Hyperfine Mapping of Donor Wave Function Deformations in Si:P based Quantum Devices

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

2. Outline • 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. Quantum Picture Conventional Picture Si Si Si CB CB e- ED Si P+ Si ED Donor Si Si Si ED(P) = -45.6 meV ED(As) = -54 meV Basic Donor Physics Donor QD • 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. 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 (Kane) B. Kane, Nature.1998.p316 • Donor Qubits • Benefits: • Vast experience in Si:P • Long spin coherence time • Scalability • Problems: • Precise donor placement • Control is sensitive Donor Charge Qubit (Hollenberg) • Nuclear Spin Qubit Device: • Tunable Spin Qubit • Single Qubit: Hyperfine Interaction A(E) • Double Qubit: Exchange Interaction J(E) L. Hollenberg, PRB 69, 113301 (2003)

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

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

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

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

10. Outline • 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. Proposed Experiments and Shell Proposed experiments to measure hyperfine tensor for shells around donor [100] axis What is shell? Si Gate SiO2 Donor Measure hyperfine frequencies at shells near the donor site * Note: a0=0.543095 nm

12. Measure of Hyperfine Resonance Peak [100] axis E-field on [010] direction Shell 1 Shell 2 HF AHF • Points in shell 1 are equidistant • Peaks are NOT distinguishable at E=0 MV/m • (Degeneracy at E=0 MV/m) • (+/- a0,0,0) and (0,0,+/-a0) are perpendicular • to E-field -> Produce a single resonance peak • Curves start splitting with E-filed Relative change of Hyperfine coupling peak for various E-field at shells on the [100] axis

13. Usefulness of the hyperfine peak curves Q: Can experimentalists figure out how WF is deformed before measurement? Shell 2 Shell 1 Fit curves to HF ,where Provide Table of hyperfine Stark coefficients η2 and η1 β at (0,0,4) β at (0,0,8) AHF η2 η1 η2 η1 -3.8 1.7 -4.1 1.8 Answer) Yes! Be able to expect WF deformations before measurement. Relative change of Hyperfine coupling for various E-field at nearest neighbors on [100] axis

14. Outline • 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. Issues for Experiments Shell 1 Shell 2 HF 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 AHF Relative change of Hyperfine coupling for various E-field at nearest neighbors on the [100] axis

16. Summary • Simple Donor Physics • - Basic single donor physics • 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