Bingyang ZhangYasuhiko Arakawa (Tokyo)Colin Stanley (Glasgow)Klaus Lischka (Paderborn)Kohei Ito (Keio)(MBE)

Stephan GötzingerDirk EnglundShinichi KosekiDavid Press(Quantum dots)

Kai-Mei FuSusan ClarkKaoru SanakaAlex PawlisCharles Santori (HP)David Fattal (HP)(Donor bound excitons)

Thaddeus LaddFumiko YamaguchiWilliam Munro (HP)Kae Nemoto (NII)Peter van Loock (NII)(Quantum communication/ computation protocol)

Jelena VuckovicYoshihisa Yamamoto

The Forth International Symposiumon Nanotechnology

(Tokyo, Feb. 20-21, 2006)

Is Clean Atomic Physics ImplementedIs Clean Atomic Physics Implementedin Semiconductor Systems?in Semiconductor Systems?

— From Quantum Dots to Impurity Bound Excitons —— From Quantum Dots to Impurity Bound Excitons —

2

OutlineOutline

• Overview of the past work- Indistinguishable single photons from single QD microcavity- Quantum key distribution- Entangled photon-pairs (violation of Bell’s inequality)- Quantum teleportation- Limitation: What was the problem with QDs?

• Substitutional donor impurities in semiconductors- Hydrogenic spectrum- Coherent population trapping (electron spins)- 1min coherence time (nuclear spins)

• Cavity QED nodes connected by coherent state bus for photonic quantum information systems

- Entanglement distribution- Non-local two qubit operation

- Coherent emission and trapping of single photons

3

Single QD Spectroscopy: “Artificial Atoms”Single QD Spectroscopy: “Artificial Atoms”

C. Santori et al., Phys. Rev. Lett. 86, 1502 (2001)

• Sharp spectral lines at low temperature

• Multiparticle effects

• Dephasing processes (~1nsec) (phonon,electrostatic) XH XV

XX2 - 4 meV

empty

X-

e-

X+

h+

level diagram: <10GHz <50K

Above band excitation

27 W 108 W 432 W

(nm) (nm) (nm)

time

(ns)

2X3X

1X

Cascade Photon EmissionCascade Photon Emission

On resonant excitation at 2e-2h

Suppression of X– and X+ linesDeterministic single photon generation

Deterministic entangled photon-pair generation O. Benson et al., Phys. Rev. Lett. 84, 2513 (2000)

1 2 1 2

12H H V V

4

Single QD MicrocavitiesSingle QD Microcavities

ECR (I)

5Purcell factorF

G. Solomon et al.,Phys. Rev. Lett. 86, 3903 (2001)

ECR (II)

2(0) 0.02Second orderg

M. Pelton et al.,Phys. Rev. Lett.

89, 233602 (2002)

CAIBE

0.8IndistinguishabilityV

J. Vuckovic et al.,Appl. Phys. Lett. 82, 3596 (2003)

Photonic Crystal10, 0.1F F

D. Englund et al.,Phys. Rev. Lett.

95, 013904 (2005)

A. Imamoglu ( Zurich): Controlled placement of QDJ.M.Gerard (CEA Grenoble)A. Forchel (Würzburg) Strong coupling A. Scherer (Cal. Tech)A. Shields (Toshiba Cambridge): Entangled photon-pair generation

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Quantum IndistinguishabilityQuantum Indistinguishability

Suppressed due toDestructive Quantum Interference (Fermions)

Enhanced due toConstructive Quantum Interference (Bosons)

Identical Quantum Particles Indistinguishable

Final State Stimulation & BEC

Pauli Exclusion Principle

direct term exchange term

symmetrization (Boson)anti-symmetrization (Fermion)

1 or 2?

Symmetrization postulateof Quantum Mechanics

rA

rB

|> =12

{ |1,rA;2,rB > |2,rA;1,rB> }+

FERMIONBOSON Probability of Two Particlesin the Same Output Port rA = rB = r

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Indistinguishable Single Photons from a Single Quantum DotIndistinguishable Single Photons from a Single Quantum Dot— Measurement of Quantum Mechanical Overlap —— Measurement of Quantum Mechanical Overlap —

Requirements:• Negligible jitter (2e-2h 1e-1h relaxation time ~10 psec) compared to pulse duration• No phase jump (decoherence time ~2nsec) in pulse duration

Hong-Ou-Mandel dip

second-ordercoherence function g(2)(0)

pulse duration (ps)

QM overlapV ( =0)

QD#1 0.039 80 0.72

QD#2 0.027 187 0.81

QD#3 0.025 378 0.74

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

BB84 Quantum Key Distribution ExperimentBB84 Quantum Key Distribution Experimentwith Single Photon Sourcewith Single Photon Source

EOM

Amp.Data Gen.TIATIA

Alice

Bob

HeCryo.

Laser Pulsedot

LensPinhole

Lens Sm fiber

Lensgrating

Spec. slit

PBS

/2 plate /4 platePBS50-50

BSP

Det 1Det 2

Det 3

Det 4

channelCounter

Det 0

FlipMirror

E. Waks et al., Nature 420, 762 (2002)

Poissonian photon source

Single photon source

Bob- H

Bob- V

Bob- R

Bob-L

Alice -V

Alice -H

Alice -L

Alice -R

0

0.1

0.2

0.3

0.4

0.5

Communication rate 70KHzError rate 3%

Error correction

Privacy amplification

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Generation of Entangled Photon-Pairs with Generation of Entangled Photon-Pairs with Indistinguishable Single Photons and Linear OpticsIndistinguishable Single Photons and Linear Optics

Input :

Output :NPBS

from QD

HWP

HHV

Coincidence circuit = post-selection

SPCM

1 2A

B

SCHSH = 2.377 ± 0.18 > 2

Violation of Bell’s Inequality: = 0/90o ’ = 45/135o

= 22.5/112.5o ’ = 67.5/157.5o

Entanglement is induced by the quantum indistinguishability:NO optical non-linearity required. Ideal efficiency is ½. Only single pairs are created.

Mixed state due to g(2)(0)0 and V(0)<1.

Statetomography

D. Fattal et al., PRL 92, 037903 (2004)

Ekert 91/BBM92 QKD Systems

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Single Mode Quantum Teleportation with Single Mode Quantum Teleportation with Indistinguishable Single PhotonsIndistinguishable Single Photons

Finite visibility due to g(2)(0)0 and V(0)<1

D. Fattal et al., PRL 92, 037904 (2004)

Building block of linear/nonlinear optics quantum computation

Massive parallel indistinguishable single photon sources

(All QDs must have identical wavelength)

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Ｗｈａｔ　ｗａｓ　ｔｈｅ　ｐｒｏｂｌｅｍ　Ｗｈａｔ　ｗａｓ　ｔｈｅ　ｐｒｏｂｌｅｍ　ｗｉｔｈ　ＱＤｓｗｉｔｈ　ＱＤｓ ??

It is an “artificial atom” but not a “clean atom”.It is an “artificial atom” but not a “clean atom”.

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Atomic Physics in Semiconductor SystemsAtomic Physics in Semiconductor Systems– – Donor Nuclear Spin, Bound Electron Spin (DDonor Nuclear Spin, Bound Electron Spin (D00) and Exciton (D) and Exciton (D00X) System X) System ––

-+

+

-

+

-

neutral donor

neutral donor bound exciton

Radiative excitationand recombination

1s

2s,2p

L=0,1

L=2L=3

EMT Envelope

1 electron

2 electrons1 holeD0X

D0

Main transitionQuantumcommunication

TES

31P: Si29Si: GaAs 19F: ZnSe

simplest nuclear spin –½ (quantum memory)

Background nuclear spins can be depleted for Si and ZnSeby isotope engineering

electron spin -1/2 (quantum processor)

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Hydrogenic Spectrum of Impurity Bound Excitons Hydrogenic Spectrum of Impurity Bound Excitons in GaAs Systemin GaAs System

17D+XD0XX A0X D0X (TES)

2p+2p02p- 2s

long T2 time

Donor bound excitons in GaAs Acceptor bound excitons in GaAs

2S

1S

3S4S 5S

Tran

sitio

n en

e rgy

(meV

) R*y ionization energy: 25.9 meV

Central cell corr.: > 3.8 meV

short T2 time

Diamagnetic shift

Zeeman splitting

electron spin hole spin

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Electromagnetically Induced Transparency (EIT)Electromagnetically Induced Transparency (EIT)– Coherent Population Trapping Observed –– Coherent Population Trapping Observed –

Coherent trapping and release of optical pulses (or single photons)

Entanglement generation in remote nodes

Nonlinear interaction of photonic qubits

K.M.Fu et al., Phys..Rev. Lett. 95, 187405 (2005)

Enhancem

ent due to optical pum

ping effect, T1

probe only

dip depth andwidth determineT2*, C

Inte

nsity

, co

unts T2* = 1-3 ns

T1 = 2.6 secC* = 650 MHzP* = 16 MHz

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Coherence Time TCoherence Time T22 ~ 1 min for Nuclear Spins in Si ~ 1 min for Nuclear Spins in Si

natural linewidth fluctuating local magneticfield along Z-axis at

dipolar coupling to other nuclear spins

Spin echo CPMG -pulse

sequencedecoupling ( -pulse sequence)

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

Time (sec)

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Entanglement Distribution with Coherent State BusEntanglement Distribution with Coherent State BusP. van Loock et al, quant-ph/0510202 (2005)P. van Loock et al, quant-ph/0510202 (2005)

1. Initial states of two qubits

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

2. Dispersive light-matter interaction

(~0.01 : small phase shift)

4. Homodyne measurement

post-selection

detuningcavity probe

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Non-Local, Measurement-Free and Deterministic Two Qubit GateNon-Local, Measurement-Free and Deterministic Two Qubit GateT. Spiller et al, quant. Ph/0509202 (2005)T. Spiller et al, quant. Ph/0509202 (2005)

Time

displacement(beamsplitter)

controlled phase shift(reflection from cavity)

• After the entire sequence, the probe is disentangled from the qubits.No measurement and post-selection required.

• An overall phase develops proportional to area (topological phase),A desired phase shift of achieved with

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3131P:Si – Optically Active in High P:Si – Optically Active in High QQ Microcavity! Microcavity!

• Lifetime-limited atomic linewidth: 3 MHz – via Auger

recombination• Radiative lifetime: 2 ms

– via phonon assisted process

• Optimum regime for detuning is just off-resonance from atomic linewidth, but well inside bandwidth of cavity.

• Q of 6 105 for silicon microcavity already observed at Kyoto Univ. and NTT-BRL

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Nonadiabatic Coherent Trapping and Nonadiabatic Coherent Trapping and Emission of Arbitrary Single Photon PulsesEmission of Arbitrary Single Photon Pulses

ci tt e

one-side microcavity

coherent Rabifrequency (t)

Vacuum Rabifrequency g0

r

g e

control pulse (t)

atom

1. Deterministic single photon generation ,0in e pulse duration 10 ps,

quantum efficiency 99%, QM overlap 98%, no jitter, complete control of pulse amplitude

2. Single photon detector with coherent state probe after trapping

quantum efficiency 99%, no dark count,dead time 100 ps

David Fattal, Ph.D thesis (Stanford University)

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Future ProspectsFuture Prospects

• Deterministic, indistinguishable single photon generation, trapping and release

• High-speed and high-efficiency single photon detector with no dark count

• Entanglement distribution by coherent state bus• Non-local deterministic two qubit gate by coherent state bus

• Trapping and release of coherent optical pulse (or single photon)

• Entanglement distribution by single photon detection

A single donor impurity in semiconductor microcavity

Ensemble of donor impurities in bulk semiconductor

Long distance quantum communication (connected by quantum repeater)Distributed quantum computation (connected by quantum teleportation network)