Electric dipole spin resonance and spin decoherence for

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 ÜMotivation ÜSpin-Orbit Coupling of Holes ÜSpin Relaxation and Decoherence of Heavy Holes in QDs ÜSpin-Manipulation Methods for Heavy Holes ÜConclusions

Motivation QD based Quantum Computing Loss & Di. Vincenzo, PRA 57, 120 (1998)

Motivation Low T 1 (up to 170 ms*) QD based Quantum Computing Loss & Di. Vincenzo, PRA 57, 120 (1998) Koppens et al. , Science 309, 1346 (2005) *Amasha et al. cond-mat/0607110

Motivation Rabi oscillations Low T 1 (up to 170 ms*) QD based Quantum Computing Loss & Di. Vincenzo, PRA 57, 120 (1998) Koppens et al. , Science 309, 1346 (2005) *Amasha et al. cond-mat/0607110 Petta et al. , Science 309, 2180 (2005) ESR Koppens et al. , Nature 442, 766 (2006)

Motivation Rabi oscillations Low T 1 (up to 170 ms*) QD based Quantum Computing Loss & Di. Vincenzo, PRA 57, 120 (1998) Koppens et al. , Science 309, 1346 (2005) *Amasha et al. cond-mat/0607110 Petta et al. , Science 309, 2180 (2005) ESR Fast T 2 “T*2 ≈ 10 ns, limited by hyperfine interactions” Petta et 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: 3 D vs 2 D Bulk Semiconductor E HH ± 3/2 LH ± 1/2 k [001] Quantum Well E D HH ± 3/2 LH ± 1/2 kⅡ

Spin-Orbit Coupling: 2 D vs 0 D [001] Quantum Well E D HH ± 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 E No LH-HH Coupling 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 E No LH-HH Coupling 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 Sz B 0 Sx wz t

Spin Evolution. Damping Sz B 0 Sx wz t

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) Ga. As Quantum Dot (g = 2. 5) In. As Quantum Dot (g = -2. 2)

Spin Relaxation: Electrons vs. Holes DB & D. Loss, PRL 95, 076805 (2006) Ga. As Quantum Dot (g = 2. 5) In. As 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 weak strong spin-orbit coupling difficult to manipulate the spin Long T 1, T 2

ESR. Rabi Oscillations Sz B 0 w. R t wrf = wz — Spin Resonance wrf B 1 wz

ESR. Rabi Oscillations Sz B 0 w. R t wrf B 1 Koppens et al. , Nature 442, 766 (2006) Engel & Loss, PRL 86, 4648 (2001) wz

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 SO(BII) Electric-dipole transitions!!! DSO DB & D. Loss, cond-mat/0608410

Electric Dipole Spin Resonance 0 d. SO=0 (min) 0 Bloch equations: d. SO=|e| l w. Z / 2 w (max)

Electric Dipole Spin Resonance Power:

Electric Dipole Spin Resonance Power:

Rabi Oscillations B = 0. 5 T B =0. 8 T B = 0. 865 T (Rabi frequency)

Summary Heavy holes in quantum dots: 4 Spin-orbit effect suppressed for flat QDs 4 T 2 = 2 T 1 at low temperatures 4 Spin relaxation time T 1 can be milliseconds 4 Coherent spin manipulation by RF electric fields 4 Strong control of Rabi oscillations

Quantum Error Corrections scalable QC QEC threshold (Rabi frequency)