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

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
Petta et 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
Petta et al., Science 309, 2180 (2005)
ESR
Fast T2 T2 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)
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
k?
10
Spin-Orbit Coupling 2D vs 0D
001 Quantum Well
E
HH
D
3/2
LH
1/2
k?
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
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)
13
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)
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
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 dSO0 (min)
0 dSOe 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)