beam-like photon pairs entangled in polarization

Takayoshi Kobayashi and Atsushi YabushitaDepartment of Electrophysics

National Chiao-Tung University, Taiwan R.O.C.

BBOBBO

Type-II H,λ1,k1

V,λ2,k2

entangle!

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TaiwanR.O.C.

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�Universities: NCTU (��), NTHU(��) �Research and develop centers: many companies�National Research Institute: ITRI(�� )3

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time-resolved fluorescence (1ns-)

ultrafast time-resolved spectroscopy(visible 10fs)

THz spectroscopy

Quantum Information

by up-conversion (fs-1ns)

Low-temperature pump-probe

Outline Our work

�Introduction�Optical parametric processes

�Spontaneous parametric down conv. (SPDC)�Optical parametric amplifier (OPA)

�Application | ultrafast spectroscopy�Broadband generation | for short pulse

�Application | Quantum Information�lithography/ imaging / spectroscopy�communication (QKD) / multiplex QKD�Entangled photon beam

Outline Our work

Introduction

�Frequency conversionSHG � SPDC

�Why SPDC?

�SPDC�OPA

�Why OPA?

Introduction

LightX-ray

crystal structuremedical diagnosis

UV-VIS-IRspectroscopyreaction mechanism

microwavecommunicationeasy to transfar

Introduction

Light-matter interactionElectric field make dielectric polarization

How to get double frequency?Emission from dipole

oscillating in vertical directionE : exp(-iωt)E*E : exp(-i2ωt)

Second harmonic generation (SHG)using a non-linear crystal

within some limitation from physical law…

Introduction (SHG)

energy / momentum conservation in frequency mixing

BBO crystalβ-BaB2O4

Introduction (SHG �� SPDC)SHG (second harmonic generation)

ω � 2ω

Reversible? YES!

Reverse processspontaneous parametric down conversion (SPDC)

2ω=>ω+ω2ω=>0.8ω+1.2ω

2ω=>ω+ωoccur by itself

Introduction (SPDC)

How does SPDC occur?similar as OPA (optical parametric amplification)

signal SPDC starts with vacuum noise(no seed for signal)

process | difference frequency generationhνpump-hνsignal=hνidler

Energy conservationhνpump=hνsignal+hνidler

#signal=#idler

quite low efficiency ~10-10

Introduction

Why SPDC?

�interesting characterentanglement

Alice Bob

entangled

�never broken securityquantum communicationq

http://physicsworld.com/cws/article/news/44775

�easy to transfervia optical fiber

http://alby13.blogspot.com/2009/04/fiber-optics-future-of-internet.html©tECHNICAL dESIGN

Introduction (SPDC �� OPA)

OPA (optical parametric amplification)…what is OPA?

similar as SPDC, much higher efficiencySignal(amplified)

seed | w/o amp

signal | amplified

process | difference frequency generationhνpump-hνsignal=hνidler

Energy conservationhνpump=hνsignal+hνidler

Introduction (Why OPA?)How to get other wavelength?

self phase modulation (SPM)but too weak for non-linear spectroscopy...

4 0 0 6 0 0 8 0 00

w a v e l e n g t h ( n m )

OPAincrease power by amplification

for ultrafast spectroscopy

Outline Our work

Time-resolved spectroscopytime-resolved absorption change

w/o pump 0fs (with pump) ~ps (with pump) ∞ (with pump)

0fs delay (after pump)

nλ0 λ1

λ0 λ1

PB: photo-bleaching

SE: stimulated emissionIA: induced absorption

ultrafast electronic dynamicscan be studied to ~100fs

Ultrashort pulse generationelectronic and vibrational dynamics

ultrafast dynamics of vibration?Not Available: typical vibration period = ~20 fs

requires much higher resolutionNoncollinear OPA (NOPA)

broadband amplification � ultrashort pulse (~5fs)

non-degenerate

Application | ultrafast spectroscopy

Optical parametric amplifier (OPA) Non-collinear OPA (NOPA)

Broadband generation | for short pulse

degenerate

Application | ultrafast spectroscopyBroadband generation | for short pulse

WLC OPA (OPG with WLC)

Spectrum diffracted by gratingVisible broadband

��

pulse width<10fs=1×10-14s (ultrashort)

Ultrashort pulse generationelectronic and vibrational dynamics

��

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real-time frequency change is observed

Real-time change of vibration(photo-isomerization of retinal)

Outline Our work

Quantum lithography

Let’s remind “Young’s double slit”photon comes one by oneif you block one of the slits…

I t f l if th i kInterference only if path is unknownpath entanglement

Interference of “probability”, “wavefunction”statistics of classical phenomena?

http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/

Quantum lithography

Let’s remind “Young’s double slit”photon comes one by oneif you block one of the slits…

I t f l if th i kInterference only if path is unknownpath entanglement

Interference of “probability”, “wavefunction”statistics of classical phenomena � quantum

What happens if you use SPDC photon pairs?quantum lithography

http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/

quantum lithography | wave vector

resolution 2times higher ((((~ λλλλp= λ /λ /λ /λ /2)2)2)2)

(cf. classical: ~λλλλ)

Schematic set up

Y. Shih, J. Mod. Opt. 49, 2275 (2002)Application | quantum

“SPDC photon pairs” v.s. “classical light”

Schematic set-up

SPDCphoton1: path A?B?photon2: path A?B?

Experimental result (quantum lithograph)

quantum

classical

Y. Shih, J. Mod. Opt. 49, 2275 (2002)

Outline Our work

SPDC for quantum information

ghost imaging (wave vector)

coincidence countBBOBBOBBO

CC1 CC2 CC3

ghost imaging (wave vector)

BBOBBOBBO

coincidence count

CC3CC1 CC2 CC3

ghost imaging (wave vector)measure the shape of an objectDetector does NOT scan after object

classical

ω p , k p

ω s , k s

ω i , k iNLC

Y. Shih, J. Mod. Opt. 49, 2275 (2002)

Outline Our work

ghost spectroscopy? (frequency)

coincidence count

BBOBBO

CC1 CC2 CC3CC1

ghost spectroscopy! (frequency)

coincidence count

BBOBBO

CC1 CC2 CC3CC1

experiment setup BBO : non-linear crystal

M1 : parabolic mirror

M2,3 : plane mirror

P1 : prism (remove pump)

P2 : prism (compensate angular dispersion)PBS : polarizing beam splitter

G : diffraction grating

L2,3 : fiber coupling lens

S : sample ��

L1 : focusing lens(f=100mm, 8mm)

OF : optical fiber

SPCM : single photoncounting module

TAC : time-to-amplitudeconverter

Delay : delay modulePC : computer

result : absorption spectrum

� agree with the result by a spectrometercalculate absorption spectrum from the ratio

Spectrum of photon pairsand absorption spectrum of the sample

pump focusing lens (f=100mm)

more absorption in longer wavelength

result : absorption spectrum1. Broadband photon pairs

agree with the result by a spectrometer

spherical lens � objective lens(f=100 � 8mm)

spectrum was broadened (11,11�63,69nm)3

spectrum of SPDC photon pairs

Nd3+ -doped glass ( in the idler light path)

� absorption spectrum was measured

without resolving the frequency of photon transmitted through the sample

fit well with the result measured by a spectrometer

coincidence resolving signal light’s frequency

A. Yabushita et. al., Phys. Rev. A 69, 013806 (2004)

Outline Our work

Quantum information experiments

Quantum Key Distribution (QKD)

�E91 protocolby polarization entangled photon pair� l i ti t l t?�polarization entanglement?�how it works�can it be safe?

entangledQuantum Cryptography and Secret-Key Distillation, © Cambridge University Press

EPR-Bellsource

polarization-entangled photon pairs

1. Broadband photon pairs

[ ]212112

1−=Ψ

[ ]21212

( )+=2

1 ( )−=2

Application | quantum

Outline for “Quantum Key Distribution (QKD)”�BB84 protocol | single photon

�how it works�can it be safe?

�E91 protocol | polarization entangled photon pair�E91 protocol | polarization entangled photon pair�polarization entanglement?�how it works�can it be safe?

�BB84 protocol | single photon�Purpose : to share a secret key�how it works?

•key at random 0 1 0 1 1 0•base at random + × + × + +

•base at random × × + + × +

0 1 0 0 1 0

�BB84 protocol | single photon�Purpose : to share a secret key�how it works?

50% of keys can be shared(shared keys are same)

complicated…But secure!How can it be secure??

0 1 0 0 1 0

Application | quantum�BB84 protocol | single photon

�Can it be secure?•key at random 0 1 0 1 1 0•base at random + × + × + +

base? (random try) + × × × + ×

0 1 1 1 1 0

0 1 1 0 1 1

0 1 1 1 1 0result(bit)copy

�BB84 protocol | single photon�Can it be secure?

Security can be checked!

•base at random × × + + × +0 1

0 1 0 0 1 1

0 1 1 1 1 0

Error!

result(bit)copy

EPR-Bellsource

polarization-entangled photon pairs

[ ]212112

1−=Ψ

[ ]21212

1 ( )−2

HV and VH(50%-50%)

Mixed state (statistical mixture)

EPR-pair

QKD example (without Eve)

Baseselect

Alice Bob

H V0 0

… …If they use the same base,“100%” correlation(quantum key distributed!)

H V0 0

EPR-pair

QKD example (with Eve)

Baseselect

Alice Bob

H0 V V

V 0base/ get/ copy

… …HHV…

Eve also share the key (NOT secure QKD…)How can it be improved?

H 1HV…

EPR-pair

Ekert91 protocol

Baseselect

Alice Bob

H V0 0Base information

V L 01

V H1 1

L R1 1

H R0 1

Base information(classical communication)

“100%” correlation

EPR-pair

Ekert91 protocol

Baseselect

Alice Bob

V 0H0 R RBase information OKbase/ get/ copy

NG!Bob candetect Eve(secure!)

Experimental example of QKD

T. Jennewein et. al., PRL 84, 4729 (2000)

Outline Our work

Generation of photon pairs entangled in their frequencies and polarizations (for WDM-QKD)

BBO(type-II)

2ωω − δω

ω + δω

frequency-entangled

e/opolarization-entangled

polarization-entangled pairat many wavelength combinations

light source for WDM-QKD

epolarization-entangled

l i ti t l d

Standard :

Multiplex :

epolarization-entangledo/e

polarization-entangled

experimental setup L1 : focusing lens

BBO : non-linear crystal

M1 : parabolic mirror

M2,3 : plane mirror

P1 : prism (remove pump)

P2 : prism (compensate angular dispersion)

G : diffraction grating

L2,3 : fiber coupling lens

OF : optical fiber

SPCM : single photoncounting module

TAC : time-to-amplitudeconverterDelay : delay modulePC : computer

IRIS : iris ��

POL1,2 : linear polarizer

BS : non-polarizing beam splitter

simulationis

isHVefVH αψ ⋅+=

f=1α=0o

f=1α=60o

135o45o 0o

135o45o

0 60 120 180

i (degree)θ

f=1α=180o

0 60 120 180

i (degree)θ

0 60 120 180

i (degree)

f=1.732α=0o

0 60 120 180

i (degree)co

135o 45o 0o

135o45o

polarization correlation (1st diffraction@870nm)

phase shift (866nm)< h hift (870 )

isHVefVH αψ ⋅+=

< phase shift (870nm)

visibility < 100%

17.1 →=f

o180,0≠α

polarization correlation (1st diffraction@870nm)

isHVefVH αψ ⋅+=

visibility relative phase

0o 0.75

phase shift (866nm)< phase shift (870nm)

visibility<100%

17.1 →=f

o180,0≠α

45o 0.43 -25o

135o 0.31 35o

90o 0.50 -81o

entangled ��iris 1mm��

phase shift (866nm) < phase shift (870nm) 17.1 →=f�

no entanglement ��iris open��

but phase shift<45o to improve : walk-off compensation

visibility<100% (866nm, 870nm)o180,0≠α�

to improve : group velocity compensation

frequency resolved photon pairs are entangled in polarization

(light source for WDM-QKD)

future : compensations of walk-off and group velocity (improve pol-entanglement)

A. Yabushita et. al, J. Appl. Phys., 99, 063101 (2006)

Outline Our work

Quantum information experimentsentangled photon beam

SPDC has two types

Type-IType-II

BBO BBO

V��H+H(parallel polarizations)

V��H+V(orthogonal polarizations)

How to get polarization entanglement?...72

H-polarized fromBBO1Entangled photon pair

by type-I BBO *2

P.G. Kwiat et al., Phys. Rev. A, 60, R773 (1999)

V-polarized fromBBO2BBO1

H-polarized fromBBO1

V-polarized fromBBO2

Side view

V��H+Hor

H��V+V

not for entangled beams 73

photon pairs fromthe crossing points

H + Vor

Entangled photon pair

by a type-II BBO

Type-IIH

V + HV

polarization entangled!only at crossing points

V��H+V

(2ωωωω��ωωωω+ωωωω)

What a large loss... 74

How about beam-like pairs?if entangled, all pairs can be usedbut no polarization entanglement� Can we entangle them?

We have developed two new schemes

scheme #1 (path overlap)for two-photon interference

2 times higher resolution than classical limit (λ)for polarization entanglement

all photon pairs are polarization entangled

scheme #2 (2x2 fiber)easy to get entangled beams

��

H: Horizontal

��

H: Horizontal

V: vertical

]HVVH[2

12121 +=Ψ

Polarization Entangled photon pair

V: vertical

Crystal optic axis

V: vertical

� ��

��

�entangle polarization

�� !"

2 photon interference

�# �

I2, �

S2, � S1, �

I1, �

�# �

I2, �

S2, � S1, �

I1, � $%��

$%��

I1, �

S1, �

need to adjust timing between two photon pairs!78

��&#�� '�� #��

�interference only in coherence length�φφφφ=0 or ππππ for max entangle

(a) (c)��

at same timing

only (b)&(d):bunching

�� fine adjustment is needed ! but how ?

C. K. Hong, Z. Y. Ou, and L. Mandel,Phys. Rev. Lett. 59, 2044 (1987).

(d)(b)

Beam splitterBeam splitter

Beam splitterBeam splitter� (

only (b)&(d):bunching

�� no coincidence

-150 -100 -50 0 50 100 1500

Delay (μμμμm)

check whether the photons are coming coincidently79

�'�� #�� &#��

)��#��*��

��#��(��#��ππππ �� +��

HWPPol.

600 lI1

-150 -100 -50 0 50 100 1500

Delay (μμμμm)

lI1=lS1

lI2=lS2

��)��

�# �

I2, �

S2, � S1, �

I1, �

S1, �

��)��

� S1

� I1

� S2

� I2

� P1

� P2

result: 2photon interference

400nm (λ/2)

classical lithographyresolution~ λ

2-photon interference (quantum lithography)2 times higher resolution : 400nm=λλλλ/2 84

��,��

�# �

I2, �

S2, � S1, �

I1, � $%��

$%��86

��,��

]H)V(eVH[e2

i ϕφ +=Ψ

]HVVH[2

12121 +=Ψ

adjust phase

result: polarization entanglement

rotate polarization 90 degrees by QWP plates

|H1>|V1>+eiφ|H2>|V2>

|V1>|H1>+eiφ|H2>|V2>

(max entangle at φ=nπ ��)

measure coincidence scanning φvisibility = 0.90��0.05(highly entangled)

Our new scheme #1 to generate photon pair beamsfor two purposes

two-photon interferencepolarization entanglement

resolution of 2-photon interference (λ/2)λ

Summary for beam-like photon pairs generation

2 times higher than classical limit (λ)all photon pairs can be polarization entangled

efficient generation of polarization entangled pairs

cf.) traditional method : only crossing points of light cones

Hsin-Pin Lo et al., Beamlike photon-pair generation for two-photon interferenceand polarization entanglement, Phys. Rev. A 83, 022313 (2011)

You can find more detail information in this paper.91

Our new scheme #2 to entangle photon pair beams“2x2 fiber”

easy alignment & simple setup

Just adjust timingJust adjust timing

�High visibility (>0.9)

Photon pair beamshighly entangledIn polarization 94

�� (Prof. A. Yabushita)

�� (Prof. C. W. Luo)

�� (P f P C Ch

Department of Electrophysics, National Chiao Tung University

�� (Hsin-Pin Lo: Ph. D student) Department of Physics, NTHU

acknowledgement for the entangled beam generation

�� (Prof. P. C. Chen)Department of Physics, Nation Tsing Hua University

��

� �� (Prof. T. Kobayashi)Department of Applied Physics and Chemistry and Institute for Laser Science

The University of Electro-Communications, Tokyo, Japan

Acknowledgement for $upport

MOE ATU plan, Taiwan, ROC.

National Science Council, Taiwan, ROC.

NSC 98-2112-M-009-001-MY3, NSC 99-2923-M-009-004-MY3

Thank you for your attention!

Unitary operator(beam splitter)

commutator of the two creation operators and vanishes

(beam splitter)

beam-like photon pairs entangled in polarization

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