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Electric dipole spin resonance and spin decoherence for heavy holes in quantum dots

Electric dipole spin resonance and spin decoherence for heavy holes in quantum dots. Denis Bulaev and Daniel Loss Department of Physics University of Basel, Switzerland. Outline. Motivation Spin-Orbit Coupling of Holes Spin Relaxation and Decoherence of Heavy Holes in QDs

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Electric dipole spin resonance and spin decoherence for heavy holes in quantum dots

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  1. Electric dipole spin resonance and spin decoherencefor heavy holes in quantum dots Denis Bulaev and Daniel Loss Department of Physics University of Basel, Switzerland

  2. Outline • Motivation • Spin-Orbit Coupling of Holes • Spin Relaxation and Decoherence of Heavy Holes in QDs • Spin-Manipulation Methods for Heavy Holes • Conclusions

  3. Motivation QD based Quantum Computing Loss & DiVincenzo, PRA 57, 120 (1998)

  4. Motivation Low T1 (up to 170 ms*) QD based Quantum Computing Loss & DiVincenzo, PRA 57, 120 (1998) Koppens et al., Science 309, 1346 (2005) *Amasha et al. cond-mat/0607110

  5. Motivation Rabi oscillations Low T1 (up to 170 ms*) QD based Quantum Computing Loss & DiVincenzo, PRA 57, 120 (1998) Koppens et al., Science 309, 1346 (2005) *Amasha et al. cond-mat/0607110 Pettaet al., Science 309, 2180 (2005) ESR Koppens et al., Nature 442, 766 (2006)

  6. Motivation Rabi oscillations Low T1 (up to 170 ms*) QD based Quantum Computing Loss & DiVincenzo, PRA 57, 120 (1998) Koppens et al., Science 309, 1346 (2005) *Amasha et al. cond-mat/0607110 Pettaet al., Science 309, 2180 (2005) ESR Fast T2 “T*2 ≈ 10 ns, limited by hyperfine interactions” Pettaet al., Science 309, 2180 (2005) Khaetskii, Loss, Glazman, PRB 67, 195329 (2003) Koppens et al., Nature 442, 766 (2006)

  7. Motivation Heavy-Hole Spin as Qubit: weak hyperfine interactions with nuclear spins strong spin-orbit coupling difficult to manipulate the spin

  8. Motivation Heavy-Hole Spin as Qubit: weak hyperfine interactions with nuclear spins strong spin-orbit coupling difficult to manipulate the spin

  9. Spin-Orbit Coupling: 3D vs 2D Bulk Semiconductor E HH ±3/2 LH ±1/2 k [001] Quantum Well E HH D ±3/2 LH ±1/2 kⅡ

  10. Spin-Orbit Coupling: 2D vs 0D [001] Quantum Well E HH D ±3/2 LH ±1/2 kⅡ [001] Flat Quantum Dot E D HH ±3/2 LH ±1/2

  11. Spin-Orbit Coupling: QD E D HH ±3/2 LH ±1/2 Winkler, PRB 62, 4245 (2000) DB & Loss, PRL 95, 076805 (2005) Luttinger, PR 102, 1030 (1956)

  12. Spin-Orbit Coupling: QD No LH-HH Coupling E D HH ±3/2 LH ±1/2 Winkler, PRB 62, 4245 (2000) DB & Loss, PRL 95, 076805 (2005) Luttinger, PR 102, 1030 (1956)

  13. Spin-Orbit Coupling: QD No LH-HH Coupling E D HH ±3/2 LH ±1/2 Winkler, PRB 62, 4245 (2000) No SO Coupling of HHs Luttinger, PR 102, 1030 (1956)

  14. Spin-Orbit Coupling: QD E D HH ±3/2 LH ±1/2

  15. Spin-Orbit Coupling: QD E D HH ±3/2 LH ±1/2 D

  16. Effective Hamiltonian of Heavy Holes Rashba SO coupling R. Winkler, PRB 62, 4245 (2000) Dresselhaus SO coupling DB & D. Loss, PRL 95, 076805 (2006) SO due to BII-field DB & D. Loss, cond-mat/0608410

  17. Energy Level Structure RSO SO(BII) DSO

  18. Spin Evolution. No Damping B0 Sz wzt Sx wzt

  19. Spin Evolution. Damping B0 Sz wzt Sx wzt

  20. Spin Relaxation and Decoherence DB & D. Loss, cond-mat/0608410 DSO SO(BII) RSO h = 5 nm; l = 40 nm;

  21. Spin Relaxation and Decoherence DB & D. Loss, cond-mat/0608410 S.Sasaki et al., PRL 95, 056803 (2005) DSO SO(BII) RSO h = 5 nm; l = 40 nm;

  22. Spin Relaxation: Electrons vs. Holes DB & D. Loss, PRL 95, 076805 (2006) GaAs Quantum Dot (g = 2.5) InAs Quantum Dot (g = -2.2)

  23. Spin Relaxation: Electrons vs. Holes DB & D. Loss, PRL 95, 076805 (2006) GaAs Quantum Dot (g = 2.5) InAs Quantum Dot (g = -2.2) Abstreiter Group, ICPS Conference (July 2006)

  24. Spin Relaxation due LH-HH SOI 5 orders of magnitude longer than that due to RSO, DSO, and SO(BII) Other Theories Woods, Reinecke, & Kotlyar, PRB 69, 125330 (2004) Lü, Cheng, & Wu, PRB 71, 076308 (2005)

  25. Spin Manipulation Heavy-Hole Spin as Qubit: weak hyperfine interactions with nuclear spins strong spin-orbit coupling Long T1, T2 difficult to manipulate the spin weak

  26. ESR. Rabi Oscillations B0 Sz wRt B1 wrf wrf = wz — Spin Resonance wz

  27. ESR. Rabi Oscillations B0 Sz wRt B1 wrf wz Koppens et al., Nature 442, 766 (2006) Engel & Loss, PRL 86, 4648 (2001)

  28. Electric Dipole Spin Resonance No magnetic-dipole transitions!!! DB & D. Loss, cond-mat/0608410

  29. Electric Dipole Spin Resonance No magnetic-dipole transitions!!! DSO SO(BII) RSO RSO SO(BII) Electric-dipole transitions!!! DSO DB & D. Loss, cond-mat/0608410

  30. Electric Dipole Spin Resonance 0 dSO=0 (min) 0 dSO=|e| l wZ / 2w (max) Bloch equations:

  31. Electric Dipole Spin Resonance Power:

  32. Electric Dipole Spin Resonance Power:

  33. Rabi Oscillations B = 0.5 T B =0.8 T B = 0.865 T (Rabi frequency)

  34. Summary Heavy holes in quantum dots: • Spin-orbit effect suppressed for flat QDs • T2 = 2T1 at low temperatures • Spin relaxation time T1 can be milliseconds • Coherent spin manipulation by RF electric fields • Strong control of Rabi oscillations

  35. Quantum Error Corrections scalable QC QEC threshold (Rabi frequency)

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