Experiments With Entangled Photons Moura Escher , Cesar Raitz Jr., Daniel Schneider Tasca, Diney Soares Ether Jr., Gabriela Barreto Lemos, Malena Osorio Hor Meyll, Mario Leandro Aolita,

Experiments With Entangled Photons

Paulo Henrique Souto RibeiroInstituto de Física - UFRJ

Ninth J. J. Giambiagi WinterSchool – Part A Buenos Aires

July/August 2006

Quantum Optics Group at IF - UFRJ

Group membersExperiments:Prof. Paulo Henrique Souto Ribeiro Prof. Stephen Patrick Walborn

Theory:Prof. Luiz DavidovichProf. Nicim ZaguryProf. Ruynet Matos FilhoProf. Fabricio Toscano

Msc and PhD students: Adriana Auyuanet Larrieu, Adriano H. de Oliveira Aragão, Alejo Salles, Bruno de Moura Escher , Cesar Raitz Jr., Daniel Schneider Tasca, Diney Soares EtherJr., Gabriela Barreto Lemos, Malena Osorio Hor Meyll, Mario Leandro Aolita, Rafael Chaves.

UFRJ

UFMG

USP-SÃO PAULO

UFAL

UFF

Outline:Part I

-Simultaneity in parametric down-conversion-Violation of a classical inequality-Consequences of simultaneity: localized one-photon state,the Hong-Ou-Mandel interferometer, measurementof the tunneling time

Part II

-Spatial coherence and partial coherence-Double-slit interference with twin photons-The transfer of the angular spectrum-Consequences of spatial correlations: deBroglie wavelength

and spatial anti-bunching-Proof of non-separability and Bell’s inequalities

Part III

-Polarization entanglement: generation and detection-Violation of Bell’s inequality, Entanglement measurement-Quantum Criptography-Entanglement decay

Parametric Down-conversion

Espontaneous emission

Stimulated emission

TwinPhotons

p i sω ω ω= +h h h

p i sk k k= +r r r

Parametric Down-conversion

Observation of simultaneity

Observation of simultaneity

Parametric down-conversion: quantum stateFollowing L.J. Wang – PhD thesis – Rochester - 1992

Time evolution

Time evolution operator

Time integral

Simultaneity in parametric down-conversion

Quantum state for weak interaction


Quantum state including some approximations


Calculation of expectation values

Electric field operator

( ) ( ) ( ).1 ˆ, i k r t

k kk

E r t l a e ωε ω −+ =Ω∑

r rr r

r

) r

Intensity

( ) ( ) ( ), , ,ˆ ˆ( ) ( )s i s i s iI t t E t E t tτ ψ τ τ ψ− ++ = + +

Coincidence

( ) ( ) ( ) ( ) ( )ˆ ˆ ˆ ˆ, ( ) ( )i s s s i i i i s sC t t t E t E t E t E t tτ τ ψ τ τ τ τ ψ− − + ++ + = + + + +

Simultaneity in parametric down-conversion:very simple view


Quantum state: simple version

( ) ( )( )01 2( ) 1 1ω ωψ ω ω ω ω ω ω+ −= + +∫ i si t t

i s P i s i st c vac c d d v e

Electric field operator: plane wave, almost monochromatic

( ) ( ) ( )ω ττ ω ω ++ + = ∫) ) i tE t c d a e

Coincidence

( ) ( ) ( ) ( ) ( )

( ) ( )2

, ( ) ( )

( )

τ τ ψ τ τ τ τ ψ

τ τ ψ

− − + +

+ +

+ + = + + + +

= + +

) ) ) )

) )i s s s i i i i s s

i i s s

C t t t E t E t E t E t t

E t E t t


( )

( ) ( ) ( )0 02

,

1 1ω τ ω τ

τ τ

η ω ω ω ω ω ω− + + − + +

+ + =

= +∫ i i s s

i s

i t t t i t t ti s P i s i s

C t t

d d v e e

( )( ) ( )

( ) ( )( )

1 2

1 2

0

2

1 2,

1 1

ω τ ω τω ω

ω ω

ω ωτ τ η

ω ω ω ω ω ω

+ +

+ −

×+ + =

× +

∫ ∫∫

) )i s

i s

i t i t

i s i t ti s P i s i s

d a e d a eC t t

d d v e

Plane wave pumping field ( ) ( )0ω ω δ ω ω ω→ + → − −P i s i sv

( ) ( ) ( )2

, i sii s i sC t t d e ω τ ττ τ η ω η δ τ τ−+ + = = −∫

Coincidence detection

Coincidence detection

0,0 0,5 1,0 1,5 2,0 2,5 3,00,0

0,2

0,4

0,6

0,8

1,0 = 370ps

even

ts (

norm

aliz

ed)

time delay (ns)

Measurement of time delays

=168ps

=185ps

Simultaneity in parametric down-conversion:very simple view + detection filters

( )( ) ( )

( ) ( )( )

1 2

1 2

0

2

1 221,

( )

1 1

( )ω τ ω τω ω

ω ω

ω ωτ τ η

ω

ω ω

ω ω ω ω ω

+ +

+ −

×+ + =

× +

∫ ∫∫

) )i s

i s

i t i t

i s i t ti s P i s i s

d a e d a eC

f

d

ft t

d v e

( )

( ) ( ) ( )0 02

,

1 1( ) ( ) ω τ ω τ

τ τ

η ω ω ω ω ω ωω ω − + + − + +

+ + =

= +∫ i i s si s

i s

i t t t i t t ti s P i s i s

C t t

d d fv ef e

( ) ( )0ω ω δ ω ω ω→ + → − −P i s i svPlane wave pumping field

( ) ( ) ( )22 2

( ), ω τ ττ τ η ω ηω τ τ−+ = = −+ ∫ i sis si iC t t d ef F

Simultaneity in parametric down-conversion:very simple view + detection filters

Interference filter: typical ∆λ = 10nm and using λ = 700nm

12

332( . 1 /) 8 0πω ω λλ

ω→ →∆ = ∆ →∆ = ×cGaussian radf s

12 32.7 10 1/ 116 168( ) '2 '2

ω πω ωω

∆→∆ = = → ∆ ∆ = →∆ = =

∆× <<rad s fsf t f t ps

-15 -10 -5 0 5 10 15

0,0

0,2

0,4

0,6

0,8

1,0

σ = 2.7 x 1013 rad/s

tran

smitan

ce(%

)

frequency x1013(rad/s)-200 -100 0 100 200

0,0

0,2

0,4

0,6

0,8

1,0

σ = 116 x 10-15 s

amplit

ude

time(fs)

2 ( )ωf ( )tF

Simultaneity in parametric down-conversion:very simple view + timing resolution

Localized one photon state

Localized one photon state

Violation of a classical inequality

Violation of a classical inequality

Hong, Ou and Mandel Interferometer

Hong, Ou and Mandel Interferometer:single mode approach

Beam splitter Input-output relations

1 1 2

2 2 1

ˆ ˆ ˆ

ˆ ˆ ˆ

b ta ira

b ta ira

= +

= +

( ) ( )1 2 1 2 2 1

2 21 1 2 2 1 2 1 2

ˆ ˆ ˆ ˆ ˆ ˆ

ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ

b b ta ira ta ira

irt a a irt a a t a a r a a

= + +

= + + −

For r=t

( )1 2 1 1 2 2ˆ ˆ ˆ ˆ ˆ ˆb b irt a a a a= +

( ) ( )1 1 1 2 1 2

2 21 2 2 1 1 1 2 2

ˆ ˆ ˆ ˆ ˆ ˆ


b b ta ira ta ira


= + +

= + + −

( ) ( )2 2 2 1 2 1

2 21 2 2 1 2 2 1 1

ˆ ˆ ˆ ˆ ˆ ˆ


b b ta ira ta ira


= + +

= + + −

Hong, Ou and Mandel Interferometer:single mode approach

Beam splitter Two-photon input state

1 21 1a aψ ∝

( )1 2

1 2

1 2 1 1 22

1 1 2 2

ˆ ˆ ˆ ˆ ˆ ˆ( , ) 1 1

1 1 0ˆ ˆ ˆ ˆ

a a

a a

C b b b b b b

irt a a a a

ψ∝ ∝ =

= + =

Coincidence probability

1 2

1 2

1 1 1 1 11

2 21 2 2 1 1 1 2 2

ˆ ˆ ˆ ˆ ˆ ˆ( , ) 1 1

1 1 0ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ

a a

a a

C b b b b b b


ψ∝ ∝ =

= + + − ≠

1 2

1 2

2 2 2 2 2 2

2 21 2 2 1 2 2 1 1

ˆ ˆ ˆ ˆ ˆ ˆ( , ) 1 1

1 1 0ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ

a a

a a

C b b b b b b


ψ∝ ∝ =

= + + − ≠

Hong, Ou and Mandel Interferometer

( )2.1

i s

C e ω δτ

ωδτ τ τ

− ∆∝ −∆ →

= −( )ωf

( )ωf

.c δτ

2cσω

=∆

Single-photon tunneling time

Outline:Part I


Part II



Part III


Transverse correlations





Double-slit experiments with twin photons

Double-slit experiments with twin photons

Souto Ribeiro et al, PRA 49, 4176 (1994)

Double-slit experiments

( )0 12( ) ( ) 1 cosI x I x k xµ δ= +

Van Cittert-Zernike theorem

( ) ( )( ) ( ) ( )

( )

0 2 1 0 2 112

0 0 0 0

12 2 1 2 10 0 0 0

,,

,

ki x x x y y yi Re dx dy I x y e

x x y ydx dy I x y

α

σ

σ

µ

− + −⎡ ⎤⎣ ⎦

− − =⎡ ⎤⎣ ⎦∫

∫


( ) ( )( ) ( ) ( )

( )

0 2 1 0 2 112

0 0 0 0

12 2 1 2 10 0 0 0

,,

,


x x y ydx dy I x y

α

σ

σ

µ

− + −⎡ ⎤⎣ ⎦

− − =⎡ ⎤⎣ ⎦∫

∫


( ) ( )( ) ( ) ( )

( )

0 2 1 0 2 112

0 0 0 0

12 2 1 2 10 0 0 0

,,

,


x x y ydx dy I x y

α

σ

σ

µ

− + −⎡ ⎤⎣ ⎦

− − =⎡ ⎤⎣ ⎦∫

∫

Intensity

Coherence

Intensity

Coherence

The transfer of the angular spectrumto the quantum correlation


coin

ciden

ces

position

inte

nsi

ty

position


inte

nsi

ty

position

coin

ciden

ces

position


C.H. Monken et al. Phys. Rev. A, 57, 3123 (1998).

Motivação


( )1 2 1 1i s i s i sc vac c d d vψ = + +∫ q q q q q q

( ) ( ) .+ = ∫) ) iE c d a e q ρρ q q

( ) ( ) ( )2

, ψ+ +=) )

i s i i s sC E Eρ ρ ρ ρ


( ) ( ) ( )0 22

/ 2

2

0

, . W

1 1. W ;

pi Z

i s

s iis

C const d e

const Zµ µ

− −= ×

⎛ ⎞= × +⎜ ⎟

⎝ ⎠

∫k R ρ

ρ ρ ρ ρ

ρ ρ

( ), ( )W Z v= ℑρ q Pump laser amplitude profile at distance Z

Distance betweenCrystal and detectors

0Z

The two-photon deBroglie wavelength


coin

ciden

ces

position


coin

ciden

ces

position



Two-photon detector

Spatial anti-bunching

Cauchy-Swartz inequality

Homogeneity and stationarity


For 0τ =

( )( ) ( )( )0δ 2,22,2 Γ≤Γ

( )( ) ( ) ( )τττ +=Γ t,,,, 222,2 ρIρIρρ 11

2ρρδ 1 −=

( )( ) ( )222,2 ,, ρρρρ 11 C∝Γ ( ) ( ) ( )2,2 CΓ ∝δ δ

( ) ( )0C C≤δ

-15 -10 -5 0 5 10 15

0,0

0,2

0,4

0,6

0,8

1,0

C(δ

)

δ


Nogueira et al. Phys. Rev. Lett. 86, 4009 (2001)

Generation of Spatial Anti-Bunchingwith free propagating twin beams

coin

ciden

ces

position

Is this Spatial Anti-Bunching ? No, it is not!The field is not homogeneous.

( )2

2, ⎟⎟⎠

⎞⎜⎜⎝

⎛−∝

I

I

S

SCµµρρρρ1 W

OK

( )2

2, ⎟⎟⎠

⎞⎜⎜⎝

⎛+∝

I

I

S

SCµµρρρρ1 W

Generation of Spatial Anti-BunchingWith free propagating twin beams

YY ρintoρChanges −

D. P. Caetano et al.Phys. Rev. A 68 043806 (2003)

Generation of Spatial Anti-BunchingWith free propagating twin beams :

7.0 7.5 8.0 8.5 9.0 9.5 10.00

7

14

21

28

35

sing

le c

ount

s/3s

(x10

3 )

D2 position (mm)

3.0 3.5 4.0 4.5 5.0 5.5 D1 position (mm)

Calibrating detectors

Coincidencedistributions

5 6 7 8 9 10 11 12 130

50

100

150

200

250

coin

cide

nce

coun

ts/1

0s

D2 position (mm)

5 6 7 8 9 10 11 12 130

50

100

150

200

250

D2 position (mm)

coin

cide

nce

coun

ts/1

0s

5 6 7 8 9 10 11 12 130

50

100

150

200

250

coin

cide

nce

coun

ts/1

0s

D2 position (mm)

(a)

(b)

(c)

5 6 7 8 9 10 11 12 130

50

100

150

200

250

coin

cide

nce

coun

ts/1

0s

D2 position (mm)

5 6 7 8 9 10 11 12 130

50

100

150

200

250

D2 position (mm)

coin

cide

nce

coun

ts/1

0s

(b)

(a)

D. P. Caetano et al.Phys. Rev. A 68 043806 (2003)

Non-separability

Non-separability

Non-separability

Violation of a Bell inequalitywith the transverse momentum of photons

Violation of a Bell inequalitywith the transverse momentum of photons:

Fractional momentum analyzer

FFT analyzer

1φ

2φ

Tasca et al. arXiv:quant-ph/0605061 (2006)

Fractional Fourier Transform

Optical implementation of a Fourier transform. D e ZF are conjugate planes.

π2

F

Imaging of the field in plane D onto plane ZI with unitmagnification. πF

Optical implementation of a Fractional Fourier transform ofarbitrary order φ.

φF22 sin ( / 2)z fφ φ=


Integral form

[ ]( ) ( ) ( )2 2

2

2 ' /' cot cot'i

i seni iief e e e f dsen

απρ ρ απρ α πρ α

α ρ ρ ρα

−− −= ∫ g

¡

F

When α = π/2 Ordinary Fourier transform

[ ]( ) ( ) ( )2

2 '

2

' if e f dπρ ρπ ρ ρ ρ= ∫ g

¡

F


First works related:N. Wiener. Hermitian polynomials and fourier analysis. J.

Math. Phys. MIT, 8:70–73, 1929.E. U. Condon. Immersion of the fourier transform in a

continuous of functional transformations. Proc. Nat. Acad. Sc. USA, 23:158–164, 1937.

A. L. Patterson. Zeits. Kristal, 112:22–32, 1959.

First application:Method for solving partial diferential equations 1980; V. Namias, "The fractional order Fourier transform and

its application to quantum mechanics," J. Inst. Appl. Math. 25, 241–265 (1980).


Application in physics and engeneering:

R. S. Khare. Fractional fourier analysis of defocusedimages. Opt. Comm.,12:386–388, 1974.

A. W. Lohmann, "Image rotation, Wigner rotation and the fractional Fourier transform," J. Opt. Soc. Am. A 10, 2181–2186 (1993).

Luís B. Almeida, "The fractional Fourier transform and time-frequency representations," IEEE Trans. Sig. Processing 42 (11), 3084–3091 (1994).

Haldun M. Ozaktas, Zeev Zalevsky and M. Alper Kutay. "The Fractional Fourier Transform with Applications in Optics and Signal Processing". John Wiley & Sons (2001). Series in Pure and Applied Optics.


Application in physics and engeneering:

Soo-Chang Pei and Jian-Jiun Ding, "Relations between fractional operations and time-frequency distributions, and their applications," IEEE Trans. Sig. Processing 49 (8), 1638–1655 (2001).

D. H. Bailey and P. N. Swarztrauber, "The fractional Fourier transform and applications," SIAM Review33, 389-404 (1991). (Note that this article refers to the chirp-z transform variant, not the FRFT.)


Applications in quantum optics;

Yangjian Cai, Qiang Lin, and Shi-Yao Zhu; Coincidencefractional Fourier transform with entangled photonpairs and incoherent light;Appl. Phys. Lett. 86, 021112 (2005)

Fei Wang, Yangjian Cai and Sailing He; Experimental observation of coincidence fractional Fourier transform with a partially coherent beam;Opt. Exp., 16, 6999(2006)

DS Tasca, SP Walborn, MP Almeida, PH Souto Ribeiro,CH Monken and P Pellat-Finet arXiv:quant-ph/0605061

(2006) Violation of Bell inequalities using thefractional momentum of the photon.

Outline:Part I


Part II



Part III


Polarization entanglement:generation

H V12

HV ϕψ = + ie

Kwiat et al. PRL 75, 4337 (1995)


( )HH12

VVie ϕψ = +

Kwiat et al. PRA 60, R773 (1999)White et al. PRL 83, 3103 (1999)


( )V V1

2H Hie ϕψ = +

Kwiat et al. PRA 60, R773 (1999)White et al. PRL 83, 3103 (1999)

Entangled states versus mixed states

( )12 1 2 1 2

12

ρ = ±H H V V

Mixed state

( )12 1 2 1 2

12

φ ± = ±H H V V

Entangled State

Polarization entanglement:detection

Violation of a Bell´s inequality

Bell´s inequalityBell states

Bell-CHSH inequality:

( ) ( ) ( ) ( )1 1 2 2 2 1 1 2, , , , 2α β α β α β α β= + + − ≤S E E E E

( )( ) ( ) ( ) ( )( ) ( ) ( ) ( )

, , , ,,

, , , ,

α β α β α β α βα β

α β α β α β α β

+ − −=

+ + +

C C C CE

C C C C


Polarization Bell states

( )1,2 1 2 1 2

12

H V V Hψ ± = ± ( )1,2 1 2 1 2

12

H H V Vφ ± = ±

Coincidences for φ+:

( ) ( ) ( )

( )( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( )

2

2

2

2

2

,

cos cos cos cos

cos cos sin sin

cos

α β

α β α β φ

α β α β

α β α β

β α

+ + +=

∝ +

∝ − − + − −

∝ − − + − −

∝ −

) )

) )i s

i s i s

C E E

a a H H V V

H H V V

H H H H


0 0 0 01 1 2 20 , 22,5 , 45 , 67,5α β α β= = = =Maximal violation for

( ) ( ) ( )

( ) ( ) ( )

21 1 1 1

21 1 1 1

, , cos 22.5 0.854

, , cos 67.5 0.146

α β α β

α β α β

= ∝

= ∝

;

;

C C

C C

( ) ( ) ( )

( ) ( ) ( )

21 2 1 2

21 2 1 2

0.146, , cos 67.5

, , cos 22 . 5. 0 8 45

α β α β

α β α β

= ∝

= ∝

;

;

C C

C C



( ) ( ) ( )

( ) ( ) ( )

22 1 2 1

22 1 2 1

, , cos 22.5 0.854

, , cos 67.5 0.146

α β α β

α β α β

= ∝

= ∝

;

;

C C

C C

( ) ( ) ( )

( ) ( ) ( )

22 2 2 2

22 2 2 2

, , cos 22.5 0.854

, , cos 67.5 0.146

α β α β

α β α β

= ∝

= ∝

;

;

C C

C C



( )1 20.146 0.146 0.854 0.854,0.146 0.146 0.854 0 854

2. 2

α β + − −= =

+ + +−E

( )1 10.854 0.854 0.146 0.146 2,0.854 0.854 0.146 0.146 2

α β + − −= =

+ + +E

( )2 10.854 0.854 0.146 0.146 2,0.854 0.854 0.146 0.146 2

α β + − −= =

+ + +E

( )2 20.854 0.854 0.146 0.146 2,0.854 0.854 0.146 0.146 2

α β + − −= =

+ + +E

( ) ( ) ( ) ( )1 1 2 2 2 1 1 2, , , 2, 2 2 .83α β α β α β α β= + + − = ;E E E ES

Bell´s inequality and entanglement

Bell´s inequality violation:

- Detects but does not quantifyentanglement properly;

- Some entangled states does not violate- Bipartite states- Dichotomic or dichotomized degree offreedom

Quantum state tomography

A set of measurements :

(H,H) (H,V) (V,H) (V,V) (H,D) (H,L) (D,H) (R,H)(D,D) (R,D) (R,L) (D,R) (D,V) (R,V) (V,D) (V,L)

C C C C C C C CC C C C C C C C

Density matrix reconstruction



12

ρ ρ ρ ρρ ρ ρ ρ

ρρ ρ ρ ρρ ρ ρ ρ

− − − −

− − − −

− − − −

− − − −

⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

V V VV

V V V V V VV V

V

HH HH H HH H HH HH

HH H H H H H H

HH H H H H H H

HH H H

V V V V VV V

VV V VV V VV VV VV

Measurement of entanglement

Concurrency:

0,

0ψ σ σ ψ σ

−⎡ ⎤∗= ⊗ = ⎢ ⎥⎣ ⎦

y y y

iC

i

Measurement of entanglementusing copies

Mintert, Kus, and Buchleitner, Phys. Rev. Lett. 95 260502 (2005).

( ) ( )12 01 10

2C P ψ ψ− −= → = −

Pure states

( )

1 2

1 11 1 1 11 1

Product state

Two-copies state1

0;2

0C

φ θ χ

φ θ θ ψ φ ψ θ θ θ θ− −′ ′′

=

= → = = −

=

( )

1

1 1

Maximally entangled stateI /2

Two-copies state1

I / 4 ( )4

11

4P C

ρ

ρ ρ ψ ψ ψ ψ φ φ φ φ

ψ

− − + + − − − −′

−

=

⊗ = = + + +

= → =

Experiment with twin photons

Two copies in a single photon

( )1 2 1 2H H V V1

2i

Polarization state

e ϕψ = +


( )11 2 2

1

2i b ba

Momentum s

a

tate

e ϕψ = +


( ) ( )

( ) ( )

1 2 1 2 1 2 1 2

1 2 1 2 1 2 1 2

Simultaneous entanglement in momentum and polarization1 1

;2 2

12

i iMOM POL

i i

a a e b b H H e VV

a a e b b H H e VV

ϕ δ

ϕ δ

ψ ψ

ψ

= + = +

= + +

Projection onto Bell states

( ) ( )Bell states for momentum and polarization

1 1

2 2aV bH aH bVψ φ± = ± ± = ±

( )

( )

ψ

φ

± = ± = ±

± = ± = ±

1

21

2

CNOT H V b b

CNOT H V a a

CNOT – Sagnac interferometer

aH bH aV aV

bH aH bV bV

→ →

→ →

Spatial rotations with cilyndrical lenses

Spatial rotations with cilyndrical lenses


S. P. Walborn, P. H. Souto Ribeiro, L. Davidovich, F. Mintert, A. Buchleitner, Nature 440 1022 (2006)


S. P. Walborn, P. H. Souto Ribeiro, L. Davidovich, F. Mintert, A. Buchleitner, Nature 440 1022 (2006)

Quantum key distribution – BB84








Quantum key distribution – BBM

Quantum key distribution – Eckert

Quantum key distribution withposition and momentum





D. S. Lemelle, M. P. Almeida, P. H. Souto Ribeiro and S. P. Walborn, Am. J. Phys., 74, 542 (2006)





M.P. Almeida, S.P. Walborn, and P. H. Souto RibeiroPRA 72, 022313 (2005)



Higher order alphabets-septrigits(37)







Aumento de segurança:interceptação ereenvio de 25%para 42%Aumento da taxa de transmissão:de 1bit/fótonpara 4,56bits/fóton

S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. Souto RibeiroPhys. Rev. Lett. 96, 090501 (2006)

Conclusion

Muchas gracias!

-Twin photons: simultaneity, temporal quantum correlations, transversemomentum quantum correlationsPolarization entanglement: severalapplications to quantum information –q-bits-Tool for advancing the understandingand use of entanglement

Entanglement decay

0,0

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Entanglement decay

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Entanglement decay

M. P. Almeida, F. de Melo, M. Hor-Meyl, A. Salles, S. P. Walborn, P. H. Souto Ribeiro and L. DavidovichScience 316, 579 (2007)

Entanglement decay

M. P. Almeida, F. de Melo, M. Hor-Meyl, A. Salles, S. P. Walborn, P. H. Souto Ribeiro and L. DavidovichScience 316, 579 (2007)

Experiments with Twin photons: History

1970 Author(s): BURNHAM, DC; WEINBERG, DL Title: OBSERVATION OF SIMULTANEITY IN PARAMETRIC PRODUCTION OF OPTICAL PHOTON PAIRS Source: PHYSICAL REVIEW LETTERS, 25 (2): 84-& 1970 1985Author(s): FRIBERG, S; HONG, CK; MANDEL, L Title: MEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Source: PHYSICAL REVIEW LETTERS, 54 (18): 2011-2013 1985Author(s): HONG, CK; MANDEL, L Title: THEORY OF PARAMETRIC FREQUENCY DOWN CONVERSION OF LIGHT Source: PHYSICAL REVIEW A, 31 (4): 2409-2418 19851986Author(s): HONG, CK; MANDEL, L Title: EXPERIMENTAL REALIZATION OF A LOCALIZED ONE-PHOTON STATE Source: PHYSICAL REVIEW LETTERS, 56 (1): 58-60 JAN 6 1986 1987Author(s): GHOSH, R; MANDEL, L Title: OBSERVATION OF NONCLASSICAL EFFECTS IN THE INTERFERENCE OF 2 PHOTONS Source: PHYSICAL REVIEW LETTERS, 59 (17): 1903-1905 OCT 26 1987 Author(s): HONG, CK; OU, ZY; MANDEL, L Title: MEASUREMENT OF SUBPICOSECOND TIME INTERVALS BETWEEN 2 PHOTONS BY INTERFERENCE Source: PHYSICAL REVIEW LETTERS, 59 (18): 2044-2046 NOV 2 1987 Author(s): RARITY, JG; RIDLEY, KD; TAPSTER, PR Title: ABSOLUTE MEASUREMENT OF DETECTOR QUANTUM EFFICIENCY USING PARAMETRIC DOWNCONVERSION Source: APPLIED OPTICS, 26 (21): 4616-4619 NOV 1 1987 1988Author(s): OU, ZY; MANDEL, L Title: VIOLATION OF BELLS-INEQUALITY AND CLASSICAL PROBABILITY IN A 2-PHOTON CORRELATION EXPERIMENT Source: PHYSICAL REVIEW LETTERS, 61 (1): 50-53 JUL 4 1988 Author(s): OU, ZY; MANDEL, L Title: OBSERVATION OF SPATIAL QUANTUM BEATING WITH SEPARATED PHOTODETECTORS Source: PHYSICAL REVIEW LETTERS, 61 (1): 54-57 JUL 4 1988


1990Author(s): RARITY, JG; TAPSTER, PR Title: EXPERIMENTAL VIOLATION OF BELL INEQUALITY BASED ON PHASE AND MOMENTUM Source: PHYSICAL REVIEW LETTERS, 64 (21): 2495-2498 MAY 21 1990 Author(s): RARITY, JG; TAPSTER, PR; JAKEMAN, E; et al. Title: 2-PHOTON INTERFERENCE IN A MACH-ZEHNDER INTERFEROMETER Source: PHYSICAL REVIEW LETTERS, 65 (11): 1348-1351 SEP 10 1990 Author(s): KWIAT, PG; VAREKA, WA; HONG, CK; et al. Title: CORRELATED 2-PHOTON INTERFERENCE IN A DUAL-BEAM MICHELSON INTERFEROMETER Source: PHYSICAL REVIEW A, 41 (5): 2910-2913 MAR 1 1990 1991Author(s): KWIAT, PG; CHIAO, RY Title: OBSERVATION OF A NONCLASSICAL BERRY PHASE FOR THE PHOTON Source: PHYSICAL REVIEW LETTERS, 66 (5): 588-591 FEB 4 1991 Author(s): ZOU, XY; WANG, LJ; MANDEL, L Title: INDUCED COHERENCE AND INDISTINGUISHABILITY IN OPTICAL INTERFERENCE Source: PHYSICAL REVIEW LETTERS, 67 (3): 318-321 JUL 15 1991Author(s): NOH, JW; FOUGERES, A; MANDEL, L Title: MEASUREMENT OF THE QUANTUM PHASE BY PHOTON-COUNTING Source: PHYSICAL REVIEW LETTERS, 67 (11): 1426-1429 SEP 9 19911992Author(s): KWIAT, PG; STEINBERG, AM; CHIAO, RY Title: OBSERVATION OF A QUANTUM ERASER - A REVIVAL OF COHERENCE IN A 2-PHOTON INTERFERENCE EXPERIMENT Source: PHYSICAL REVIEW A, 45 (11): 7729-7739 JUN 1 1992 Author(s): EKERT, AK; RARITY, JG; TAPSTER, PR; et al.Title: PRACTICAL QUANTUM CRYPTOGRAPHY BASED ON 2-PHOTON INTERFEROMETRYSource: PHYSICAL REVIEW LETTERS, 69 (9): 1293-1295 AUG 31 1992 1993Author(s): LARCHUK, TS; CAMPOS, RA; RARITY, JG; et al. Title: INTERFERING ENTANGLED PHOTONS OF DIFFERENT COLORSSource: PHYSICAL REVIEW LETTERS, 70 (11): 1603-1606 MAR 15 1993Author(s): STEINBERG, AM; KWIAT, PG; CHIAO, RYTitle: MEASUREMENT OF THE SINGLE-PHOTON TUNNELING TIMESource: PHYSICAL REVIEW LETTERS, 71 (5): 708-711 AUG 2 1993


Author(s): ZOU, XY; GRAYSON, T; BARBOSA, GA; et al. Title: CONTROL OF VISIBILITY IN THE INTERFERENCE OF SIGNAL PHOTONS BY DELAYS IMPOSED ON THE IDLER PHOTONS Source: PHYSICAL REVIEW A, 47 (3): 2293-2295 MAR 1993 Author(s): MONKEN, CH; BARBOSA, GA Title: TEMPORAL RESPONSE OF A FABRY-PEROT CAVITY TO A SINGLE-PHOTON WAVEPACKET Source: OPTICS COMMUNICATIONS, 99 (3-4): 152-156 JUN 1 1993 1994 Author(s): HERZOG, TJ; RARITY, JG; WEINFURTER, H; et al. Title: FRUSTRATED 2-PHOTON CREATION VIA INTERFERENCE Source: PHYSICAL REVIEW LETTERS, 72 (5): 629-632 JAN 31 1994 Author(s): RIBEIRO, PHS; PADUA, S; DASILVA, JCM; et al. Title: CONTROLLING THE DEGREE OF VISIBILITY OF YOUNGS FRINGES WITH PHOTON COINCIDENCE MEASUREMENTS Source: PHYSICAL REVIEW A, 49 (5): 4176-4179 Part B MAY 1994 Author(s): RIBEIRO, PHS; MONKEN, CH; BARBOSA, GA Title: MEASUREMENT OF COHERENCE AREA IN PARAMETRIC DOWNCONVERSION LUMINESCENCE Source: APPLIED OPTICS, 33 (3): 352-355 JAN 20 1994Author(s): GRAYSON, TP; BARBOSA, GA Title: SPATIAL PROPERTIES OF SPONTANEOUS PARAMETRIC DOWN-CONVERSION AND THEIR EFFECT ON INDUCED COHERENCE WITHOUT INDUCED EMISSION Source: PHYSICAL REVIEW A, 49 (4): 2948-2961 APR 1994Author(s): JOOBEUR, A; SALEH, BEA; TEICH, MC Title: SPATIOTEMPORAL COHERENCE PROPERTIES OF ENTANGLED LIGHT-BEAMS GENERATED BY PARAMETRIC DOWN-CONVERSION Source: PHYSICAL REVIEW A, 50 (4): 3349-3361 OCT 1994 Author(s): TAPSTER, PR; RARITY, JG; OWENS, PCM Title: VIOLATION OF BELL INEQUALITY OVER 4 KM OF OPTICAL-FIBERSource: PHYSICAL REVIEW LETTERS, 73 (14): 1923-1926 OCT 3 19941995Author(s): HERZOG, TJ; KWIAT, PG; WEINFURTER, H; et al. Title: COMPLEMENTARITY AND THE QUANTUM ERASER Source: PHYSICAL REVIEW LETTERS, 75 (17): 3034-3037 OCT 23 1995Author(s): KWIAT, PG; MATTLE, K; WEINFURTER, H; et al. Title: NEW HIGH-INTENSITY SOURCE OF POLARIZATION-ENTANGLED PHOTON PAIRS Source: PHYSICAL REVIEW LETTERS, 75 (24): 4337-4341 DEC 11 1995


Author(s): STREKALOV DV, SERGIENKO AV, KLYSHKO DN, et al.Title: OBSERVATION OF 2-PHOTON GHOST INTERFERENCE AND DIFFRACTIONSource: PHYSICAL REVIEW LETTERS 74 (18): 3600-3603 MAY 1 1995Author(s): RIBEIRO, PHS; PADUA, S; DASILVA, JCM; et al. Title: CONTROL OF YOUNG FRINGES VISIBILITY BY STIMULATED DOWN-CONVERSION Source: PHYSICAL REVIEW A, 51 (2): 1631-1633 FEB 1995 Author(s): KWIAT, P; WEINFURTER, H; HERZOG, T; et al.

Title: INTERACTION-FREE MEASUREMENT Source: PHYSICAL REVIEW LETTERS, 74 (24): 4763-4766 JUN 12 1995 Author(s): TORGERSON, JR; BRANNING, D; MONKEN, CH; et al. Title: EXPERIMENTAL DEMONSTRATION OF THE VIOLATION OF LOCAL REALISM WITHOUT BELL INEQUALITIES Source: PHYSICS LETTERS A, 204 (5-6): 323-328 AUG 28 1995 1996 Author(s): Mattle, K; Weinfurter, H; Kwiat, PG; et al. Title: Dense coding in experimental quantum communication Source: PHYSICAL REVIEW LETTERS, 76 (25): 4656-4659 JUN 17 1996 Author(s): Ribeiro, PHS; Barbosa, GA Title: Direct and ghost interference in double-slit experiments with coincidence measurements Source: PHYSICAL REVIEW A, 54 (4): 3489-3492 OCT 1996 1997Author(s): Bouwmeester, D; Pan, JW; Mattle, K; et al. Title: Experimental quantum teleportation Source: NATURE, 390 (6660): 575-579 DEC 11 1997 1998

Author(s): Monken, CH; Ribeiro, PHS; Padua, S Title: Transfer of angular spectrum and image formation in spontaneous parametric down-conversion Source: PHYSICAL REVIEW A, 57 (4): 3123-3126 APR 1998 Author(s): Weihs, G; Jennewein, T; Simon, C; et al. Title: Violation of Bell's inequality under strict Einstein locality conditions Source: PHYSICAL REVIEW LETTERS, 81 (23): 5039-5043 DEC 7 1998Author(s): Pan, JW; Bouwmeester, D; Weinfurter, H; et al. Title: Experimental entanglement swapping: Entangling photons that never interacted


Author(s): Buttler, WT; Hughes, RJ; Kwiat, PG; et al. Title: Practical free-space quantum key distribution over 1 km Source: PHYSICAL REVIEW LETTERS, 81 (15): 3283-3286 OCT 12 1998 Author(s): Fonseca, EJS; Monken, CH; Padua, S Title: Measurement of the de Broglie wavelength of a multiphoton wave packetSource: PHYSICAL REVIEW LETTERS, 82 (14): 2868-2871 APR 5 1999Author(s): Fonseca, EJS; Ribeiro, PHS; Padua, S; et al. Title: Quantum interference by a nonlocal double slit Source: PHYSICAL REVIEW A, 60 (2): 1530-1533 AUG 1999 Author(s): Kwiat, PG; Waks, E; White, AG; et al. Title: Ultrabright source of polarization-entangled photons Source: PHYSICAL REVIEW A, 60 (2): R773-R776 AUG 1999 Author(s): White, AG; James, DFV; Eberhard, PH; et al. Title: Nonmaximally entangled states: Production, characterization, and utilizationSource: PHYSICAL REVIEW LETTERS, 83 (16): 3103-3107 OCT 18 1999 Author(s): Ribeiro, PHS; Padua, S; Monken, CH Title: Image and coherence transfer in the stimulated down-conversion process Source: PHYSICAL REVIEW A, 60 (6): 5074-5078 DEC 19992000Author(s): Jennewein, T; Simon, C; Weihs, G; et al. Title: Quantum cryptography with entangled photons Source: PHYSICAL REVIEW LETTERS, 84 (20): 4729-4732 MAY 15 2000 Author(s): Saleh, BEA; Abouraddy, AF; Sirgienko, AV; et al. Title: Duality between partial coherence and partial entanglement Source: PHYSICAL REVIEW A, 62 (4): Art. No. 043816 OCT 2000 Author(s): Kwiat, PG; Berglund, AJ; Altepeter, JB; et al. Title: Experimental verification of decoherence-free subspaces Source: SCIENCE, 290 (5491): 498-501 OCT 20 2000 Author(s): Tsegaye, T; Soderholm, J; Atature, M; et al. Title: Experimental demonstration of three mutually orthogonal polarization states of entangled photons Source: PHYSICAL REVIEW LETTERS, 85 (24): 5013-5017 DEC 11 2000


2001Author(s): Abouraddy, AF; Saleh, BEA; Sergienko, AV; et al. Title: Role of entanglement in two-photon imaging Source: PHYSICAL REVIEW LETTERS, 87 (12): Art. No. 123602 SEP 17 2001Author(s): Ribeiro, PHS; Caetano, DP; Almeida, MP; et al. Title: Observation of image transfer and phase conjugation in stimulated down-conversion Source: PHYSICAL REVIEW LETTERS, 87 (13): Art. No. 133602 SEP 24 2001 Author(s): Nogueira, WAT; Walborn, SP; Padua, S; et al. Title: Experimental observation of spatial antibunching of photons Source: PHYSICAL REVIEW LETTERS, 86 (18): 4009-4012 APR 30 2001 Author(s): Kwiat, PG; Barraza-Lopez, S; Stefanov, A; et al. Title: Experimental entanglement distillation and 'hidden' non-locality Source: NATURE, 409 (6823): 1014-1017 FEB 22 2001 Author(s): Abouraddy, AF; Saleh, BEA; Sergienko, AV; et al. Title: Quantum holography Source: OPTICS EXPRESS, 9 (10): 498-505 NOV 5 2001Author(s): Kim, YH; Kulik, SP; Shih, Y Title: Quantum teleportation of a polarization state with a complete Bell state measurement Source: PHYSICAL REVIEW LETTERS, 86 (7): 1370-1373 FEB 12 2001 Author(s): D'Angelo, M; Chekhova, MV; Shih, Y Title: Two-photon diffraction and quantum lithography Source: PHYSICAL REVIEW LETTERS, 87 (1): Art. No. 013602 JUL 2 2001 Author(s): Mair, A; Vaziri, A; Weihs, G; et al. Title: Entanglement of the orbital angular momentum states of photons Source: NATURE, 412 (6844): 313-316 JUL 19 2001


1993Author(s): MONKEN, CH; BARBOSA, GA Title: TEMPORAL RESPONSE OF A FABRY-PEROT CAVITY TO A SINGLE-PHOTON WAVEPACKET Source: OPTICS COMMUNICATIONS, 99 (3-4): 152-156 JUN 1 1993 1994Author(s): RIBEIRO, PHS; MONKEN, CH; BARBOSA, GA Title: MEASUREMENT OF COHERENCE AREA IN PARAMETRIC DOWNCONVERSION LUMINESCENCE Source: APPLIED OPTICS, 33 (3): 352-355 JAN 20 1994Author(s): RIBEIRO, PHS; PADUA, S; DASILVA, JCM; et al. Title: CONTROLLING THE DEGREE OF VISIBILITY OF YOUNGS FRINGES WITH PHOTON COINCIDENCE MEASUREMENTS Source: PHYSICAL REVIEW A, 49 (5): 4176-4179 Part B MAY 1994 1995Author(s): RIBEIRO, PHS; PADUA, S; DASILVA, JCM; et al. Title: CONTROL OF YOUNG FRINGES VISIBILITY BY STIMULATED DOWN-CONVERSION Source: PHYSICAL REVIEW A, 51 (2): 1631-1633 FEB 1995 1996Author(s): Ribeiro, PHS; Barbosa, GA Title: Direct and ghost interference in double-slit experiments with coincidence measurements Source: PHYSICAL REVIEW A, 54 (4): 3489-3492 OCT 19961998Author(s): Monken, CH; Ribeiro, PHS; Padua, S Title: Transfer of angular spectrum and image formation in spontaneous parametric down-conversion Source: PHYSICAL REVIEW A, 57 (4): 3123-3126 APR 1998Author(s): Monken, CH; Ribeiro, PHS; Padua, S Title: Optimizing the photon pair collection efficiency: A step toward a loophole-free Bell's inequalities experiment Source: PHYSICAL REVIEW A, 57 (4): R2267-R2269 APR 1998 1999Author(s): Fonseca, EJS; Monken, CH; Padua, S Title: Measurement of the de Broglie wavelength of a multiphoton wave packetSource: PHYSICAL REVIEW LETTERS, 82 (14): 2868-2871 APR 5 1999Author(s): Fonseca, EJS; Ribeiro, PHS; Padua, S; et al. Title: Quantum interference by a nonlocal double slit Source: PHYSICAL REVIEW A, 60 (2): 1530-1533 AUG 1999Source: PHYSICAL REVIEW LETTERS, 87 (13): Art. No. 133602 SEP 24 2001


Author(s): Nogueira, WAT; Walborn, SP; Padua, S; et al. Title: Experimental observation of spatial antibunching of photons Source: PHYSICAL REVIEW LETTERS, 86 (18): 4009-4012 APR 30 2001Author(s): Ribeiro, PHS; Caetano, DP; Almeida, MP; et al. Title: Observation of image transfer and phase conjugation in stimulated down-conversion Source: PHYSICAL REVIEW LETTERS, 87 (13): Art. No. 133602 SEP 24 2001 Author(s): Santos, MF; Milman, P; Khoury, AZ; et al. Title: Measurement of the degree of polarization entanglement through position interference Source: PHYSICAL REVIEW A, 64 (2): Art. No. 023804 AUG 2001 Author(s): Caetano, DP; Almeida, MP; Ribeiro, PHS; et al. Title: Conservation of orbital angular momentum in stimulated down-conversion Source: PHYSICAL REVIEW A, 66 (4): Art. No. 041801 OCT 2002 Author(s): Caetano, DP; Ribeiro, PHS Title: Generation of spatial antibunching with free-propagating twin beams Source: PHYSICAL REVIEW A, 68 (4): Art. No. 043806 Part B OCT 2003

Double-slit experiment without slits

Two-photondetector

PHSR, Braz. J. Phys. 31, 478 (2001)

Double-slit experiment without slits

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Documents

Experiments With Entangled Photons Moura Escher , Cesar Raitz Jr., Daniel Schneider Tasca, Diney Soares Ether Jr., Gabriela Barreto Lemos, Malena Osorio Hor Meyll, Mario Leandro Aolita,