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Electronic transport in nanostructures

Electronic transport in nanostructures. Thomas Ihn ETH Zürich FS 17. After this lecture you know and understand…. ... how Rabi oscillations work as single qubit operations in quantum dots ... how spin-blockade and hyperfine interaction are used in spin manipulations

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Electronic transport in nanostructures

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  1. Electronic transport in nanostructures Thomas Ihn ETH Zürich FS 17

  2. After this lecture you knowand understand… • ... how Rabi oscillations work as single qubit operations in quantum dots • ... how spin-blockade and hyperfine interaction are used in spin manipulations • ... how a two qubit operation has been implemented in a double quantum dot system

  3. Requirements • Number of qubits: 105 • Scalability • Decoherence times much longer than gate operations • Universal set of qubit gates • Readout • Flying qubits, conversion

  4. How we can compute… … what is computable Classical computing Quantum computing NAND or NOR or NOT and OR or … arb. single qubit rotations and CNOT or arb. single qubit rotations and SWAP or …

  5. Steps to be taken • Decoherence: Determine coherence times in two-level systems, Investigate decoherence mechanisms Develop methods to avoid decoherence • Preparation: prepare two-level systems in a well-defined initial state 3.Single qubit manipulation: Observe single-qubit rotations (Rabi oscillations) • On-demand entanglement: find schemes for controlled qubit interaction • Detection: get the results of a calculation from measuring the qubits 6. Coherent transportation of qubits

  6. Qubits in quantum dots • Single electron spin in one quantum dot • Two energy levels in a double quantum dot • Presence/absence of an electron-hole pair in a single quantum dot spin qubit charge qubit excitonic qubit

  7. Qubit: Bloch sphere representation

  8. Single qubit manipulation

  9. Free oscillations of a charge qubit

  10. Rabi oscillations

  11. Rabi oscillations

  12. Spin qubits in semiconductors D. Loss, DiVincenzo, 1998

  13. Few-electron double quantum dots

  14. Spin states in two-electron double quantum dots

  15. Spin blockade

  16. Hyperfine interaction from D.J. Klauser, PhD thesis Basel 2008 HF-interaction mixes (1,1)S and (1,1)T

  17. Electron spin resonance experiment F. Koppens et al., Nature 442, 766 (2006)

  18. Electron spin resonance experiment F. Koppens et al., Nature 442, 766 (2006) couples to the spin via AC magnetic field

  19. Electron spin resonance experiment Higher power -> larger Rabi frequency Burst time F. Koppens et al., Nature 442, 766 (2006)

  20. Electrically driven electron spin resonance (EDSR) K.C. Nowack et al., Science 318, 1430 (2007) couples to the spin via spin-orbit interaction

  21. Spins in an artificial magnetic field gradient spin resonance M. Pioro-Ladrière et al., Nature Physics 4, 776 (2008) couples to the spin via magnetic field gradient

  22. Spin evolution in the Overhauser field J.R. Petta et al., Science 309, 2180 (2005)

  23. Spin evolution in the Overhauser field J(ε)=gμBB J.R. Petta et al., Science 309, 2180 (2005)

  24. Spin evolution in the Overhauser field Probability of return to the singlet state

  25. Spin evolution in the Overhauser field 2 qubit operation: SWAP operation, if J(ε)τE/h=1/2

  26. Spin evolution in the Overhauser field Spin-echo technique

  27. Possible physical implementations • NMR • Ions in ion traps • Atoms in atom traps • Coherent photons • Charge qubits in superconductors • Flux qubits in superconductors • Nuclear spins (Phosphorous in Silicon) • Electron spins in quantum dots • Charge states in double quantum dots • Excitons in quantum dots • ...

  28. Possible physical implementations • NMR (Degen) • Ions in ion traps (Home) • Atoms in atom traps (Esslinger) • Coherent photons • Charge qubits in superconductors (Wallraff) • Flux qubits in superconductors • Nuclear spins (Phosphorous in Silicon, IBM Rüschlikon) • Electron spins in quantum dots (Ensslin/Ihn) • Charge states in double quantum dots (Ensslin/Ihn) • Excitons in quantum dots (Imamoglu) • ...

  29. Viel Spass mit der Physik „Das Erstaunlichste an der Welt ist, dass man sie verstehen kann.“

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