Ultrafast optical control of semiconductor spin qubits toward ...

Ultrafast Optical Control of 

Semiconductor Spin Qubits 

David Press, Susan Clark, 

Thaddeus Ladd, Kaoru Sanaka, 

Charles Santori, David Fattal, Kai Mei Fu, 

Yoshihisa Yamamoto 

(Stanford University & 

National Institute of Informatics) 

Sven Höfling, Stephan Reitzenstein, 

Alfred Forchel 

(University of Würzburg) 

International Conference on 

Quantum Foundation and Technology 

Shanghai, China, July 18-21, 2009

3rd Asia Pacific Physics Conference (World Scientific, Singapore, 1988) p.779 

Quantum mechanical aspects of 

optical communication and optical computing 

Y. Yamamoto, M. Kitagawa and K. Igeta 

Basic Research Laboratories, Nippon Telegraph and Telephone Corporation 

Musashino-shi, Tokyo 180, Japan 

Controlled-NOT Gate for Flying Qubits 

using Nonlinear Interferometer 

control 

|0 C / |1 C 

phase 

shift 

output 1 

output 2 

Controlled-Phase Gate for Matter Qubits 

using Stimulated Raman Scattering 

input 1 

|0 1 / |1 1 

A Fredkin gate using two three-level atoms 

and -pulse coherent state field 

input 2 

|0 2 

A nonlinear single photon interferometer 

operates as a Fredkin gate. 

2

Outline 

• Physical qubits Optically controlled semiconductor spins 

• Essential elements for fault-tolerant quantum information processing 

• Qubit initialization 

• Single qubit gate 

• Two qubit gate 

• Projective measurement and entanglement distribution 

• Indistinguishable single photons 

• Quantum memory (electron and nuclear spins) 

3

Physical Qubits 

Cavity QED Systems with Single-Electron 

Electron-Doped Quantum Dots 

100 nm 

“Random” 

“Scalable” 

A post-microcavity with top and bottom DBRs 

and self-assembled InGaAs QDs 

D. Press, S. Gotzinger, S. Reitzenstein, C. Hofmann, A. Loffler, 

M. Kamp, A. Forchel, and Y. Yamamoto, PRL 98, 117402 (2007). 

A simple planar microcavity with 

a 2D array of position-controlled QDs 

C. Schneider, M. Strauss, T. Sunner, 

A. Huggenberger, D. Wiener, S. Reitzenstein, M. Kamp, 

S. Hofling and A. Forchel APL 92, 183101 (2008) 

4

Magnetic Spectrum of Charged Exciton in InAs Quantum Dot 

Magnetic field in Voigt geometry 

= - B g h B ext 

M. Bayer et al., Phys. Rev. B 65, 195305 (2002) 

Trion X - 

Electron spins in singlet 

Spin is governed by hole 

= B g e B ext 

Electron e - 

D. Press et al., Nature 456, 218 (2008) 

5

Single QD Cavity QED System in Strong Coupling Regime 

D. Press et al. Phys. Rev. Lett. . 98, 117402 (2007) 

QD lifetime in free space 620ps 

QD lifetime in resonant cavity 11.3ps 

Purcell factor 

Device fabricated at 

Wurzburg 

Quantum efficiency 

under resonant pumping 

Direct proof of a single QD 

cavity QED system 

(Also see K. Hennessy et al., Nature 445, 896 

(2007) 

6

Outline 









7

Motivation Why Optically Controlled QDs 

Fault-tolerant and scalable quantum information processing systems 

based on semiconductor cavity QED systems 

Nested-purification-based quantum repeaters 

Concept: H.J. Briegel, W. Dür, J.I. Cirac and P. Zoller, PRL 81, 5932 (1998) 

Fault-tolerant Implementation: T.D. Ladd, P. van Loock, K. Nemoto, W.J. Munro 

and Y. Yamamoto, NJP 8, 184 (2006) 

One-way quantum computers with topological cluster states 

Concept: R. Raussendorf and J. Harrington, PRL 98, 190504 (2007) 

Fault-tolerant Implementation: R. Van Meter, T.D. Ladd, A.G. Fowler 

and Y. Yamamoto, quant-ph/0906271 (2009) 

Unique features of QDs as “artificial atoms” 

i ) Large oscillator strength: f exciton 100 f atom 

Ultrafast optical control of electron spins with small optical power 

ii ) Permanent placement of QDs in monolithic microcavities 

Scalable multi-qubit operation (two-qubit gate, entanglement distribution) 

iii) Excitonic transition wavelength tailored to =1.3/1.5 m 

Natural interface to long-distance/broad-band optical communication 

networks 

8

Outline 









9

Spin Initialization and Measurement 


Optical pumping + Rotation pulse of Θ = π 

pump laser 

Population in 

Single Photon 

Detection 

T = 1.5 K, B ext 

= 7 T 

Initialization fidelity: 

F 0 

= 92±7% 

Time for initialization: 

10 -3 sec (thermal equilibrium scheme) 10 -9 sec (optical pumping) 

10

Outline 









11

Spin Rotation with Single Optical Pulses 

• A single broadband optical pulse can implement 

an arbitrary one-bit gate with fidelity of 0.999. 

If 

an effective Rabi frequency 

Numerical simulation 

based on the three-level 

master equation 

100fs /2 - pulse 

rotation angle is proportional to 

pulse energy 

• A system clock is provided by the pulse arrival time 

from the mode-locked laser. 

100fs -pulse 

Arbitrary single qubit gates SU(2) can be implemented in a half 

period of Larmor oscillation. 

Theory: S. Clark et al., Phys. Rev. Lett. 99, 040501 (2007) 

Experiment with an ensemble of donor spins : K.M. Fu et al., Nature Physics 4, 780 (2008) 

12

Single QD Experiment: Coherent Rabi Oscillations 

Circularly-polarized 4 ps Rotation Pulse 

δ e = 26 GHz 

BW = 110 GHz 

Δ = 270 GHz 

Population in 

D. Press et al., 

Nature 456, 218 (2008) 

(cf. J. Berezovsky et al., 

Science 320, 349 (2008)) 

13

Two-Pulse Experiment: Ramsey Interference 

π/2-pulse fidelity:F π/2 ~ 94% π-pulse fidelity:Fπ ~ 91% 

Total time for arbitrary single qubit gate 19 ps (one-half of Larmor period) 


14

Outline 









15

Basic Concept of Qubus 

– Non-Local, Measurement-Free and Deterministic Two Qubit Gate – 

T. Spiller et al, New J. Phys. 8, 30 (2006) 

cavity 

input 

qubit 

output 

Time 

displacement 

(beamsplitter) 

controlled phase shift 

(reflection from cavity) 

• After the entire sequence, the probe is disentangled from the two qubits. 

No measurement and post-selection required. 

• An overall phase develops proportional to area (topological phase), 

A desired phase shift of achieved with 

16

Dissipative, Measurement-Free and Deterministic 

Two Qubit Gate 

Driving 

Driving field 

field 

D 

pulse 

• Cavity resonance depends on qubit state 

• Cavity field amplitude from detuned pulse 

depends on resonance position 

Amplitude “path” of cavity 

internal field depends on 

qubit states 

qubit 

Qubit 

qubit 

Qubit 

3 

2 

Qubit-dependent phase space path 

of cavity field 

1 

cavity 

field 

0 

Area difference 

-1 

enough phase for CZ gate 

Instantaneous phase difference 

-2 

smaller than vacuum fluctuation 

-1 0 1 2 3 4 5 6 quantum 7 8 erasure 9 10 

AC-stark shift depends on cavity field amplitude 

Qubits therefore alter each other’s phase 

CZ gate for universal logic or cluster state creation 

Master equation simulations indicate >99% fidelity with Q=10 5 

17

Outline 









18

Differential Phase Shift Projective Measurement and 

Entanglement Distribution with Coherent State Pulses 

P. van Loock et al, Phys. Rev. Lett. . 96, 240501 (2006) 

detuning 

cavity 

probe 

1. Initial states of two qubits 

2. Dispersive light-matter interaction 

4. Homodyne measurement 

(~0.01 : small phase shift in weak coupling cavity QED) 

3. Same interaction with qubit 2, followed by dc phase shift - 

post-selection 

Automatic phase stabilization in fiber transmission line 

High probability of success at a cost of low fidelity (cf. single photon detection schemes) 

19

Entanglement Distribution based on Indistinguishable 

Single Photon generation and Coincidence Detection 

1 

2 1 2 

D1 D2 D3 D4 

click at D1/D2 or D3/D4 

click at D2/D4 or D2/D3 

Theory: 

C. Simon et al., Phys. Rev. Lett. 91, 110405 (2003) 

Experiment with trapped ions: 

D.L. Moehring et al., Nature 449, 68 (2007) 

S. Olmschenk et al., Science 323, 486 (2009) 

20

Outline 









21

Generation of Indistinguishable Single Photons 

from a Single QD in a Post-Microcavity 

C. Santori et al., Nature 419, 594 (2002) 

Hong-Ou-Mandel dip 

22

Indistinguishable Single Photons 

from Two Independent 19 F:ZnSe Sources 

K. Sanaka et al., to appear in Phys. Rev. Lett. 

28nm 

1nm 

28nm 

15nm 

100nm 

ZnMgSe 

ZnMgSe 

ZnSe 

GaAs 

F:ZnSe QW 

Coincidence count rates as a function of delay time 

(Hong-Ou-Mandel dip) 

a 

Coincidence 

probability 

b 

0.68 0.96 

Coincidence 

probability 

ZnMgSe/ZnSe 

nanostructure B 

GaAs 

substrate 

42m 

ZnMgSe/ZnSe 

nanostructure A 

Pulse laser 

spot region 

c 

Coincidence probability 

Delay (ns) 

Delay (ns) 

Minimum 

coincidence 

0.68 

source 

A 

source 

B 

t 

50%-50% 

beamsplitt 

er 

Visibility 

Indistinguishability 

Coherence time 

Interferometer delay time (ns) 

PC 

V 

0.2ns PC 0 

P 0.2ns 

C 

I 65 13% 

 

 

74 38 ps 

C 

 

31 % 

 

 

23

Outline 









24

Clean Atomic Systems in Semiconductors 

– Donor Nuclear Spin, Bound Electron Spin (D 0 ) and Exciton (D 0 X) System – 

neutral donor bound exciton 

+ 

- 

Diamagnetic shift, Zeeman splitting, 

Two electron satellite emission 

2p - 

2p 0 

2s 

2p + 

- 

+ 

Radiative excitation 

and recombination 

(Interface to qubus) 

+ 

- 

simplest 

nuclear spin –½ 

(quantum memory) 

neutral donor 

31 

P: Si 

19 

F: ZnSe 

29 

Si:GaAs 

electron spin with 

homogeneous g-factor 

(quantum processor) 

Background nuclear spins 

can be depleted for Si and ZnSe by 

isotope engineering 

A0X transition energy (meV) 

1520 

1515 

1510 

1505 

1500 

1495 

1490 

1s 

D + X 

X D 0 X A 0 X D 0 X (TES) 

Hydrogenic spectrum 

2s 

A0 ionization energy: 25.9 meV 

central cell corr.: > 3.8 meV 

3s 

4s 

17 

5s 

25 

1485 

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 

final−state n quantum number

T 1 

and T 2 

Time of 29 Si:GaAs Semiconductor Spins 

4 ms 

T1 >4msec at B < 4T 

Maximum measurable T1 

T2 ~7sec at B=10 T 

(optical pulse spin echo) 

T 1 

(ms) 

Measurement 

of T1 at 6 T 

1 

= 1s 

.5 1.5 

Pulse sequence: 

Optical pumping 

B field (T) 

Pulse sequence: 

Optical pumping 

Exponential decay ~7s 

(Free induction decay~ 1-2ns) 

Fu, K.-M. C. et al. PRB 74 121304 (2006). 

26 

S. Clark. et al. Phys. Rev. Lett. 102, 247601(2009)

Summary and Outlook 

Essential elements for semiconductor spin-based quantum information processing 

Initialization in 3nsec with F=92% 

Single qubit gate in 20 psec with F=91-94% 

Quantum memory with T 2 

7sec (electron spin) and T 2 

1min (nuclear spin) 

Time (sec) 

Two qubit gate by single optical pulses 

Entanglement distribution by coincidence 

detection of indistinguishable single photons 

Patterned 

QDs 

Planar 

Microcavity 

control optical pulse 

27

Nuclear Spin Memory 

Nuclear spin Electron spin Excitonic dipole Photon 

31 

P: Si 

19 

F: ZnSe 

13 

C: NV center 

nuclear 

spin 

nuclear 


29 

Si:GaAs QD 

Ga and As nuclear 

spins 

31 

P 

19 

F 

29 

Si 

Hyperfine 

interaction 

PL linewidth 

PL lifetime 

electron 


PL efficiency 

 

Indistinguishable 

single photons 

entanglement formation 

Isotope 

engineering 

~ 60MHz ~ 10MHz ~ 130MHz 

1GHz 150MHz 

 

 

~ 3msec 1nsec ~ 20 nsec 

 

 

10 4 ~ 1 1 

~ 1 

 

10MHz 

electron 


electron 


~ 100KHz 

1GHz 

 

1nsec 

28

Measurement of Nuclear Polarization 

of optically pumped 29 Si/ 28 Si 

/2 /2 /2 /2 /2 /2 

t 

saturation comb saturation comb 

t+t 

> T 2 

free induction signal (FID) 

Natural Si Crystal 

T 1 

= 2 X 10 4 seconds 

28 

Si (spin 0) 

Natural silicon 

92.21% 

29 

Si enriched silicon 

2.4% 

29 

Si (spin 1/2) 

4.67% 

96.9% 

30 

Si (spin 0) 

3.09% 

0.7% 

T 1 

(300K) 

2 hrs. 30 min 

2 hrs. 20 min 

T 1 

(77K) 

15 hrs 

2 hrs. 30 min 

T 1 

(10K) 

unmeasurable 

8 hrs. 30 min 

29

T 2 Time of 29 Si Nuclear Spins in Natural Crystal Silicon 

T. Ladd et al., Phys. Rev. B. 71, 014401 (2005) 

natural linewidth 

fluctuating local magnetic 

field along Z-axis at 

Spin echo 

CPMG -pulse 

sequence 

dipolar coupling among 

Iso-nuclear spins 

decoupling 

( -pulse sequence) 

Time (sec) 

30

The Dependence of Decoherence Time T 2 

on Decoupling Cycle Time t c 

2 

1 

0.3 

echo intensity 

1 

97% 29 Si 

1.392 ms 

1.636 ms 

1.876 ms 

2.596 ms 

0 1 2 3 Time (sec) 

0.7 

2 

1 

t c 

(ms) 

echo intensity 

2 

4.7% 29 Si 

1.568 ms 

2.288 ms 

3.008 ms 

4.688 ms 

0 10 20 30 Time (sec) 

3 

4 

20 

10 

7 

5 

3 

• MREV decouples to 

second order in average 

Hamiltonian theory 

• Consequently, the residual 

interaction Hamiltonian 

scales as t 

2 

c 

• At high t c 

, the data agrees 

very well with this 

prediction 

• At low t c 

, the pulse width 

approaches the pulse 

separation, and MREV 

begins to fail. 

• The residual T 2 

improves 

with isotopic depletion. 

For low 29 Si density , 

expect T 

-1 

2 

 

31

̶ 

̶ 

Essential Elements for Fault-Tolerant Quantum Information Processing 

̶ The story in Optically Controlled Semiconductor Spins ̶ 

Initialization ̶ Optical pumping 

high field/low temperature not required, fast, high fidelity 

Single qubit gate ̶ Single optical pulse stimulated Raman scattering 

ultrafast (pulse duration

Entanglement Distribution with Single Photons 

Stimulated Raman Adiabatic Passage (STIRAP) 

control pulse 

J.I. Cirac, P. Zoller, H.J. Kimble and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997) 

single photon pulse 

Detection of single photons (post-selection) 

control pulse 

• two strictly identical nodes 

• photon bandwith much smaller 

than atom-cavity coupling constant 

(adiabaticity) 

solved by W. Yao et al., 

Phys. Rev. Lett. 92, 30504 (2005) 

• strong coupling regime 

• large detuning 

• solution unknown 

for arbitrary (distorted) 

pulse shape 

solved by 

D. Fattal et al., 

Quant-ph/0606204 

(2006) 

L.-M. Duan, 

M.D. Lukin, 

J. I. Cirac, 

P. Zoller, 

Nature 414, 413 

(2001) 

L. Childress, 

J.M. Taylor, 

A.S. Sörensen, 

M.D. Lukin 

Phys. Rev. A 72, 

52330 (2005) 

33

Ultrafast Optical Control of 

Semiconductor Spin Qubits 

David Press, Susan Clark, 

Thaddeus Ladd, Kaoru Sanaka, 

Charles Santori, David Fattal, Kai Mei Fu, 

Yoshihisa Yamamoto 

(Stanford University & 

National Institute of Informatics) 

Sven Höfling, Stephan Reitzenstein, 

Alfred Forchel 

(University of Würzburg) 

International Conference on 

Quantum Foundation and Technology 

Shanghai, China, July 18-21, 2009

Ultrafast optical control of semiconductor spin qubits toward ...

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