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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

• 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)

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

• 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)

9


Spin Initialization and Measurement

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

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

• 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)

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)

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

14


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)

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

• 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)

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

• 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)

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

• 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)

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

spin

29

Si:GaAs QD

Ga and As nuclear

spins

31

P

19

F

29

Si

Hyperfine

interaction

PL linewidth

PL lifetime

electron

spin

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

spin

electron

spin

~ 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

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