Rajib Rahman Orbital Stark Shift of donor-interface states Lansbergen, Rahman, GK, LH, SR, Nature Physics, 4, 656 (2008) ε Oxide-Si-impurity ε=0 Donor-interface system Smit et al. PRB 68 (2003) Martins et al. PRB 69 (2004) Calderon et al. PRL 96 (2006)

Rajib Rahman Transport through donor states DeviceE1 (meV)E2 (meV)E3 (meV) 10G G G HSJ GLG GLJ Energies w.r.t. ground state (below CB) Exp. Measurements Energies different from a bulk donor (21, 23, 44) Donor states – depth & field dependent Orbital Stark Shift of donor-interface states

Rajib Rahman

Friesen, PRL 94 (2005) Si:P (Bulk) A B C Si:As (Depth 7a0) Features found 3 regimes Interface effects anti-crossing p-manifold valley-orbit Orbital Stark Shift of donor-interface states A (Coulomb bound) Rahman, Lansbergen, GK, LH, SR (Orbital Stark effect theory paper, to be submitted) B (Hybridized)C (Surface bound)

Rajib Rahman Stark Effect in donor-interface well Lansbergen, Rahman, GK, LH, SR, Nature Physics (2008), IEDM (2008) Interpretation of Exp. Indirect observation of symmetry transition P vs As Donor distinction Exp data with TB simulations Where are the exp. points?

Rajib Rahman Stark Shift of Hyperfine Interaction ESES ETET e n A(ε) |  (ε, r 0 )| 2 Contact HF: => Nuclear spin site => Impurity site ∆A(ε)/A(0) =  2 ε 2 (bulk) Theory: Rahman et al. PRL. 99, (2007) Exp: Bradbury et al., PRL 97, (2006) BMB TB ∆A(ε)/A(0) = (  2 ε 2 +  1 ε) (interface) D oxideDonor

Rajib Rahman Why linear Stark Effect near interfaces? Asymmetry in wf 1 st order PT: Oxide-Si-impurity Small Depth: Large Depth: Even symmetry broken Rahman et al. PRL. 99, (2007) Stark Shift of Hyperfine Interaction Quadratic Stark Coefficients MethodDepth(nm)  2 (µm 2 /V 2 ) EXP (Sb) x EMT (P) ∞ -2x BMB (P) x TB (P) x x EMT: Friesen, PRL 94, (2005) How good are the theories?

Rajib Rahman Hyperfine Map of Donor Wave-functions Park, Rahman, Klimeck, Hollenberg (submitted) ESR Experiments can measure A => Direct measure of WF Usefulness of HF – an example 29 Si (S=1/2) 28 Si (S=0)Si isotopes: Observables in QM:Hyperfine: Application: Experimentally mapping WF deformations (idea: L. Hollenberg)

Rajib Rahman Stark Shift of the donor g-factor Zeeman effect:B-field response => g-factor Spin-orbit (LS) interaction:very important in QC g-factor Stark shift:Indirect measure of SO ε [010] Si:P Anisotropic Zeeman Effect

Rajib Rahman Stark Shift of the donor g-factor Multi-valley g to single-valley g transition in Si (g||-g|_=8e-3) Rahman, Park, GK, LH (Gate induced g-factor control, to be submitted) ImpurityE || valley-axis 22 Si:PB||-1.0x10 -5 Ge:PB||1.43x10 -1 GaAs:SiB||-9.4x10 -3 Quadratic Stark Shift (bulk): ∆g(ε)/g(0) =  2 ε 2 Conclusions SO strength valley-structure anisotropic Zeeman single-valley anisotropy Exp. Magnitude verified

Rajib Rahman Vs1=0.05V Vs1=0.1V E1 E2 E1 E2 E1 E2 Vs1=0.3V Vs1=0.0V E1 E2 Vs1=0.4V E1 E2 P P+ 15 nm Vs1Vb1Vb2Vs2 V=0V>0 Electrostatic gating of single donors Nano-TCAD+TB

Rajib Rahman Coherent Tunneling Adiabatic Passage (CTAP) Solid-state analogue of STIRAP (Quantum Optics), Greentree et al., PRB 70 (2004) Molecular states: no middle donor occupation Pathways in Eigen-space connecting end states Spin state transport Many-donor chain: Less gating, more robust Purpose (NEMO-CTAP): Relax assumptions Real solid-state system: bands, interfaces, excited states, gate-cross talk, realistic donor models Does the adiabatic path exist ? Quantum Info Transport Hollenberg et al., PRB 74 (2006)

Rajib Rahman Anti-crossing gap => tunneling times Barrier gate modulation Rahman, Park, GK, LH (Atomistic simulations of CTAP, in prep.) |Ψ 2 | 2 at various voltages Left localized Middle stage Right localized No population at center donor any time Atomistic simulations of CTAP3

Rajib Rahman Donor Based Charge Qubits S B P+P+ P0P0 TCAD Gate Molecular States Sensitivity to impurity positioning Molecular states of P 2 + encode info Proposal: Hollenberg EMT work: X. Hu, B. Koiller, Das Sarma Tunnel Coupling:  12 = E 2 - E 1 Excited states ignored so far:  23 = E 3 – E 2 TB result similar to EMT

Rajib Rahman Control of Charge Qubits Goal: Establish limiting conditions for operation Characterize gate control Explore design parameter space Molecular Spectrum Surface Gate Control Some Findings R > 8 nm Smooth Control Surface Ionization Saturated regime  12 =  23

Rajib Rahman Surface Gate Control of Charge Qubits V=0 Wf 1Wf 2 V=0.2 V=-0.2 V=0.5 Wf 1Wf 2 V=-0.5 Saturation Linear Ionization Bonding

Rajib Rahman Many-body Interactions in Donor Qubits ee P+ R=|R 2 -R 1 | 2e Hamiltonian Koiller, Hu, Das Sarma, PRL 88, No 2 (2002) Kane Qubit: Two qubit interaction Exchange coupling J between donors Modify WF overlap by gate voltage Known facts: J oscillates with R (Koiller) SiGe strain can reduce oscillations (conditionally) (Koiller) Gate control smooth (mostly) – Wellard, Hollenberg A BMB (Wellard) work showed reduced oscillatons. Goal: TB wfs, extended band structure, VO interaction Beyond Heitler-London (CI) Effect of strain, interfaces, gates Other systems: spin-measurement

Rajib Rahman Exchange Interaction in Heitler-London Formalism Singlet: Triplet: Many-body wfs must be anti-symmetric w.r.t. interchange of r and s P Vb L Dot P Vb R Dot Basis: 2P Vb 2 electron system HL valid for “large” donor separations TB Voltage Controllability Problem. Similar result in EMT: Wellard et al., J. Phys.: Condens. Matter – 5704 (2004).

Rajib Rahman Conf. 1Conf. 2Conf. 3 Conf. 4Conf. 5Conf. 6 Example: 4 states 4 choose 2 Many Body configurations 6 x 6 CI Hamiltonian Possible Future Work with CI P-P Molecular Spectrum D- State of P: Charging Energy Donor-Interface 2e problem (spin read- out prop. by Kane) Exchange Interaction in FCI Formalism (on-going) New goal: Refine HL by including spin, HM states (TCI)

Rajib Rahman Hyperfine Stark Effect of P-Impurities Objective: Study Stark Shift of hyperfine coupling Compare with experiment, BMB & EMT Investigate interface effects Establish the physics of quadratic and linear Stark coefficients Approach: Use 3.5 M atomistic domain P impurity under E-fields TB approach optimized for P donors Vary impurity depth from interface Solve the 20 band spin Hamiltonian by parallel Lanczos algorithm Results / Impact: Quadratic Stark coefficient from TB, BMB & experiment agree well EMT estimate differs by an order of magnitude Proximity of impurity to interface produces significant linear Stark effect MethodDepth (nm)  2 (µm 2 /V 2 ) EXP (Sb) x10 -3 EMT (P)∞-2x10 -2 BMB (P) x10 -3 TB (P) x x10 -3 Quadratic Stark Coefficients Rahman et al. PRL. 99, (2007) wavefunction change with E field Hyperfine coupling in E field / depths

Rajib Rahman Hyperfine maps of donor wave functions Challenge / Objective: Can a single impurity donor wavefunction(wf) be experimentally mapped? Approach: Indirectly probe wfs by measuring Hyperfine tensors (idea: L. Hollenberg). Use Si-29 as a single probe atom or a sample of probe atoms Calculate donor wfs in realistic geometries and electric fields Propose experiment: Distort wf by electric fields and interfaces => distort HF => measure HF based on lattice symmetries => map the wavefunction Results / Impact: Probe local values of WF instead of global expectation values Demonstrated distortion of the WF through its hyperfine map Verified feasibility of detecting such distortions. Fermi termDipolar term Park, Rahman, GK, LH, Rogge (paper submitted) 28 Si host, 29 Si probe

Rajib Rahman Gate control of donor g-factors and dimensional isotropy transition Objective: Investigate Stark Shift of the donor g-factor. g-factor shift for interface-donor system. Probes spin-orbit effects with E-fields and symmetry transition. Relative orientations of B and E field. Approach: The 20 band nearest neighbor sp3d5s* spin model captures SO interaction of the host. Same atom p-orbital SO correction g-factor obtained from L and S operators. Donor wfs with E-field are obtained from NEMO Results / Impact: Quadratic trend with E-field for bulk donors. Stark parameter larger in Ge and GaAs Anisotropic Zeeman effect – E and B field Dimensional transition- multi-valley to single valley g-factors. Exp. Quadratic coef. matches in magnitude. Si:P Rahman, Park, GK, LH (to be submitted)

Rajib Rahman Coherent Tunneling Adiabatic Passage (CTAP) Objective: Investigate CTAP in realistic setting. Include Si full band-structure, TCAD gates, interfaces, excited states, cross-talk. Verify that adiabatic path exists: 3 donor device. Approach: TCAD gates coupled with a 3 donor TB. Hamiltonian: obtain molecular states in the solid state. Simulate 3-4 M atoms for a realistic device. Compute time of 4-5 hours on 40 procs. Fine tune gate voltages to explore the CTAP. regime. Results / Impact: Demonstrated that the CTAP regime exists for a 3 donor test device. Verification of results (under relaxed assumptions) CTAP despite noisy solid-state environment. Developed the framework to guide future CTAP expt. Rahman, Park, GK, LH ( to be submitted)

Rajib Rahman Charge qubit control Objective: Control & design issues: donor depths, separation, gate placement. Feasible S and B gate regimes. Effect of excited states: charge state superposition. Approach: S and B gates - TCAD potentials Empirical Donor model + TB+ TCAD: bound molecular states. Lanczos + Block Lanczos solver Results: Smooth voltage control excited states at higher bias mingle with operation. Placement of S and B gates important relative to donors. Comparison with EMT RR, SHP, GK, LH (to be submitted) Surface gate response of tunnel barriers Molecular Spectrum + Tunnel barriers

Rajib Rahman D- Modeling for As/P Donor Objective: Obtain 2e binding energy of donors with E- fields and donor depths: important in spin- dependent tunneling and measurement. D- ground and excited states : Analyze measured Coulomb diamonds from Transport Spectroscopy measurements. Approach: 1 st approximation: SCF Hartree method. Use a domain of 1.4 M atoms with 1 donor. SCF: 1. Obtain wf from NEMO 2. Calculate electron density and Coulomb repulsion potential 3. Repeat NEMO with the new potential. 4. Stop when D- energy has converged. On-going: D- from configuration interaction Results: D- energy for a bulk donor within 2 meV from measured value. D- vs. Depth & field calculations. Explains charging energy of some samples Screening likely to play a role. D-, D0 vs E D7a0 D- vs charging energy D- D Ec comparison Rahman, Arjan, Park, GK, LH, Rogge (in prep)

Rajib Rahman Control of exchange for adjacent qubits Objective: Investigate gate control of exchange(vs EMT) Reconfirm controllability issues (from BMB) Treatment of interfaces & strain From Heitler London to Full CI Approach: atomistic basis for exchange calculations orbital interactions for short distances Interpolate TCAD potential on atomistic lattice Heitler-London scaled and tested for 4 M atoms removing previous computational bottlenecks. FCI is still a computational challenge Results / Impact: Similar exchange trends obtained as BMB Controllability issues at some specific angular separations verified Magnitude an order less from EMT Basis functions for short range interactions? J(V) for various impurity separations along [100] Sensitivity of J(V) to donor placement