformations before measurement. Q: Can experimentalists figure out how WF is deformed before measurement? β at (0,0,4)β at (0,0,8) η2η2 η1η1 -3.81.7 η2η2 η1η1 -4.11.8

14. Seung Hyun Park Outline 1.Single Donor Physics - Basic single donor physics 2. Single donor wave function engineering - Hyperfine mapping of donor electron wave function deformations - Feasibility and usefulness of the technique - Measurement of hyperfine resonance peak for experiments - Practical issues from the perspectives of an experimentalist

15. Seung Hyun Park Issues for Experiments Relative change of Hyperfine coupling for various E-field at nearest neighbors on the [100] axis Shell 1Shell 2 HF AHF For practical implementation issues from the perspective of an experimentalist 1. Distinguishablity of each peak ? Yes! (Degeneracy at E=0 MV/m) A) Error bars for an uncertainty of 0.1 MV/m in the E-field 2. Inhomogeneity of field perturbation due to gates? Yes, but it can be resolved. A) Parallel plate capacitor like structure

16. Seung Hyun Park Summary 1.Simple Donor Physics - Basic single donor physics 2.Single donor wave function engineering - Mapping donor electron wave function deformation  Usefulness of measurement for hyperfine coupling probing by 29Si  Measurement of hyperfine resonance peak at points grouped into shell  Practical implementation issues from the perspectives of an experimentalist Recently Accepted in PRL 103, 106802 (Sept. 2009) S.H. Park, R. Rahman, G. Klimeck, and L. Hollenberg