Laterally confined Semiconductor Quantum dots

1. LaterallyconfinedSemiconductor Quantum dots Martin Ebner and Christoph Faigle

2. Semiconductor Quantum Dots • Material Composition & Fabrication • Biasing • Energy diagram • Coulombblockade • Spin blockade • QPC • Readout • Rabioscillations • Summary

3. Materials and Fabrication AlGaAs layer doped with Si introduces free electrons which accumulate at the AlGaAs/GaAs interface creation of 2D electron gas (height ca. 10 nm) at interface. Throughmolecularbeamepitaxy, electrodesarecreated (~10 nm). Throughchoice of structure, depletedareascanbeisolatedfromtherest of theelectrons -> QDs Byapplyingvoltages to metal electrodes on top of AlGaAslayer, localdepletionareas in the 2DEG arecreated To be able to measure the quantum effects, the device is cooled to 20mK.

5. Biasingthe Quantum Dot Drain Source VSD IDOT VQPC-L VQPC-R IQPC IQPC QPC-L QPC-R

6. adjustingtunnelrates T Source Drain ΓD ΓS ΓLR M QPC-L L R QPC-R

7. Gate voltages Drain Source PL QPC-L PR QPC-R

9. Energy diagrams

10. Zeemansplitting by application of a magnetic field -> Zeeman splitting

11. Zeemansplitting

12. State transitionenergies

13. Transitionenergies and potentials StatePreparation: alignsource potential and transitionenergy bytuning VG

15. Coulombblockade

16. Hanson, Vandersypenet al. 2004: Coulombdiamonds

17. Transition potentials and tunneling • Source-drain potential differences lead to single-electron tunneling, depending on the potential of thegate • Tunnelingworksonlywhenground to ground-statetransitionlevelsaretunedintothebiaswindow. Onceinitialcurrentflowsexcitedstatetransitionscancontribute to thetunnelingtwo-pathtunneling • If the next ground state also falls into the potential window, there can be two-electrontunneling • Allowed regions are mapped by the coulomb diagram, in Coulomb blockade regions, there is no tunneling and thus no current flow

18. Spin blockade • According to the Pauli principle, no two electrons with the same spin are allowed on one orbital

19. QPC VQPC has to betuned to regime of maximumsensitivity steepestslope

21. Charge sensing • determine number of electrons on dot • non-invasive (no current flow) • only one reservoir needed • conductance of QPC electrometer depends on electrostatic environment • failure for long tunnel times and high tunnel barriers • measurement time about 10us

22. Single shot spin readout • Spin-to-charge conversion • Energy selective readout only excited state can tunnel off quantum dot due to potential • Tunnel-rate-selective readout difference in tunnel rate leads to high probability of one state then charge is measured on dot, original state is determined

23. Energy selectivereadout

24. Elzermanet al. 2004: fidelity: 82%, T1: 0.5ms @10 T

25. EOR Problems • requires large Energy splitting: kbT << ΔEZ • sensitive to fluctuations of el.stat. potential • photonassistedtunnelingfrom|> to reservoirdue to high frequencynoise ???

27. RABI Oscillations • ESR: electronspinresonance • alternatingBacperpendicular to Bextand resonant to statesplitting

28. continuousRabioscillationdetectionscheme

29. Koppenset al.: Tuning Bextwith/withoutBac

30. Koppenset al.: Tuning Bext and Bac

31. pulsedRabioscillationdetectionscheme

32. Koppenset al.: Rabioscillations

33. Rabiperformance • fidelity: 73% (131° instead of 180°) • usestrongerBac • application of compositepulses • measure and compensatenuclearfieldfluctuations (nuclearstatenarrowing) • qbitdiscrimination: • BacorBextgradient • localg-factorengineering • useelectricfield (spin-orbit-interaction)

34. Summary • A scalablephysicalsystemwithwell-characterizedqubits._✔ • Theability to initializethestate of thequbits to a simple fiducialstate._✔ • Long (relative) decoherencetimes, muchlongerthanthegate-operation time.? (T1 ≈ 1ms, T2* ≈ 10ns, T2 > 1μs [spin echo]) • A universal set of quantumgates.✖NO ENTANGLEMENT YET (2005) • A qubit-specificmeasurementcapability. ✔ (Treadout≈ 10μs)

35. Thanksforyourattention!