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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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**Electric dipole spin resonance and spin decoherencefor 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 • Spin-Manipulation Methods for Heavy Holes • Conclusions**Motivation**QD based Quantum Computing Loss & DiVincenzo, PRA 57, 120 (1998)**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**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)**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)**Motivation**Heavy-Hole Spin as Qubit: weak hyperfine interactions with nuclear spins strong spin-orbit coupling difficult to manipulate the spin**Motivation**Heavy-Hole Spin as Qubit: weak hyperfine interactions with nuclear spins strong spin-orbit coupling difficult to manipulate the spin**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**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**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)**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)**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)**Spin-Orbit Coupling: QD**E D HH ±3/2 LH ±1/2**Spin-Orbit Coupling: QD**E D HH ±3/2 LH ±1/2 D**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**Energy Level Structure**RSO SO(BII) DSO**Spin Evolution. No Damping**B0 Sz wzt Sx wzt**Spin Evolution. Damping**B0 Sz wzt Sx wzt**Spin Relaxation and Decoherence**DB & D. Loss, cond-mat/0608410 DSO SO(BII) RSO h = 5 nm; l = 40 nm;**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;**Spin Relaxation: Electrons vs. Holes**DB & D. Loss, PRL 95, 076805 (2006) GaAs Quantum Dot (g = 2.5) InAs Quantum Dot (g = -2.2)**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)**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)**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**ESR. Rabi Oscillations**B0 Sz wRt B1 wrf wrf = wz — Spin Resonance wz**ESR. Rabi Oscillations**B0 Sz wRt B1 wrf wz Koppens et al., Nature 442, 766 (2006) Engel & Loss, PRL 86, 4648 (2001)**Electric Dipole Spin Resonance**No magnetic-dipole transitions!!! DB & D. Loss, cond-mat/0608410**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**Electric Dipole Spin Resonance**0 dSO=0 (min) 0 dSO=|e| l wZ / 2w (max) Bloch equations:**Rabi Oscillations**B = 0.5 T B =0.8 T B = 0.865 T (Rabi frequency)**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**Quantum Error Corrections**scalable QC QEC threshold (Rabi frequency)

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