entangled photon pair generation by spontaneous parametric down conversion atsushi yabushita...
TRANSCRIPT
![Page 1: Entangled photon pair generation by spontaneous parametric down conversion Atsushi Yabushita Department of Electrophysics National Chiao-Tung University](https://reader037.vdocument.in/reader037/viewer/2022103006/56649e895503460f94b8ded6/html5/thumbnails/1.jpg)
Entangled photon pair generationby spontaneous parametric down conversion
Atsushi YabushitaDepartment of Electrophysics
National Chiao-Tung University
?
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Our work
Outline
IntroductionOptical parametric processes
Opt. param. amplifier (OPA)Spontaneous param. down conv. (SPDC)
Application | classicalBroadband generation | for short pulse
Application | quantumEntangled photon pairsGhost imaging | wave vectorGhost spectroscopy | frequencyQuantum key distribution (QKD) | polarizationMultiplex QKD | polarization and frequencyEntangled photon beam
Conclusion
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Our work
Outline
IntroductionOptical parametric processes
Opt. param. amplifier (OPA)Spontaneous param. down conv. (SPDC)
Application | classicalBroadband generation | for short pulse
Application | quantumEntangled photon pairsGhost imaging | wave vectorGhost spectroscopy | frequencyQuantum key distribution (QKD) | polarizationMultiplex QKD | polarization and frequencyEntangled photon beam
Conclusion
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Outline
Introduction | OPA and SPDCLight is …Light-matter interactionFrequency conversion
•SHG and SPDC•SPDCOPA•OPA is …?
Why OPA?Why SPDC?
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Introduction
Lightgamma-rayX-rayUltravioletvisibleinfraredradio wave
=> Electro-magnetic wave
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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…
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Introduction
energy / momentum conservation in frequency mixing
k2,
k1,
BBO crystal-BaB2O4
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Introduction
Reversible? YES!
Reverse process spontaneous parametric down conversion (SPDC)
2=>1+12=>0.8+1.2
2=>1+1occur by itself
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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)
pump
idler
seed | w/o amp
pump
seed
signal | amplified
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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
pump
idler
SPDC starts with vacuum noise(no seed for signal)
quite low efficiency ~10-10
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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
1
2
3
wavelength (nm)
inte
nsity (
arb. units)
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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
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Our work
Outline
IntroductionOptical parametric processes
Opt. param. amplifier (OPA)Spontaneous param. down conv. (SPDC)
Application | classicalBroadband generation | for short pulse
Application | quantumEntangled photon pairsGhost imaging | wave vectorGhost spectroscopy | frequencyQuantum key distribution (QKD) | polarizationMultiplex QKD | polarization and frequencyEntangled photon beam
Conclusion
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Application | classicalBroadband generation | for short pulse
1
Shorter pulse needs broader spectrum
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non-degenerate
degenerate
Application | classical
Optical parametric amplifier (OPA) Non-collinear OPA (NOPA)
Broadband generation | for short pulse
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Application | classicalBroadband 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 .2
0 .4
0 .6
0 .8
1 .0
0 .0 0
1 .5 7
3 .1 4
4 .7 1
6 .2 8
Inte
ns
ity
(a
rb.
un
it)
de lay (f s )
puls e tra in
ph
as
e (
rad
.)
pulse width=~9fs
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Our work
Outline
IntroductionOptical parametric processes
Opt. param. amplifier (OPA)Spontaneous param. down conv. (SPDC)
Application | classicalBroadband generation | for short pulse
Application | quantumEntangled photon pairsGhost imaging | wave vectorGhost spectroscopy | frequencyQuantum key distribution (QKD) | polarizationMultiplex QKD | polarization and frequencyEntangled photon beam
Conclusion
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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 :
p , k
p
s , k s
i , k iNLC
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Application | quantum
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!
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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)
Application | quantum
])2/2[(cos2 b(Young’s : )
half!
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Experimental result (quantum lithograph)
quantum
classical
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Application | quantum
ghost imaging | wave vector
coincidence count
CC1 CC2 CC3
CC1
CC2
CC3
BBO
CC1
CC2
CC3
BBO
CC1
CC2
CC3
BBO
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Application | quantum
ghost imaging | wave vector
CC1
CC2
CC3
BBO
CC1
CC2
CC3
BBO
CC1
CC2
CC3
BBO
coincidence count
CC1 CC2 CC3
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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
Application | quantum
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ghost spectroscopy | frequency
Application | quantum
CC1
CC2
CC3
BBO
coincidence count
CC1 CC2 CC3CC1
CC2
CC3
BBO
CC1
CC2
CC3
BBO
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CC1
CC2
CC3
BBO
ghost spectroscopy | frequency
Application | quantum
coincidence count
CC1 CC2 CC3CC1
CC2
CC3
BBO
CC1
CC2
CC3
BBO
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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
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pump focusing lens (f=100mm)
Spectrum of photon pairs and absorption spectrum of the sample
more absorption in longer wavelength
1. Broadband photon pairs
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result : absorption spectrum
→ agree with the result by a spectrometercalculate absorption spectrum from the ratio
1. Broadband photon pairs
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result : absorption spectrum
agree with the result by a spectrometer
1. Broadband photon pairs
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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)
1. Broadband photon pairs
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Our work
Outline
IntroductionOptical parametric processes
Opt. param. amplifier (OPA)Spontaneous param. down conv. (SPDC)
Application | classicalBroadband generation | for short pulse
Application | quantumEntangled photon pairsGhost imaging | wave vectorGhost spectroscopy | frequencyQuantum key distribution (QKD) | polarizationMultiplex QKD | polarization and frequencyEntangled photon beam
Conclusion
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Application | quantum
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?
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0 1
+
Application | quantum
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
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0 1
+
Application | quantum
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
50% of keys can be shared(shared keys are same)
complicated…But secure!How can it be secure??
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0 1
+
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
0 1 1 1 1 0
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BB84 protocol | single photonCan it be secure?
•key at random 0 1 0 1 1 0•base at random + + + +
•base at random + + +0 1
+
Application | quantum
0 1 0 0 1 1
base? (random try) + +
0 1 1 1 1 0
Error!
Security can be checked!
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212112
2
1
21212
1
EPR-Bellsource
Alice
Bob
polarization-entangled photon pairs
1. Broadband photon pairs
2
1 2
1
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HV and VH(50%-50%)
Alice
Bob
Mixed state (statistical mixture)
1. Broadband photon pairs
?
?
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EPR-pair
QKD example (without Eve)
Baseselect
Baseselect
Alice Bob
H VHV
0 0
1 1
… …If they use the same base,“100%” correlation(quantum key distributed!)
R L
RL
0 0
1 1
HV1 1
H V0 0
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EPR-pair
QKD example (with Eve)
Baseselect
Baseselect
Alice Bob
H0 VV1 H
… …VHHV
…
?
Eve also share the key (NOT secure QKD…)How can it be improved?
V H1
H V0
VH
0
1
HV
…
1
0
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EPR-pair
Ekert91 protocol
Baseselect
Baseselect
Alice Bob
H V0 0
LR0 0
VR0 0
V L 01
HL1 1
V H1 1
L R1 1
H R0 1
Base information(classical communication)
“100%” correlation
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EPR-pair
Ekert91 protocol
Baseselect
Baseselect
Alice Bob
V 0
L 0
R 0
V 0
H 1
H 1
L 0
R 1
L1 V
V1 H
H0 V
L1 H
H0 R
R0 L
R0 L
V1 R
V
H
V
H
R
L
L
R
Base information OK
OK
OK
NG!Bob candetect Eve(secure!)
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T. Jennewein et. Al., PRL 84, 4729 (2000)
Experimental example of QKD
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Our work
Outline
IntroductionOptical parametric processes
Opt. param. amplifier (OPA)Spontaneous param. down conv. (SPDC)
Application | classicalBroadband generation | for short pulse
Application | quantumEntangled photon pairsGhost imaging | wave vectorGhost spectroscopy | frequencyQuantum key distribution (QKD) | polarizationMultiplex QKD | polarization and frequencyEntangled photon beam
Conclusion
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Generation of photon pairs entangled in their frequencies and polarizations (for WDM-QKD)
BBO(type-II)
2
frequency-entangled
e o/e
e/opolarization-entangled
polarization-entangled pairat many wavelength combinations
light source for WDM-QKD
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epolarization-entangled
epolarization-entangledo/e
polarization-entangled
polarization-entangled
o/e
o/e
o/e
Standard :
Multiplex :
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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
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simulationis
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1. Broadband photon pairs
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polarization correlation (1st diffraction@870nm)
phase shift (866nm) < phase shift (870nm)
visibility < 100%
is
i
isHVefVH
17.1 f
o180,0
0o
45o
90o
135o
1. Broadband photon pairs
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polarization correlation (1st diffraction@870nm)
phase shift (866nm)< phase shift (870nm)
visibility<100%
is
i
isHVefVH
17.1 f
o180,0
visibility relative phase
0o 0.75
45o 0.43 -25o
135o 0.31 35o
90o 0.50 -81o
0o
45o
90o
135o
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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)
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Our work
Outline
IntroductionOptical parametric processes
Opt. param. amplifier (OPA)Spontaneous param. down conv. (SPDC)
Application | classicalBroadband generation | for short pulse
Application | quantumEntangled photon pairsGhost imaging | wave vectorGhost spectroscopy | frequencyQuantum key distribution (QKD) | polarizationMultiplex QKD | polarization and frequencyEntangled photon beam
Conclusion
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Beam-like polarization entangled photon pair
generation
羅信斌 (Hsin-Pin Lo)Department of Physics, NTHU
1
2
3
4
1 2 3 4
0 .2
0 .0
0 .2
0 .4
1
2
3
4
1
2
3
4
0 .2
0 .0
0 .2
先 進 超 快 雷 射 研 究 中 心 超 快 動 力 學 研 究 室
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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 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
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SPDC photon image
]HVVH[2
12121
Polarization Entangled photon pair
H: Horizontal
V: vertical
Beam-like photon pair
Crystal optic axisCrystal optic axis
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Generation rate ~ 32,000 s-1
H
H
V
V
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Main idea and experiment setup
]H)V(eVH[e2
121
i21
i
]HVVH[2
12121 L1=L2=L3
H1
V1
V2
H2
QWP
L1
L2
L3
SPCM
Coincidence measurement
H1
V1
V2
H2
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PRL 90, 240401 (2003)
2 by 2 fiber
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HOM interference measurement
QWP
HWPPol.
L1
L3
-3000 -2000 -1000 0 1000 2000 30000
5
10
15
20
25
30
35
40
45
50
55
60
Co
inci
de
nce
Co
un
t (1
se
c)
Delay (100 nm/ step)
-1500 -1000 -500 0 500 10000
10
20
30
Coi
ncid
ence
Cou
nt p
er s
ec
Delay (100 nm/ step)
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Our work
IntroductionOptical parametric processes
Opt. param. amplifier (OPA)Spontaneous param. down conv. (SPDC)
Application | classicalBroadband generation | for short pulse
Application | quantumEntangled photon pairsGhost imaging | wave vectorGhost spectroscopy | frequencyQuantum key distribution (QKD) | polarizationMultiplex QKD | polarization and frequencyEntangled photon beam
Summary
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Thank you for your attention!
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