Triple photon quantum correlations

Benoît Boulanger(1)

Audrey Dot(1), Kamel Bencheikh(2), Ariel Levenson(2), Patricia Segonds(1), Corinne Félix(1)

(1)Institut Néel CNRS/UJF, Grenoble, France(2)Laboratoire de Photonique et Nanostructures CNRS, Marcoussis,

France

FRISNO - AussoisMarch 28 – April 1st, 2011

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OUT LINE

Introduction & motivation

Generation of triple photons

Coherence study of triple photons

Conclusion & perspectives

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OUT LINE

Introduction & motivation

Generation of triple photons

Coherence study of triple photons

Conclusion & perspectives

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PROBLEMATICS

Generation, study and manipulation of triple photons

Crystal non linear optics

Quantum optics

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1

02

3

0 1 2 3

(3)

1

3

2

0

Four-Wave-MixingStimulated Raman ScatteringKerr effectTwo Photon Absorption

THIRD ORDER NON LINEAR PARAMETRIC INTERACTIONS

12

3

0

1 2 3 0

(3)

0 1

3

2

3

3

3(3)

Third Harmonic Generation

Triple Photons Generation

ħ0 + ħ1 = ħ2 + ħ3

ħ3 = ħ + ħ + ħ

ħ1 + ħ2 + ħ3 = ħ0

Third order Parametric Fluorescence

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INTEREST OF GENERATING TRIPLE PHOTONS

Fundamental interest in quantum optics:New state of light (GHZ Greenberger, Horne, Shimony, Zeilinger,

Am. J. Phys. 1990 ) ; 3 photons created from the splitting of a single photon exhibit specific quantum correlations different than those of twin photons (Breitenbach, Schiller, Mlynek, Nature 1997).

Fundamental interest in non linear optics :Specific properties of triple photons generation.

Potential interest in quantum cryptography and information : possibility to use two keys instead of one (twin photons), protocole of announced pairs.

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WIGNER FUNCTION OF TRIPLE PHOTONS

Banaszek, Knight, Phys. Rev. A (1997)

Bencheikh, Douady, Gravier, Levenson, Boulanger, Compt. Rend. Phys. Acad. Sciences (2007)

1ˆ( , ) 2 2

2ipxW q p e q x q x dx

.

The case of a degenerate three-photon quantum state:

2 1/ 2

,1 , 10 1 0

( ) ,3!

l

nn nir

l l kn l k

t e e u u n k kn

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Simultaneous production of 2 pairs of photons(Pan, Daniell, Gasparoni, Weihs, Zeilinger, PRL, 2001)

New tests of Bell theorem, but : Observation by destructive selection

forbids any manipulation a posteriori Conditional protocol (small amount of events)

ALTERNATIVE FOR TRIPLE PHOTONS GENERATION

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Interest in producing prepared triple photons states :

at first, a challenge in non linear optics !!!

OUT LINE

Introduction and motivation

Generation of triple photons

Coherence study of triple photons

Conclusion & perspectives

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SPECTRAL SPREADING OF THIRD ORDER PARAMETRIC FLUORESCENCE

Energy conservationħ0 - ħ1 - ħ2 - ħ3 = 0

Momentum conservationħk0 - ħk1 - ħk2 - ħk3 = 0

2 equations and 3 quanta {ħ1, ħ2, ħ3}

Continuum of solutions

KTP crystalPump : 532 nmDirection of propagation : X

Fève, Boulanger, Douady, Phys. Rev. A (2002)

NB : 2 equations and two quanta to fixe for twin photons.

WEAK AMPLITUDE OF THE THIRD ORDER PARAMETRIC FLUORESCENCE

Rate of transition

2

12

3

00 1

3

2

2

321 0,0,0ˆ,,2

iHkkkW

0,0,0

321 ,, kkk

2 5 22(3) 1 2 2 2

2 02 2 3 60 0 3 1 2 3

288( )

8

n n d dcP P L F mismatch

n n

Radiated power in the mode k2

Oxide crystals 10-17 W 10-21 m2/V2 100 GW/cm2 1

Chalcogenide glasses 10-22 W 10-18 m2/V2 1 GW/cm2 10-6 Polymers

P2 Triple photons << 10-9 W of Twin photons

THE IDEAL CRYSTAL FOR TRIPLE PHOTONS GENERATION …

… IS NOT YET BORN!

Centrosymmetric structure

High damage threshold > 100 GW/cm2

High (3) nonlinearity > 10-17 m2/V2

Phase-matchable, i.e. birefringence n > 10-2

10-9 W of Third order parametric fluorescence

NECESSITY TO STIMULATE THE PHOTON SPLITTING

1

3

2

12

3

0

1 2 3 0

(3)

0

3

2

3

2

Choice of a double stimulation

One photon detected at λ1

One generated triple {λ1, λ2, λ3}

λ0- = 532 nm

λ1+

= 1449 nm

λ2+

= λ3- =1681 nm

Phase-matching in KTPfor the generation of triple photons

around 1500 nm

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CLASSICAL THEORY OF TRIPLE PHOTONS GENERATION

Fève, Boulanger, Douady, Phys. Rev. A (2002)Interaction length (a.u.)

Inte

nsiti

es (

W/c

m²)

2 3I I

1I

0I

20 31 01 1 1

0

231 01 1 1

1

2 22,3 31 01 2,3 1 1 1 1

2,3

, 0 |1,

|1,

, 0 . |1 |1,

I Z cn a L mI Z L

sn a L mI Z L

I Z sn a L m cn a L mI Z L

sn(u/m), cn(u/m) : Jacobi elliptic functions

Energy transferbetween photons populations

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Nd:YAG

20 ps -10 Hz x3 OPG

420 - 2300 nm

1679 nm

max = 100 µJ/pulse

32

x2532 nm

max = 1 mJ/impulsion

Optical Delay 0

Power Meter

lenses

Glan-Taylor

2

2

Power Meter prism

32

0

1

KTPx-cut

25 mm

filters

HTHR 532 nm

32

High intensities : 100 GW/cm² sub-nanosecond pulses, focalised beams

Perfect phase-matching tunability of the source

PIONEER EXPERIMENT OF TRIPLE PHOTONS GENERATION

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1650 1655 1660 1665 1670 1675 16801450

1460

1470

1480

1490

1500 CalculMesures

Long

ueur

d'o

nde

géné

rée

1 (n

m)

Longueur d'onde d'injection 3=

2 (nm)

Accord de phase (pompe 4=532 nm)

1 20 3

1 1 1 1

Parametric signature

(nm)32

(nm

)

Phase-matching obtained at : 532 nm(o) 1473.5 nm(e) + 1665.2 nm(e) + 1665.2 nm(o)

SPECTRAL PROPERTIES

Gen

erat

ed e

nerg

y at

(a

.u)

(nm)

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1665.21665.2((

-) -)

1665.21665.2((

+)+) 1473.51473.5((

+) +)

Number of pump photons (532 nm) : 2.0x1015

Number of stimulation photons (1665.2 nm) : 8.4x1014

First experiment of triple photons generation

NUMBER OF GENERATED TRIPLES

3.3x1013 triple photons per pulse

Douady & Boulanger, Optics Letters (2004)

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NEW TRIPLE PHOTONS GENERATOR

Nd:YAG1064 nm-20 ps

x3

x2

OPG accordable420 – 2300 nm

KTPX-cut

λ0 = 532 nm

λ0

λ2=λ

3

λ1 λ1

1064 nm-150 ps

Home-made OPO (fixed wavelength)

L

ξ 1

ξ0

ξi=ξ2+ ξ3

1064 nm(2)

λ/2

(2) (2)F

KTP KTP KTP λ2=λ3=1665.2 nm

High intensities

Possibilityof resonant interactions

λ2=λ3=1665.2 nm

15/39

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VALIDATION OF THE CLASSICAL MODEL

ξ0 = 4.5 mJξi = 182 μJ

ξ0 = 4.5 mJL = 13 mm

ξi = 182 μJL = 13 mm

Gravier & Boulanger, JOSA B (2008)

3 223 0 1 11 1

1

|1²( )

2 2

sn a L mwL

The calculation under the UPA gives a surestimation of a factor 500 !

2(3) 21 0 2 3( ) (0) (0) (0)effL L

<<

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OUT LINE

Introduction & motivation

Generation of triple photons

Coherence study of triple photons

Conclusion & perspectives

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PROTOCOL OF CORRELATIONS STUDIES

Recombinations @ 2 photons @ 3 photons

Delay 2

Delay 3

(3)(2)

1 1474e nm

2 1662e nm

3 1662o nm

1 2 3e e o 1 3

e o 2 3e o

Delay 1

G

Spectral analysis

( )GI f 1 2 3 0

2 31, , )(I f Temporal analysis

at

1 2 3 0

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(3)Stimulated generation

Triple photons + stimulating fields

Sum field Sum field

Following Izo Abram et al in the case of twin photons PRL (1986)

• Quantum calculations Quantization of each electromagnetic field

LPNQUANTUM MODELISATION OF THE TRIPLE FIELDS

• Description of the photons evolution in the non linear crystal by their non linear momentum operator :ˆ

NLG

creation and destruction of a photon

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Non linear momentum evolution of the operators and for all the fields in the crystal, since :

ˆ( , )a z

• Access to the 3 quantum field operators in each point of the crystal

ˆ ( , )a z

1 2 3ˆ ˆ ˆ, and

outgoing photons generated in each mode of the triplet

sum fields issued from the 2 and 3 fields recombination

QUANTUM EXPRESSION OF THE TRIPLE FIELDS

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NUMBER OF GENERATED PHOTONS

np

(3)medium

n20

n30

n2(L)

z0 L

n1(L)

n3(L)

n20

n30

Quantified recombined field, given by the integration of its creation and annihilation operators at each frequency :

• 3-photons recombined field :

or

EXPRESSION OF THE RECOMBINED FIELD

Ap

(3)medium

z0 L1

n20

n30

1 1ˆ ( )L

2 1ˆ ( )L

3 1ˆ ( )L3ˆ (0)

2ˆ (0)

(3)medium

z0 L2

2ˆ ( )sum L

(2)medium

z0 L2

2ˆ ( )sum L

• 2-photons recombined field :

Hence the spectrum of the recombined field:

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3-PHOTON RECOMBINATION

Outgoing photons spectra

(3)

nm

nm

nm

nm

nm

(3)

L L

N2=107

N3=107

N0=1015

Triple photons

Classical Background

Dot, Bencheikh, Boulanger, Levenson PRA, to be published

OUT LINE

Introduction & motivation

Generation of triple photons

Coherence study of triple photons

Conclusion & perspectives

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CONCLUSION

Theory & experiments of triple photons generation from a third order parametric generation

Protocols & calculations showing the quantum correlations

Corresponding experiments in progress

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PERSPECTIVES

Spontaneous triple photons generation in optical fiber using modal phase-matching

! Aaaaaaaaaaaaaaaaaaaaaaa

Measurement of the Wigner functions Quantum information based on triplets

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Third order parametric fluorescence ratefrom 1 W input power at 532 nm

in a one-meter optical fiber

!

Twin photons

FROM TWIN TO TRIPLE PHOTONS

A new storyfor the next 30 years?

0

123

pq

2

Strong impact on :

-Classical nonlinear optics – OPO

-Quantum mechanics and cryptography Aspect, Grangier, Roger, PRL (1981)

Triple photons

An exciting storyover the past 30 years!

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CALL FOR PAPER

Nonlinear Optics (NLO)17-22 July 2011

Marriott Kauai Beach ResortKauai, Hawaii, USA

Submission deadline 15 April 2011

Including a Symposium Celebrating the 50th Anniversary of Nonlinear Optics

Bloembergen, Harris, Yariv, Shen, Byer, …

General chairsDaniel Gautier & Takunori Taira

Program chairsBenoît Boulanger & Steven Cundiff

The Optical Society of America

(2)0 0

0 0

. . . ( )( ) effi E

n

22

4

k

0

2 22 2 2

2 2

22 42 2 2 4

2 4

2

| ( ) | sinh ( ) sinh ( )

sinh ( ) cosh ( ) sinh ( ) sinh ( )2

n m

n

n mn m

nn n n n

n n n

E L L

kL L L L

520 525 530 535 540 545 lambda (nm)

|E

|2 (a

.u.)

SAME PROTOCOLE PREVIOUSLY USED FOR TWIN PHOTONS

Dayan, Phys. Rev. A (2007)

Abram et al, PRL (1986)

ω1ω0 (2)

ω2

(2) ω

22

4

k

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2(2) (2)

, ,

2(2),1

(3) (3)1

cos,

,

I IIeff i eff i

quadi ii i i

eff

knI Z L

I Z L

Cas

cad

ing

rate

(%

) ( . .)(3)

a ueff

Douady & Boulanger, J. Opt A, 2005

SUPPRESSION OF THE SECOND ORDER CASCADING IN KTP

.

Partially non degenerate three-photon quantum state : 1 ≠2=3

Photons in the mode at 1 Photons in the mode at 2=3

WIGNER FUNCTION OF TRIPLE PHOTONS

Bencheikh, Douady, Gravier, Levenson, Boulanger, Compt. Rend. Phys. Acad. Sciences (2007)

RUTILE TiO2 : A PROMISING CRYSTAL FOR TRIPLE PHOTONS GENERATION

Gravier & Boulanger, Optics Express (2006)

THG in KTP :

2

2 2

3 3/ 7.5eff eff

TiO KTPn n

1618 1618 1618 539.3o e e onm nm nm nm

THG in TiO2 : 1840 1840 1840 613.3o e e onm nm nm nm