hyperfine mapping of donor wave function deformations in si:p based quantum devices
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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
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
Seung Hyun Park
Basic Donor Physics
Si
Si
Si
P+
Si
Si
Si
Si
Si
e-
Quantum Picture
CB
ED
Donor QD
Conventional Picture
CB
DonorED
ED(P) = -45.6 meV
ED(As) = -54 meVDonor 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
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 QubitsBenefits: • Vast experience in Si:P• Long spin coherence time• Scalability
Problems:• Precise donor placement• Control is sensitive
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
Seung Hyun Park
29Si (S=1/2)28Si (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
Seung Hyun Park
Aij =γ IγSh2 (
8π3
Ψ(0) 2 + Ψ3rirj −r2δ ij
r5 Ψ )
A(,r0) C | Ψ(,r0) |2Hyperfine:
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
B(,r) C Ψ | B | Ψ AHF :
Hyperfine Interaction
Usefulness of the study
=> Possible to WFObservables in QM: E H
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
0.02E
E-0.04
0
015
E=20 MV/m
E=20 MV/m
0 10
0.16
0.02
0.01
-0.04
X (nm)
-0.02
E=40 MV/m
E=40 MV/m
0 10
0.4
0
0.015
Coulomb Confinement Hybridization Interface Confinement
A (Coulomb Confinement) B (Hybridization) 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)]
Seung Hyun Park
Measurement of deformed WF
|Ψ|2
E=0 MV/m
Byy
E=0 MV/mY
(n
m)
015
0 10
E
E0
15
E=20 MV/m
E=20 MV/m
0 10
X (nm)
E=40 MV/m
E=40 MV/m
0 10
Coulomb Confinement Hybridization Interface Confinement
015
Mapping deformed donor electron WF
29 Si atom act as a probe
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
Seung Hyun Park
Gat
e
SiO
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: a0=0.543095 nm
Donor
Seung Hyun Park
Relative change of Hyperfine coupling peak for various E-field at shells on the [100] axis
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
[100] axis E-field on [010] direction
Measure of Hyperfine Resonance Peak
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
Δα(Eur
) = α (0)(η 2E2 +η1E)
,where α (,ij )
Fit curves to
Provide Table of hyperfine Stark coefficients η2 and η1
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)
η2 η1
-3.8 1.7
η2 η1
-4.1 1.8
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
Seung Hyun Park
Issues for Experiments
Relative change of Hyperfine coupling for various E-field at nearest neighbors on the [100] axis
Shell 1 Shell 2HF
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
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
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