Single Photon Generation &

Application in Quantum Cryptography

• Single Photon Sources

• Photon Cascades

• Quantum Cryptography

Single Photon SourcesMethods to Generate Single Photons on Demand

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)

10nm

[110]

10nm

[110] AFM

Contains ~10000 atoms

InP dots grown on GaInP

Single Photon SourcesQuantum Dots

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

Transmission electron microscope images Atomic force microscope image

Single Photon SourcesQuantum Dots

Biexciton

Exciton

Ground state(empty QD)

Photoluminescenceimage of a set of InP quantum dots

n=1n=1n=1n=1

n=2n=2n=2n=2

n=1n=1n=1n=1

n=2n=2n=2n=2

GaInP InP GaInPGaInP InP GaInPGaInP InP GaInPGaInP InP GaInP

EEEE nn nnee ee

rr rr gg ggyy yy

SSSSiiiizzzzeeee:::: OOOO((((11110000 nnnnmmmm))))

Exciton in a QD:Exciton in a QD:Exciton in a QD:Exciton in a QD: Biexciton:Biexciton:Biexciton:Biexciton:

Photoluminescence of an ensemble of InAs quantum dots

exciton biexciton

Specific advantages of single quantum dots

Single Photon SourcesQuantum 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• Non-uniformity• Device production yield• Decoherence• Efficiency AFM

Single Photon SourcesExperimental Setup

Spec

trog

raph Coincidence

counterLa

ser

( cw

o rpu

lsed

)

Filter

Start-APD

Stop

-A

PD

CC

D

Michelsoninterferometer

Dichroicmirror

Hanbury Brown-Twisscorrelator

Liquid HeCryostat

(4 K)

Sample

g1 g2SPS

Single Photon SourcesExperimental Setup

Single Photon SourcesInP 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 1 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

nsity

(a.u

.)

Wavelength (nm)

-1 0 10

50

Num

ber o

f coi

ncid

ence

s(r

aw d

ata,

a.u

.)

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

0

50

100

150

N

umbe

r of c

oinc

iden

ces

(raw

dat

a, a

.u.)

Delay time (ns)

-40 -20 0 20 400

Num

ber o

fco

inci

denc

es (a

rb. u

nits

)Delay time (ns)

pulsed

Single Photon SourcesIntensity 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

Cor

rela

tions

(arb

. uni

ts)

Delay time (ns)

Single Photon SourcesWave and Particle Aspects

Start-APD

Stop

-A

PD

Pulse counter(DAC)

200 250 3000

25

50

Num

ber o

f cou

nts

per 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)J. T. Höffges, et al. Opt. Comm., 133, 170–174 (1997)

Photon Cascades Cascaded Emission

biexciton

exciton

ground state(empty QD)

n=1n=1n=1n=1

n=2n=2n=2n=2

n=1n=1n=1n=1

n=2n=2n=2n=2

GaInP InP GaInPGaInP InP GaInPGaInP InP GaInPGaInP InP GaInP

EEEE nn nnee ee

rr rr gg ggyy yy

SSSSiiiizzzzeeee:::: OOOO((((11110000 nnnnmmmm))))

Exciton in a QD:Exciton in a QD:Exciton in a QD:Exciton in a QD: Biexciton:Biexciton:Biexciton:Biexciton:exciton biexciton

σ-

σ+σ−

σ+

Different energy of exciton, biexciton, triexciton, ... due to Coulomb interaction

670 675 680 685 690

250

5000

50010001500

0

2500

5000

Wavelength / nm

ExcitonInte

nsity

/ a.

u.

Biexciton

Triexciton

Photon Cascades Cascaded Emission

670 675 680 685 690

250

5000

50010001500

0

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:

Photon Cascades Cascaded Emission

Coincidence counter

Start-APD

Stop

-A

PD

biexc.

exc.biexciton

triexciton

-40 -20 0 20 400

50

100

Coi

ncid

ence

s (a

.u.)

Delay time (ns)

exciton

biexcitonCorrelation 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

Coi

ncid

ence

s, a

.u.

Delay time (ns)

Photon Cascades Single Photon Multiplexing

Separating spectral lines using a Michelson interferometer

One quantum emitter acts as twoindependent single photon sources.Delay=

1/2 Rep.Rate

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

Coi

ncid

ence

s (a

. u.)

Delay time (ns)

Quantum CryptographyThe 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)

Quantum CryptographyBB84 Protocol

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

• Bob randomly 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 ...

Michelson

Delay

FromSingle Pho tonSource

ALICE

EOM

Quantu m Channelw1

w2

Michelson EOMAnaly

EOMFromSinglePho tonSource

ALICE EOM

Quantu m Channelw1

w2 MUX DEM UX

Michel son Miche lsonMichelson EOM

EOM

Analyz

Michelson

Delay

FromSingle Photon

Source

ALICE

EOM

Quantum Channelw1

w2

Michelson

BOB

DetectionEOM

Analyzer

EOMFromSingle Photon

Source

ALICEEOM

Quantum Channelw1

w2 MUX DEMUX

Michelson MichelsonMichelson

Detection

BOB

EOM

EOM Detection

Analyzer

Quantum CryptographyMultiplexed Quantum Cryptography

Quantum CryptographyMultiplexed Quantum Cryptography

EOM EOM APD

From singlephoton 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)