Entangled photon pair generation
by spontaneous parametric down conversion
Atsushi Yabushita
Department of Electrophysics
National Chiao-Tung University
?
Outline
Introduction
Optical parametric processes
Opt. param. amplifier (OPA)
Spontaneous param. down conv. (SPDC)
Application | classical
Broadband generation | for short pulse
Application | quantum
Entangled photon pairs
Ghost imaging | wave vector
Ghost spectroscopy | frequency
Quantum key distribution (QKD) | polarization
Multiplex QKD | polarization and frequency
Entangled photon beam
Conclusion
Our work
Outline
Introduction
Optical parametric processes
Opt. param. amplifier (OPA)
Spontaneous param. down conv. (SPDC)
Application | classical
Broadband generation | for short pulse
Application | quantum
Entangled photon pairs
Ghost imaging | wave vector
Ghost spectroscopy | frequency
Quantum key distribution (QKD) | polarization
Multiplex QKD | polarization and frequency
Entangled photon beam
Conclusion
Our work
Outline
Introduction | OPA and SPDC
Light is …
Light-matter interaction
Frequency conversion
•SHG and SPDC
•SPDCOPA
•OPA is …?
Why OPA?
Why SPDC?
Introduction
Light
gamma-ray
X-ray
Ultraviolet
visible
infrared
radio wave
=> Electro-magnetic wave
Introduction
Light-matter interaction
Electric field make dielectric polarization
Emission from dipole
oscillating in vertical direction
E : exp(-iwt)
E*E : exp(-i2wt)
Second harmonic generation (SHG)
using a non-linear crystal
within some limitation from physical law…
BBO crystal
b-BaB2O4
Introduction
energy / momentum conservation in frequency mixing
k2,w
k1,w
Introduction
Reversible? YES!
Reverse process
spontaneous parametric down conversion (SPDC)
occur by itself
2=>1+1
2=>0.8+1.2
2=>1+1
seed | w/o amp
Introduction
How does SPDC occur?
similar as OPA (optical parametric amplification)
…what is OPA?
Signal
(amplified)
pump
pump
seed
idler
process | difference frequency generation
hnpump-hnsignal=hnidler
Energy conservation
hnpump=hnsignal+hnidler
signal | amplified
Introduction
How does SPDC occur?
similar as OPA (optical parametric amplification)
signal
SPDC starts with vacuum noise
(no seed for signal)
pump
idler
process | difference frequency generation
hnpump-hnsignal=hnidler
Energy conservation
hnpump=hnsignal+hnidler
#signal=#idler
quite low efficiency ~10-10
Introduction
Why OPA? complicated setup
intense laser at different wavelength
non-linear spectroscopy in UV/visible/IR…
(ultrafast spectroscopy, Raman for vibration study, …)
Other method?
self phase modulation (SPM) | low efficiency
intensity (arb. units)
3
2
1
0
400
600
wavelength (nm)
800
Introduction
Why SPDC? low conversion efficiency
interesting character of entanglement
never broken security | quantum communication
easy to transfer | via optical fiber
Other method?
singlet (a pair of spin ½ particle)
Outline
Introduction
Optical parametric processes
Opt. param. amplifier (OPA)
Spontaneous param. down conv. (SPDC)
Application | classical
Broadband generation | for short pulse
Application | quantum
Entangled photon pairs
Ghost imaging | wave vector
Ghost spectroscopy | frequency
Quantum key distribution (QKD) | polarization
Multiplex QKD | polarization and frequency
Entangled photon beam
Conclusion
Our work
Application | classical
Broadband generation | for short pulse
 1

Shorter pulse needs broader spectrum
 
Application | classical
Broadband generation | for short pulse
Optical parametric amplifier (OPA)
nondegenerate
degenerate
Non-collinear OPA (NOPA)
Application | classical
Broadband generation | for short pulse
OPA (OPG with WLC)
WLC
pulse width=~9fs
6.28
pulse train
4.71
0.8
0.6
3.14
0.4
1.57
0.2
0.0
-80
-60
-40
-20
0
delay (fs)
20
40
60
0.00
80
phase (rad.)
Intensity (arb. unit)
1.0
Spectrum diffracted by grating
Visible broadband
Outline
Introduction
Optical parametric processes
Opt. param. amplifier (OPA)
Spontaneous param. down conv. (SPDC)
Application | classical
Broadband generation | for short pulse
Application | quantum
Entangled photon pairs
Ghost imaging | wave vector
Ghost spectroscopy | frequency
Quantum key distribution (QKD) | polarization
Multiplex QKD | polarization and frequency
Entangled photon beam
Conclusion
Our work
Application | quantum
SPDC generates photon pairs (low efficiency)
w s, ks
w p, kp
NLC
w i, ki
correlated parameters
(1) wave vector : k p = k s + k i
(2) frequency ： w p = w s + w i
(3) polarization：
(in case of Type-II crystal)
1
 H s | V i  |V s | H i 
2
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…
Interference only in unknown case
path entanglement
Interference of “probability”, “wavefunction”
different from statistics of classical phenomena=quantum
Are there any other entanglements?
Yes, we will see them in the following pages!
Application | quantum
Y. Shih, J. Mod. Opt. 49, 2275 (2002)
quantum lithography | wave vector
better resolution ( than classical limit ) ~ lp= l /2
Schematic set-up
half!
(Young’s :
“SPDC photon pairs” v.s. “classical light”
cos2 [(2b / 2l ) ] )
Experimental result (quantum lithograph)
quantum
classical
Application | quantum
ghost imaging | wave vector
BBO
coincidence count
CC1
CC2
CC3
CC1 CC2 CC3
Application | quantum
ghost imaging | wave vector
BBO
coincidence count
CC1
CC2
CC3
CC1 CC2 CC3
Application | quantum
ghost imaging
measure the shape of an object
Detector does NOT scan after object
classical
w s, ks
w p, kp
NLC
w i, ki
Y. Shih, J. Mod. Opt. 49, 2275 (2002)
Application | quantum
ghost spectroscopy | frequency
BBO
coincidence count
CC1
CC2
CC3
CC1 CC2 CC3
Application | quantum
ghost spectroscopy | frequency
BBO
coincidence count
CC1
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
OF : optical fiber
SPCM : single photon
counting module
TAC : time-to-amplitude
converter
Delay : delay module
PC : computer
S : sample (Nd+3-doped glass)
L1 : focusing lens
(f=100mm, 8mm)
1. Broadband photon pairs
Spectrum of photon pairs and absorption spectrum of the sample
pump focusing lens (f=100mm)
more absorption in longer wavelength
1. Broadband photon pairs
result : absorption spectrum
calculate absorption spectrum from the ratio
→ agree with the result by a spectrometer
1. Broadband photon pairs
result : absorption spectrum
agree with the result by a spectrometer
1. Broadband photon pairs
summary of this section
spectrum of SPDC photon pairs
spherical lens → objective lens
(f=100 → 8mm)
spectrum was broadened (11,11→63,69nm)
Nd3+ -doped glass ( in the idler light path)
coincidence resolving signal light’s frequency
→ absorption spectrum was measured
fit well with the result measured by a spectrometer
without resolving the frequency of photon transmitted
through the sample
A. Yabushita et. al., Phys. Rev. A 69, 013806 (2004)
Outline
Introduction
Optical parametric processes
Opt. param. amplifier (OPA)
Spontaneous param. down conv. (SPDC)
Application | classical
Broadband generation | for short pulse
Application | quantum
Entangled photon pairs
Ghost imaging | wave vector
Ghost spectroscopy | frequency
Quantum key distribution (QKD) | polarization
Multiplex QKD | polarization and frequency
Entangled photon beam
Conclusion
Our work
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
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
+  +  + +
•base at random
0
  + +  +
1
0
+

1
0
0
1
0
Application | quantum
50% of keys can be shared
(shared keys are same)
complicated…But secure!
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
+

1
0
0
1
0
How can it be secure??
Application | quantum
0
1 1 1 1 0
BB84 protocol | single photon
Can it be secure?
•key at random
0 1 0 1 1 0
•base at random
+  +  + +
base? (random try) +    + 
0
•base at random
0

1
1
1
0
  + +  +
1
0
+
1
1
1
0
1
1
Security can be checked!
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
•base at random
0

1
1
1
0
  + +  +
1
0
+
1
1
0
0
1
1
Error!
1. Broadband photon pairs
polarization-entangled photon pairs
Alice
EPR-Bell
source
Bob
12
1

2
1

2
1

2

1
2

1
2




1
2

1
2

1

2


1. Broadband photon pairs
Mixed state (statistical mixture)
Alice
HV and VH
(50%-50%)
Bob
?
?
QKD example (without Eve)
Base
select
Alice
0
1
1
0
H
V
V
H
1
R
L
If they use the same base,
“100%” correlation
(quantum key distributed!)
Bob
Base
select
V
H
H
V
0
1
1
0
…
…
0
EPR-pair
L
R
0
1
QKD example (with Eve)
Base
select
Alice
V
H
H
V
…
…
V
H
H
V
…
1
1
0
V
H
H
V
…
H
V
V
H
0
Bob
Base
select
EPR-pair
0
1
1
0
Eve also share the key (NOT secure QKD…)
How can it be improved?
?
Ekert91 protocol
Base
select
Alice
0
1
0
0
0
1
1
1
H
L
R
H
R
L
V
V
EPR-pair
Base information
(classical communication)
“100%” correlation
Bob
Base
select
V
H
L
R
V
R
L
H
0
1
0
1
0
1
0
1
Ekert91 protocol
Base
select
Alice
Base
select
EPR-pair
Bob
OK
Base information
0
1
0
0
0
1
1
1
H
L
R
H
R
L
V
V
Bob can
detect Eve
(secure!)
R
V
L
V
L
H
R
H
R
V
L
V
L
H
R
H
V
H
L
R
V
L
R
H
0
1
OK
0
1
0NG!
0
0 OK
1
Experimental example of QKD
T. Jennewein et. Al., PRL 84, 4729 (2000)
Outline
Introduction
Optical parametric processes
Opt. param. amplifier (OPA)
Spontaneous param. down conv. (SPDC)
Application | classical
Broadband generation | for short pulse
Application | quantum
Entangled photon pairs
Ghost imaging | wave vector
Ghost spectroscopy | frequency
Quantum key distribution (QKD) | polarization
Multiplex QKD | polarization and frequency
Entangled photon beam
Conclusion
Our work
Generation of photon pairs entangled
in their frequencies and polarizations
(for WDM-QKD)
2w
w  dw
frequency-entangled
w  dw
BBO
(type-II)
e
o/e
polarization-entangled
e/o
polarization-entangled pair
at many wavelength combinations
light source for WDM-QKD
Standard :
e
o/e
Multiplex :
polarization-entangled
polarization-entangled
o/e
e
o/e
polarization-entangled
o/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 photon
counting module
TAC : time-to-amplitude
converter
Delay : delay module
PC : computer
IRIS : iris diaphragms
BS : non-polarizing beam splitter
POL1,2 : linear polarizer
1. Broadband photon pairs
simulation
  H s V i  f  ei V
1
45o
0o
f=1
=60o
0.5
45o
60
0.5
90o
120
0
0
180
60
180
3
135o
0o
45o
f=1.732
=0o
0.5
coincidence counts (arb. units)
coincidence counts (arb. units)
1
0o
2
45o
135o
1
90o
90o
0
0
120
 i (degree)
 i (degree)
f=1
=180o
i
135o
90o
0
0
H
0o
135o
coincidence counts (arb. units)
coincidence counts (arb. units)
1
f=1
=0o
s
60
 i (degree)
120
180
0
0
60
 i (degree)
120
180
1. Broadband photon pairs
polarization correlation (1st diffraction@870nm)
  H s V i  f  ei V
0o
s
H
45o
135o
phase shift (866nm)
< phase shift (870nm)
f  1.7  1
90o
visibility < 100%
  0, 180
o
i
polarization correlation (1st diffraction@870nm)
i
  H s V i  f e V
0o
45o
H
i
visibility relative
phase
135o
90o
s
0o
0.75
45o
0.43
-25o
135o 0.31
35o
90o
-81o
0.50
phase shift (866nm)
f  1.7  1
< phase shift (870nm)
visibility<100%
  0, 180
o
no entanglement （iris open）
entangled （iris 1mm）
phase shift (866nm) < phase shift (870nm)
but phase shift<45o
 f  1.7  1
to improve : walk-off compensation
visibility<100% (866nm, 870nm)
  0, 180
o
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 polentanglement)
A. Yabushita et. al, J. Appl. Phys., 99, 063101 (2006)
Outline
Introduction
Optical parametric processes
Opt. param. amplifier (OPA)
Spontaneous param. down conv. (SPDC)
Application | classical
Broadband generation | for short pulse
Application | quantum
Entangled photon pairs
Ghost imaging | wave vector
Ghost spectroscopy | frequency
Quantum key distribution (QKD) | polarization
Multiplex QKD | polarization and frequency
Entangled photon beam
Conclusion
Our work
1
2
3
4
0.4
0.2
0.2
0.0
0.0
4
0.2
0.2
3
1
2
1
2
2
3
1
3
4
4
Beam-like polarization entangled
photon pair generation
羅信斌 (Hsin-Pin Lo)
Department of Physics, NTHU
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)
Department of Electrophysics, National Chiao Tung University
羅志偉 (Prof. C. W. Luo)
Department of Electrophysics, National Chiao Tung University
陳柏中 (Prof. P. C. Chen)
Department of Physics, Nation Tsing Hua University
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
超 快 動 力 學 研 究 室
先 進 超 快 雷 射 研 究 中 心
SPDC photon image
Beam-like photon pair
H: Horizontal
V: vertical
1
 
[ H1 V2  V1 H 2 ]
2
Polarization Entangled photon pair
Crystal optic axis
H
V
V
H
Generation rate ~ 32,000 s-1
Main idea and experiment setup
V2
H1
Coincidence measurement
H2
V1
V2 H
1
SPCM
L1
L2
H2
V1
L3
QWP
1 i
 
e [ H 1 V2  (ei V1 ) H 2 ]
2
L1=L2=L3

1
 
[ H 1 V2  V1 H 2 ]
2
PRL 90, 240401 (2003)
2 by 2 fiber
HOM interference measurement
60
HWP
Pol.
55
50
Coincidence Count (1 sec)
QWP
45
40
35
30
25
20
15
10
5
0
-3000
-1000
0
1000
Delay (100 nm/ step)
30
Coincidence Count per sec
-2000
L1
20
10
L3
0
-1500
-1000
-500
0
Delay (100 nm/ step)
500
1000
2000
3000
Summary
Introduction
Optical parametric processes
Opt. param. amplifier (OPA)
Spontaneous param. down conv. (SPDC)
Application | classical
Broadband generation | for short pulse
Application | quantum
Entangled photon pairs
Ghost imaging | wave vector
Ghost spectroscopy | frequency
Quantum key distribution (QKD) | polarization
Multiplex QKD | polarization and frequency
Entangled photon beam
Our work
Thank you for your attention!