Oliver Benson Humboldt-Universität zu Berlin, Nano Optics Group Thanks to: T. Aichele 1, M. Scholz, S. Ramelow, V. Zwiller

Oliver Benson

Humboldt-Universität zu Berlin, Nano Optics Grouphttp://nano.physik.hu-berlin.de

Thanks to: T. Aichele1, M. Scholz, S. Ramelow, V. Zwiller2 1CEA, Grenoble (F); 2Tech. Univ. Delft (NL)

Funding:

Single photons on demand:New light for quantum information

processing

SQE 2005, Beijing, Nov. 23-27

Einstein 1905 (Annalen der Physik): Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt

„Es scheint mir nun in der Tat, daß die Beobachtungen über die „schwarze Strahlung“, ..., und andere die Erzeugung bzw. Verwandlung des Lichtes betreffende Erscheinungsgruppen besser verständlich erscheinen unter der Annahme, daß die Energie des Lichtes diskontinuierlich im Raume verteilt sei. ... es besteht dieselbe aus einer endlichen Anzahl von in Raumpunkten lokalisierten Energiequanten, welche sich bewegen, ohne sich zu teilen und nur als Ganze absorbiert und erzeugt werden können.

Photoelectric Effect:Ekin=h-W

e-


• Introduction and Overview

• Single Photon Sources based on Quantum Dots

• Multi-Photon Sources

• Multiplexed Quantum Cryptography

• Demonstration of Deutsch-Jozsa Algorithm

• Summary & Outlook

Outline


Motivation

Prerequisites for Quantum Computing*

1. A scalable physical system with well characterized qubits

2. The ability to initialize the state of the qubits to a simple initial state

3. Long relevant decoherence times, much longer than gate operations

4. A universal set of quantum gates (single and two-qubit gates)

5. A qubit-specific measurement capability

*David DiVicenzo, Fortschr. Phys. 48, 9-11, p. 771 (2000)

Quantum information processing relies on the controlled manipulation of qubits.

+|> =


Motivation

Why photons?

• They interact very weakly with the environment (kbT<<h in the visible).

• They are quick (v = c, “flying qubits”).

• They can be easily detected (commercial detectors with >70% efficiency).

Any problems?• They interact only very weakly with each other.

• They are difficult to store (flying qubits!).

For the moment: Photon as tools to transfer quantum information from

one place to another (quantum cryptography, teleportation)

or among different quantum systems (quantum interfaces)

Future: Proposals and first steps towards optical quantum

computing

[Knill, Laflamme, Milburn, Nature 409, 46 (2001); P. Walther, et al.,

Nature 434, 169 (2005); O'Brien, et al. Phys. Rev. Lett. 93, 080502 (2004);

Okamoto et al. quant-ph/0506263 ].


SPS with 100% efficiency

SPS with 25% efficiency

Introduction

Single photons from attenuated light?

• Attenuation of a light pulse does not change the Poissonian photon statistics.

• Attenuted light pulses only mimick real single photon sources.

• There is always a finite probability to find more than one photon per pulse

0 1 2 30.00

0.25

0.50

0.75

1.00

Pro

bab

ilit

y

Number of photons

Weak pulse with <n> = 0.25


1. Coherent evolution (STIRAP and cavity QED)Atoms/ions in cavities

Methods to Generate Single Photons on Demand

Pu

mp

5P 3/2

5S 1/2

ST

IRA

P

Ato

m-c

avi

tyco

upl

ing

Dec

ay

|e ,0

|g ,1

A. Kuhn et al., Phys. Rev. Lett. 89, 067901 (2002)A. Kreuter et al., Phys. Rev. Lett. 92, 203002 (2004)W. Lange et al., Nature 431, 1075 (2004)C. Maurer et al., New Journal of Physics 6, 04 (2004)P. Bertet et al., Phys. Rev. Lett. 88, 143601 (2002)B. Varcoe et al., Nature 403, 743 (2000)



2. Projection (down-conversion and cavity QED)• parametric down-conversion in a non-linear crystal

• Rydberg atoms

C. K. Hong et al., Phys. Rev. Lett. 59, 2044 (1987)P. Kwiat et al., Phys. Rev. Lett. 24, 4337 (1995)G. Weihs et al., Phys. Rev. Lett. 81, 5039 (1998)B. Varcoe et al. Nature 403, 743 (2000)



3. Spontaneous emission (single emitters)• atoms, molecules, quantum dots, defect centers

• optical, electrical and STIRAP excitation

pulsed,(non-resonant)

excitation

spontaneoussingle photon

emission

relaxation

decay

QD: Kim et al., Nature 397, 500 (1999) Michler et al., Science 290, 2282 (2000) Santori et al., PRL 86, 1502 (2001) Yuan et al., Science 295, 102 (2002)

DC: Kurtsiefer et al., PRL 85, 290 (2000) Beveratos et al., PRA 64, 061802(R) (2001)

M: Brunel et al., PRL 83, 2722 (1999) Lounis & Moerner, Nature 407, 491 (2000)








Outline


10nm

[110]

10nm

[110] AFM

Contains ~10000 atoms

InP dots grown on GaInP

Quantum Dots

K. Georgsson et al., Appl. Phys. Lett. 67, 2981 (1995)

Transmission electron microscope images Atomic force microscope image


Quantum Dots

Biexciton

Exciton

Ground state(empty QD)

Photoluminescence image of a set of InP quantum dots

n= 1

n= 2

n= 1

n= 2

G a InP InP G a InP

Ene

rgy

Size : O (10 nm )

Exc ito n in a Q D: Biexc ito n:

Photoluminescence of an ensemble of InAs quantum dots

exciton biexciton


Specific advantages of single quantum dots

Quantum Dots

• Stability• Compatible with chip-technology• Wide spectral range• Electrical Pumping• High repetition rate• Strong interactions “available”

Specific disadvantages of single quantum dots

• Low temperature operation• Device production yield• Decoherence• Efficiency

TEM

AFM


Experimental Setup

Sp

ectr

og

rap

h

Coincidence counter

Las

er( c

w o

r p

uls

ed)

Filter

Start-APD

Sto

p-

AP

D

CC

D

Michelsoninterferometer

Dichroicmirror

Hanbury Brown-Twisscorrelator

Liquid HeCryostat

(4 K)

Sample

g1 g2SPS


Experimental Setup


InP Quantum Dots in GaInP

Si substrate

EpoxyAl mirror (200 nm)

GaInP (400 nm)InP QDs

Si substrate

EpoxyAl mirror (200 nm)

GaInP (400 nm)InP QDs

• Emission around 690 nm (@ maximum detection efficiency of Si detectors)

• Lifetime around 2 ns

• Dot density: 108 cm-2 through 2 nm bandpass filter

• Linewidth around 100 µeV

670 675 680 685

without filtering

with 2-nm bandpass filter

Inte

nsi

ty (

a.u

.)

Wavelength (nm)


-1 0 10

50

Nu

mb

er o

f co

inci

den

ces

(raw

dat

a, a

.u.)

Delay time (ns)-40 -20 0 20 40

0

50

100

150

Nu

mb

er o

f co

inci

den

ces

(raw

dat

a, a

.u.)

Delay time (ns)

-40 -20 0 20 400

Nu

mb

er o

fco

inci

den

ces

(arb

. un

its)

Delay time (ns)

pulsed

Intensity Correlation Measurements

V. Zwiller, et al., Appl. Phys. Lett. 82, 1509 (2003)

cw

• Central peak vanishes nearly completely

generation of only one photon per pulse

• Single photon generation observed up to 40 K

ZOOM


Coincidence counter

-40 -20 0 20 400

Co

rrel

atio

ns

(arb

. un

its)

Delay time (ns)

Wave and Particle Aspects

Start-APD

Sto

p-

AP

D

Pulse counter(DAC)

200 250 3000

25

50

Nu

mb

er o

f co

un

ts p

er 1

0 m

s

Time after starting the measurement (s)

Taylor-experiment (1906)

Path length difference

T. Aichele, et al., AIP proc. Vol. 750, 35 (2005)V. Jacques, et al. Eur. Phys. J. D 35, 561 (2005)








Outline


Cascaded Emission

Young et al., PRB 72, 113305 (2005)

biexciton

exciton

ground state(empty QD)

n= 1

n= 2

n= 1

n= 2

G a InP InP G a InP

Ene

rgy

Size : O (10 nm )

Exc ito n in a Q D: Biexc ito n:exciton biexciton

-

+

+

Benson & Yamamoto, PRL 84, 2513 (2000)


Cascaded Emission

670 675 680 685 690

250

5000

500

1000

15000

2500

5000

Wavelength / nm

ExcitonInte

nsity

/ a.

u.

Biexciton

Triexciton

40 60 800

25

50

300

400

500

200

400

600

t / ns

Exciton

Triexciton

Cor

rela

tions

/ a.

u.

Biexciton

Spectra and anti-bunching in photon cascades:


Cascaded Emission

Coincidence counter

Start-APD

Sto

p-

AP

D

biexc.

exc.biexciton

triexciton

-40 -20 0 20 400

50

100

Co

inci

den

ces

(a.u

.)

Delay time (ns)

exciton

biexciton

Correlation measurements reveal dynamics of multiphoton cascades

J. Persson et al., Phys. Rev. B 69, 233314 (2004) D. V. Regelmann, et al. Phys. Rev. Lett. 87, 257401 (2001)E. Moreau et al., Phys. Rev. Lett. 87, 163601 (2001)A. Kiraz et al. Phys. Rev. B 65, 161303 (2002)

-20 -10 0 10 20800

1000

1200

1400

Co

inci

den

ces,

a.u

.

Delay time (ns)


Single Photon Multiplexing

Separating spectral lines using a Michelson interferometer

One quantum emitter acts as two independent single photon sources.D e lay=

1 /2 R ep .R a te

Delaying the two photons by half the excitation repetition time doubles the photon rate.

-40 -20 0 20 400

10

20

30

406.6 ns

Co

inci

den

ces

(a. u

.)

Delay time (ns)








Outline


Quantum Cryptography:the BB84 Protocol

Alice Bob

Quantum channel

Classical public channel:

1 0

1 0

Eve Eve cannot copy the photon(no cloning theorem)

Bennett, Brassard, Proc. IEEE Int. Conf. on Computers, Systems & Signal Processing (1984), First realization with QDs: Waks et al., Nature 420, 762 (2002)


BB84 Protocol

• Alice sends randomly polarized photons (0, 45, 90 or 135°) to Bob.

• Bob randomily measures in the straight or diagonal base.

• Bob keeps his results secret.

• Bob publically tells his measurement bases (not the results!). Alice publically tells him if he chose the right base.

• Alice and Bob keep only the results with the common bases.

• They both have now a common and random key: 1 1 0 0 1 ...


M i c h e l s o nD e l a yF r o mS i n g l e P h o t o nS o u r c e A L I C E E O M Q u a n t u m C h a n n e lw 1

w 2 M i c h e l s o n B O BD e t e c t i o nE O M A n a l y z e r

E O MF r o mS i n g l e P h o t o nS o u r c e A L I C E E O M

Q u a n t u m C h a n n e lw 1

w 2 M U X D E M U XM i c h e l s o n M i c h e l s o nM i c h e l s o n D e t e c t i o n

B O B

E O ME O M D e t e c t i o n

A n a l y z e r

M iche lson

D e lay

F romS ing le P ho ton

S ource

ALIC E

E O M

Q uantum C hannelw 1

w 2

M iche lson

BO B

D etectionE O M

A na lyzer

E O MF rom

S ing le P ho tonS ource

ALIC EE O M

Q uantum C hannelw 1

w 2 M U X D E M U X

M iche lson M iche lsonM iche lson

D etection

BO B

E O M

E O M D etection

A na lyzer

Multiplexed Quantum Cryptography


Multiplexed Quantum CryptographyBB84 Protocol

EO M EO M AP D

From sing lephoton source

Alice Bob

Polarizer Analyzer

Alice´s original data Encoded image Bob´s decoded image

Transmission to Bob: 30 successfull counts/s at a laser modulation of 20 kHz

Similarity between Alice´s and Bob´s keys: 95%

T. Aichele, G. Reinaudi, O. Benson, Phys. Rev. B, 70, 235329 (2004)








Outline


Deutsch-Jozsa-Problem

0

1

0

1

1

0

0

0

1

1

f01 f10 f00 f11

Counterfeighterproblem

Mathematical problem:constant or balanced function?


U

x,

1

0

y x,y0 1

H

H

y

x

x,x,y2

y f(x)

x

f

H

y3

21 x

Quantum circuit: Four possible functions f(x):

f00 f11 f01 f10

f(0) 0 1 0 1

f(1) 0 1 1 0

constant balanced

|<1|x>|2 0 0 1 1

• possibility to decide, if f(x) is balanced or constant using only one evaluation of f(x)!

• any classical apparatus would need at least two evaluations of f(x)!

Deutsch-Jozsa-Algorithm


qubit |x>: spatial modes of the photon

qubit |y>: polarization of the photon

• photon state behind polarizer

|y>=( |0> - |1> )/21/2

= Hadamard gate for |y>

• BS1 and BS2 representHadamard gates for |x>

Implementation of Uf by /2 plates flipped in the beam.

f00 f11 f01 f10

/2 at

{|x>= |0>}

out in out In

/2 at

{|x>= |1>}

out in In out

Realization with Linear Optics

Polarisator

x1

=x

BS1= 0

0

21 xBS2

Uf

1

Polarizer

E. Brainis et al., Phys. Rev. Lett. 90, 157902 (2003)M. Michler et al., Phys. Rev. Lett. 84, 5457 (2000)S. Takeuchi, Phys. Rev. A 62 , 032301 (2000) N. J. Cerf et al., Phys. Rev. A 57,1477 (1998)

Singlephoton


• distinguishability of balanced from constant function in a single quantum computation with a probability of 85%M. Scholz, S. Ramelow, T. Aichele, O. Benson, submitted

• well controllable single photonic qubit • feasibility of upscaling and use in LOQC

D. Fattal, E. Diamanti, K. Inoue, Y. Yamamoto, PRL 92, 037904 (2004)

Deutsch-Jozsa-Algorithm: Experimental Results


from source

BS

PBS

PBS

phasenoise

BS

Hb -Vb

Ha -Va

Hb -Va

Ha -Vb

Hb -Vb

Ha -Va

/2

Demonstration of Algorithms and Influence of Decoherence

• Scholz, et al., submitted • M. Mohseni, et al., PRL 91,

187903 (2003)• M. Bourennane, et al. PRL 92,

107901(2004)

Single photon sources based on single quantum dots can be used to demonstrate and test influence of noise and decoherence on qubits in quantum algorithms.

E.g.: Encoding of qubits in states that are insensitive to a certain class of (phase) noise








Outline


Optical quantum computing

based on single photons and

linear optics requires triggered

indistinguishable photons

[Knill, Laflamme, Milburn, Nature

409, 46 (2001)].

Realization of indistinguishable

photons and entangled photon

pairs in recent experiments by

Yamamoto

[Santori, et al., Nature 419, 594

(2002)]:

Quantum Computing with Single Photons


Demonstration of multiplexed quantum cryptography and realization of a quantum computing algorithm

Single photon sources based on quantum dots are a reliable tool for quantum information processing

Efficient LOQC based on qdot sources according to KLM [E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2000)] can be envisioned

Realization of indistinguishable photons (ancillas)Entangled photon pairs on demandImplementations in controlled experiment

Next stepsReliable sources of multiple ancilla states Formation of entanglement using cascaded emissionStorage of single photons from single quantum dots

Summary and Outlook

Documents

Oliver Benson Humboldt-Universität zu Berlin, Nano Optics Group Thanks to: T. Aichele 1, M. Scholz, S. Ramelow, V. Zwiller