beam-like photon pairs entangled in polarization
Takayoshi Kobayashi and Atsushi YabushitaDepartment of Electrophysics
National Chiao-Tung University, Taiwan R.O.C.
1
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
4
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�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
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
k2,ω
BBO crystalβ-BaB2O4
k1,ω
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
pump
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
13
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
pump
idler
pump
seed
Introduction (Why OPA?)How to get other wavelength?
self phase modulation (SPM)but too weak for non-linear spectroscopy...
3
ts)
4 0 0 6 0 0 8 0 00
1
2
w a v e l e n g t h ( n m )
inte
nsity
(ar
b. u
nit
OPAincrease power by amplification
for ultrafast spectroscopy
16
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
Time-resolved spectroscopytime-resolved absorption change
λ0
λ1
w/o pump 0fs (with pump) ~ps (with pump) ∞ (with pump)
PBSE
IA
λ0
abso
rptio
n
λ1
ΔA
0fs delay (after pump)
abso
rptio
nλ0 λ1
abso
rptio
n
λ0 λ1
abso
rptio
n
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)
pump
seed
pump
seed
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
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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)
24
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�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
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/
27
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/
28
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
SPDC
SPDCphoton1: path A?B?photon2: path A?B?
29
Experimental result (quantum lithograph)
quantum
classical
Y. Shih, J. Mod. Opt. 49, 2275 (2002)
30
31
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
SPDC for quantum information
ghost imaging (wave vector)
coincidence countBBOBBOBBO
CC1 CC2 CC3
CC1
CC2
CC3
CC1
CC2
CC3
CC1
CC2
CC3
ghost imaging (wave vector)
BBOBBOBBO
coincidence count
SPDC for quantum information
CC1
CC2
CC3
CC1
CC2
CC3
CC1
CC2
CC3CC1 CC2 CC3
ghost imaging (wave vector)measure the shape of an objectDetector does NOT scan after object
classical
SPDC for quantum information
ω p , k p
ω s , k s
ω i , k iNLC
Y. Shih, J. Mod. Opt. 49, 2275 (2002)
36
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
ghost spectroscopy? (frequency)
BBO
coincidence count
BBOBBO
SPDC for quantum information
CC1
CC2
CC3
CC1 CC2 CC3CC1
CC2
CC3
CC1
CC2
CC3
BBO
ghost spectroscopy! (frequency)
coincidence count
BBOBBO
SPDC for quantum information
CC1
CC2
CC3
CC1 CC2 CC3CC1
CC2
CC3
CC1
CC2
CC3
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)
45
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
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
47
EPR-Bellsource
Alice
Bob
polarization-entangled photon pairs
1. Broadband photon pairs
[ ]212112
2
1−=Ψ
[ ]21212
1−=
( )+=2
1 ( )−=2
148
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?
Application | quantum
�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 + × + × + +
0 1
+
×
•base at random × × + + × +
0 1 0 0 1 0
Application | quantum
�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 + × + × + +
50% of keys can be shared(shared keys are same)
complicated…But secure!How can it be secure??
0 1
+
×
•base at random × × + + × +
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
+
×
•base at random × × + + × +
0 1 1 0 1 1
base? (random try) + × × × + ×
0 1 1 1 1 0result(bit)copy
�BB84 protocol | single photon�Can it be secure?
•key at random 0 1 0 1 1 0•base at random + × + × + +
Application | quantum
base? (random try) + × × × + ×
Security can be checked!
•base at random × × + + × +0 1
+
×
0 1 0 0 1 1
base? (random try) + × × × + ×
0 1 1 1 1 0
Error!
result(bit)copy
EPR-Bellsource
Alice
Bob
polarization-entangled photon pairs
1. Broadband photon pairs
[ ]212112
2
1−=Ψ
[ ]21212
1−=
( )+2
1 ( )−2
1
HV and VH(50%-50%)
Alice
Bob
Mixed state (statistical mixture)
1. Broadband photon pairs
?
?
EPR-pair
QKD example (without Eve)
Baseselect
Baseselect
Alice Bob
H V0 0
HV1 1
… …If they use the same base,“100%” correlation(quantum key distributed!)
R LRL
0 0
1 1
HV1 1
H V0 0
EPR-pair
QKD example (with Eve)
Baseselect
Baseselect
Alice Bob
H0 V V
?
V 0base/ get/ copy
V1 H
… …HHV…
Eve also share the key (NOT secure QKD…)How can it be improved?
V H1
H V0
H 1HV…
1
0
EPR-pair
Ekert91 protocol
Baseselect
Baseselect
Alice Bob
H V0 0Base information
LR0 0
VR0 0
V L 01
HL1 1
V H1 1
L R1 1
H R0 1
Base information(classical communication)
“100%” correlation
EPR-pair
Ekert91 protocol
Baseselect
Baseselect
Alice Bob
V 0H0 R RBase information OKbase/ get/ copy
L 0
R 0
V 0
H 1
H 1
L 0
R 1
L1 V
V1 H
H0 V
L1 H
R0 L
R0 L
V1 R
V
H
V
H
L
L
R
OK
OK
NG!Bob candetect Eve(secure!)
Experimental example of QKD
T. Jennewein et. al., PRL 84, 4729 (2000)
61
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
Generation of photon pairs entangled in their frequencies and polarizations (for WDM-QKD)
BBO(type-II)
2ωω − δω
ω + δω
frequency-entangled
e o/e
e/opolarization-entangled
polarization-entangled pairat many wavelength combinations
light source for WDM-QKD
epolarization-entangled
l i ti t l d
o/e
Standard :
Multiplex :
epolarization-entangledo/e
polarization-entangled
polarization-entangled
o/e
o/e
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
i
isHVefVH αψ ⋅+=
f=1α=0o
0
0.5
1
coin
cide
nce
cou
nts
(arb
.uni
ts)
f=1α=60o
0
0.5
1
coin
cide
nce
cou
nts
(arb
.uni
ts)0o
90o
135o45o 0o
90o
135o45o
1. Broadband photon pairs
0 60 120 180
i (degree)θ
f=1α=180o
0 60 120 180
i (degree)θ
0 60 120 180
0.5
1
i (degree)
coin
cide
nce
cou
nts
(arb
.uni
ts)
θ
f=1.732α=0o
0 60 120 180
1
2
3
i (degree)co
inci
denc
eco
unt
s(a
rb.u
nits
)θ
0o
90o
135o 45o 0o
90o
135o45o
polarization correlation (1st diffraction@870nm)
phase shift (866nm)< h hift (870 )
is
i
isHVefVH αψ ⋅+=
0o
45o
135o
1. Broadband photon pairs
< phase shift (870nm)
visibility < 100%
17.1 →=f
o180,0≠α
90o
polarization correlation (1st diffraction@870nm)
is
i
isHVefVH αψ ⋅+=
visibility relative phase
0o 0.75
0o
45o
135o
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
90o
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)
70
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
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
BBO1
BBO2
H-polarized fromBBO1Entangled photon pair
by type-I BBO *2
P.G. Kwiat et al., Phys. Rev. A, 60, R773 (1999)
V-polarized fromBBO2BBO1
BBO2
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
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?
75
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
76
���������� ���
H: Horizontal
��� ��������������
H: Horizontal
V: vertical
]HVVH[2
12121 +=Ψ
Polarization Entangled photon pair
V: vertical
Crystal optic axis
V: vertical
77
� ���� ��� � ���
���� ���
�����
�entangle polarization
����������� ����� ��!"
2 photon interference
�# �
BBO
Mp
Ms
Mi
I2, �
S2, � S1, �
I1, �
�# �
BBO
Mp
Ms
Mi
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
100
200
300
400
500
600
Co
inci
den
ce c
ou
nts
(1/s
)
Delay (μμμμm)
check whether the photons are coming coincidently79
�'������ ������� ���#�� �����&#������������
)���������#���*����������������������
��������#���(��#�������ππππ �� �+��������
QWP
HWPPol.
600 lI1
-150 -100 -50 0 50 100 1500
100
200
300
400
500
600
Co
inci
den
ce c
ou
nts
(1/
s)
Delay (μμμμm)
I1
lS1
lI1=lS1
lI2=lS2
lI2
lS2
80
81
�����������)�������� �������
�# �
BBO
Mp
Ms
Mi
I2, �
S2, � S1, �
I1, �
I1, �
S1, �
82
�����������)�������� �������
H
V H
V
VH
BBO
�L
l1’
l2’
l1
l2
BBO
BBO
lP1
lP2
lS1
lS2
lI1
lI2
� S1
� I1
� S2
� I2
� P1
� P2
1
2
pump
FCS
FCI
FCS
FCI
result: 2photon interference
400nm (λ/2)
classical lithographyresolution~ λ
2-photon interference (quantum lithography)2 times higher resolution : 400nm=λλλλ/2 84
85
����������������,����������� ���
�# �
BBO
Mp
Ms
Mi
I2, �
S2, � S1, �
I1, � $%��
$%��86
����������������,����������� ���
H
V H
V
λ/4
λ/4H
V
VH
]H)V(eVH[e2
121
i21
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)
88
89
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)
90
You can find more detail information in this paper.91
92
Our new scheme #2 to entangle photon pair beams“2x2 fiber”
easy alignment & simple setup
93
Just adjust timingJust adjust timing
�High visibility (>0.9)
Photon pair beamshighly entangledIn polarization 94
95
96
���������������� (Prof. A. Yabushita)
������������ (Prof. C. W. Luo)
���� (P f P C Ch
Department of Electrophysics, National Chiao Tung University
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
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� ��� ��� ��� �� (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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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!
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100
Unitary operator(beam splitter)
commutator of the two creation operators and vanishes
(beam splitter)
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