Entangled photon pair generation by spontaneous parametric down conversion Atsushi Yabushita...

Entangled photon pair generationby spontaneous parametric down conversion

Atsushi YabushitaDepartment of Electrophysics

National Chiao-Tung University

Our work

Outline

IntroductionOptical parametric processes

Opt. param. amplifier (OPA)Spontaneous param. down conv. (SPDC)

Application | classicalBroadband generation | for short pulse

Conclusion

Our work

Outline

Conclusion

Outline

Introduction | OPA and SPDCLight is …Light-matter interactionFrequency conversion

•SHG and SPDC•SPDCOPA•OPA is …?

Why OPA?Why SPDC?

Introduction

Lightgamma-rayX-rayUltravioletvisibleinfraredradio wave

=> Electro-magnetic wave

Introduction

Light-matter interactionElectric field make dielectric polarization

Emission from dipole oscillating in vertical direction E : exp(-it) E*E : exp(-i2t)

Second harmonic generation (SHG) using a non-linear crystal within some limitation from physical law…

Introduction

energy / momentum conservation in frequency mixing

BBO crystal-BaB2O4

Introduction

Reversible? YES!

Reverse process spontaneous parametric down conversion (SPDC)

2=>1+12=>0.8+1.2

2=>1+1occur by itself

Introduction

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

process | difference frequency generationhpump-hsignal=hidler

Energy conservation hpump=hsignal+hidler

Signal(amplified)

seed | w/o amp

signal | amplified

Introduction

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

process | difference frequency generationhpump-hsignal=hidler

Energy conservation hpump=hsignal+hidler

#signal=#idler

signal

SPDC starts with vacuum noise(no seed for signal)

quite low efficiency ~10-10

IntroductionWhy OPA? complicated setup

intense laser at different wavelengthnon-linear spectroscopy in UV/visible/IR…

(ultrafast spectroscopy, Raman for vibration study, …)Other method? self phase modulation (SPM) | low efficiency

400 600 8000

wavelength (nm)

nsity (

arb. units)

Why SPDC? low conversion efficiency

interesting character of entanglementnever broken security | quantum communicationeasy to transfer | via optical fiber

Other method?singlet (a pair of spin ½ particle)

Introduction

Our work

Outline

Conclusion

Shorter pulse needs broader spectrum

non-degenerate

degenerate

Application | classical

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

Broadband generation | for short pulse

WLC OPA (OPG with WLC)

Spectrum diffracted by gratingVisible broadband

- 8 0 - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 8 00 .0

0 .0 0

1 .5 7

3 .1 4

4 .7 1

6 .2 8

de lay (f s )

puls e tra in

pulse width=~9fs

Our work

Outline

Conclusion

Application | quantum

SPDC generates photon pairs (low efficiency)

(2) frequency ： p = s + i

(1) wave vector : k p = k s + k i

correlated parameters

(in case of Type-II crystal)

isis | H|VV|H2

1(3) polarization ：

s , k s

i , k iNLC

So, what is entanglement? Let’s remind “Young’s double slit” photon comes one by one if you block one of the slits…

Are there any other entanglements?

Interference only in unknown casepath entanglement

Interference of “probability”, “wavefunction” different from statistics of classical phenomena=quantum

Yes, we will see them in the following pages!

quantum lithography | wave vector

better resolution ( than classical limit ) ~ p=

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

Schematic set-up

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

])2/2[(cos2 b(Young’s : )

Experimental result (quantum lithograph)

quantum

classical

ghost imaging | wave vector

coincidence count

CC1 CC2 CC3

ghost imaging | wave vector

coincidence count

CC1 CC2 CC3

p , k p

s , k s

i , k iNLC

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

ghost imagingmeasure the shape of an objectDetector does NOT scan after object

classical

ghost spectroscopy | frequency

coincidence count

CC1 CC2 CC3CC1

ghost spectroscopy | frequency

coincidence count

CC1 CC2 CC3CC1

S : sample (Nd+3-doped glass)

experiment setup

L1 : focusing lens　　　 (f=100mm, 8mm)

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

OF : optical fiber

SPCM : single photon counting module

TAC : time-to-amplitude converter

Delay : delay module

PC : computer

pump focusing lens (f=100mm)

Spectrum of photon pairs and absorption spectrum of the sample

more absorption in longer wavelength

1. Broadband photon pairs

result : absorption spectrum

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

result : absorption spectrum

agree with the result by a spectrometer

summary of this section

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

spectrum was broadened (11,11→63,69nm)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

spectrum of SPDC photon pairs

coincidence resolving signal light’s frequency

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

Our work

Outline

Conclusion

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

how it workscan it be safe?

E91 protocol | polarization entangled photon pairpolarization entanglement?how it workscan it be safe?

BB84 protocol | single photonPurpose : to share a secret keyhow 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 photonPurpose : to share a secret keyhow it works?

•base at random + + + 0 1 0 0 1 0

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

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

Application | quantumBB84 protocol | single photon

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

•base at random + + +

0 1 1 0 1 1

base? (random try) + +

0 1 1 1 1 0

BB84 protocol | single photonCan it be secure?

•base at random + + +0 1

0 1 0 0 1 1

base? (random try) + +

0 1 1 1 1 0

Error!

Security can be checked!

212112

EPR-Bellsource

polarization-entangled photon pairs

HV and VH(50%-50%)

Mixed state (statistical mixture)

EPR-pair

QKD example (without Eve)

Baseselect

Alice Bob

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

H V0 0

EPR-pair

QKD example (with Eve)

Baseselect

Alice Bob

H0 VV1 H

… …VHHV

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

EPR-pair

Ekert91 protocol

Baseselect

Alice Bob

H V0 0

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

Base information OK

NG!Bob candetect Eve(secure!)

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

Experimental example of QKD

Our work

Outline

Conclusion

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

BBO(type-II)

frequency-entangled

e/opolarization-entangled

polarization-entangled pairat many wavelength combinations

light source for WDM-QKD

epolarization-entangled

epolarization-entangledo/e

polarization-entangled

Standard :

Multiplex :

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 photon counting module

TAC : time-to-amplitude converterDelay : delay modulePC : computer

IRIS : iris diaphragms

POL1,2 : linear polarizer

BS : non-polarizing beam splitter

simulationis

isHVefVH

f=1=0o

0 60 120 1800

i (degree)

f=1=60o

f=1=180o

0 60 120 1800

i (degree)

0 60 120 1800

i (degree)

f=1.732=0o

0 60 120 1800

i (degree)

135o 45o

135o45o 0o

135o45o

polarization correlation (1st diffraction@870nm)

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

visibility < 100%

isHVefVH

17.1 f

o180,0

polarization correlation (1st diffraction@870nm)

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

visibility<100%

isHVefVH

17.1 f

o180,0

visibility relative phase

0o 0.75

45o 0.43 -25o

135o 0.31 35o

90o 0.50 -81o

entangled （ iris 1mm ）

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

visibility<100% (866nm, 870nm)

17.1 f

o180,0

no entanglement （ iris open ）

to improve : group velocity compensation

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

Our work

Outline

Conclusion

Beam-like polarization entangled photon pair

generation

羅信斌 (Hsin-Pin Lo)Department of Physics, NTHU

1 2 3 4

先進超快雷射研究中心超快動力學研究室

Acknowledgement籔下篤史 (Prof. A. Yabushita)

羅志偉 (Prof. C. W. Luo)

陳柏中 (Prof. P. C. Chen)

Department of Electrophysics, National Chiao Tung University

Department of Physics, Nation Tsing Hua University

先進超快雷射研究中心超快動力學研究室

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

The University of Electro-Communications, Tokyo, Japan

SPDC photon image

]HVVH[2

Polarization Entangled photon pair

H: Horizontal

V: vertical

Beam-like photon pair

Crystal optic axisCrystal optic axis

Generation rate ~ 32,000 s-1

Main idea and experiment setup

]H)V(eVH[e2

]HVVH[2

12121 L1=L2=L3

Coincidence measurement

PRL 90, 240401 (2003)

2 by 2 fiber

HOM interference measurement

HWPPol.

-3000 -2000 -1000 0 1000 2000 30000

Delay (100 nm/ step)

-1500 -1000 -500 0 500 10000

Delay (100 nm/ step)

Our work

Summary

Thank you for your attention!

Entangled photon pair generation by spontaneous parametric down conversion Atsushi Yabushita...

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