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Quantum Imaging - UMBC
Objective
• Study the physics of multi-photon imaging for
entangled state, coherent state and chaotic
thermal state: distinguish their quantum and
classical nature, in particular, the necessary
and/or unnecessary role of quantum entanglement in quantum imaging and lithography.
• Study the “magic mirror” for “ghost” imaging.
New type of
ghost imaging
experiment: a
successful
collaboration
with ARL.
• Muti-photon sources and measurement devices.
Approach
Accomplishments
• Using entangled two-photon and three-photon
states created via optical nonlinear interaction in
spontaneous and stimulated modes for multiphoton spatial correlation study and imaging;
*The physics: Y.H. Shih, “Quantum Imaging”,
IEEE Journal of Selected Topics in Quantum
Electronics, 13, 1016 (2007).
*The experiment: R. Meyers, K.S. Deacon, and
Y.H. Shih, “A new type of ghost imaging experiment”, submitted to Phys. Rev. Lett., (2007).
*The photon source: J.M. Wen, P. Xu, M.H.
Rubin, Y.H. Shih, “Transverse correlations in
triphoton entanglement: geometrical and physical
optics, Phys. Rev. A76, 023828 (2007).
• Using chaotic light source, coherent light source
for two-photon spatial correlation study and ghost
imaging;
• Using photon counting and classical currentcurrent correlation circuit to explore the nature of
two-photon correlation.
* The detector: High uniformity, stability, and
reliability large-format InGaAs APD arrays.
Papers published in peer-reviewed journals
* J.M. Wen, S.W Du , and M.H. Rubin, Spontaneous Parametric Down-Conversion in a
Three-Level SystemΣ, Phys. Rev. A 76 (2007).
* S.W Du, E. Oh, J. Wen, and M.H. Rubin, our-Wave Mixing in Three -Level Systems:
Interference and EntanglementΣ, Phys. Rev. A 76, 013803 (2007).
* S.W. Du, J. Wen, M.H. Rubin, and GY. Yin, our-Wave Mixing and Biphoton
Generation in a Two-Level SystemΣ, Phys. Rev. Lett. 98, 053601 (2007).
* J.M. Wen, S.W. Du, and M.H. Rubin, Biphoton Generation in a Two-Level Atomic
EnsembleΣ, Phys. Rev. A 75, 033809 (2007).
* J.M. Wen, P. Xu, M.H. Rubin, and Y.H. Shih, Transverse Correlation in Triphoton
Entanglement: Geometrical and Physical OpticsΣ, Phys. Rev. A 76, 023828 (2007).
* Y.H. Shih, Quantum ImagingΣ, IEEE J. of Selected Topics in Quantum Electronics,
13, 1016 (2007).
* Y.H. Shih, The Physics of 2 ­ 1+1Σ, Front. Phys., 2, 125 (2007).
Papers published in non-peer-reviewed journals/conference proceedings
* Y.H. Shih, Quantum ImagingΣ, Front. in Optics, OSA annual meeting, San Jose, CA,
2007.
* Y.H. Shih, Quantum ImagingΣ, CLEO Pacifi c Rim 2007, Seoul, Korea, 2007.
* R. Meyers, K.S. Deacon, and Y.H. Shih,
new two-photon ghost im aging
experim entΣ, SPIE Annual Meeting, San Diego, CA, 2007.
* X. Wu, Y Gu, F. Yan, F.S. Choa, P. Shu, High Unif ormity, Stabil ity, and Reli abili ty
Large-Format InGaAs APD ArraysΣ, CLEO/QELSΥ07, Baltimore, MD, 2007.
* Y. Zhou, P. Xu, S.N. Zhu, and Y.H. Shih, The Generation and Temporal Correlation
Measurement of TriphotonΣ, CLEO/QELSΥ07, Baltim ore, MD, 2007.
* J. Wen, S.W. Du, and M.H. Rubin, Biphoton in a Two-Level Cooled Atomi c
EnsembleΣ, CLEO/QELSΥ07, Baltim ore, MD, 2007.
* Y.H. Shih, Quantum ImagingΣ, International Conference on Quantum Information,
Rochester, NY, 2007.
* J. Wen, M.H. Rubin, and S.W Du,
New Beating Experim ent Using Biphotons
Generated from a Two-Level SystemΣ, Slow Light and Fast Light Conference, Salt
Lake City, Utah, 2007.
Part I: The Physics of Quantum Imaging
Objective: “Study the physics of multi-photon imaging,
distinguish their quantum and classical nature, in particular, the necessary and/or unnecessary role of quantum
entanglement in quantum imaging.”
Quantum imaging has demonstrated two peculiar
features:
(1) Enhancing the spatial resolution beyond diffraction limit;
(2) Reproducing “ghost” images in a “nonlocal” manner.
Either the nonlocal behavior observed in ghost imaging or the
apparent violation of the uncertainty principle explored in the
quantum lithography are due to the coherent superposition of
two-photon amplitudes, a nonclassical entity corresponding to
different yet indistinguishable alternative ways of triggering a
joint-detection event.
Classical Imaging
- the concepts
Idealized Classical Imaging
1 1 1
 
so si f
Gaussian thin lens
equation
o
F(i ) 
 i
 d A( ) (   /m)
o
o
o
i
m  si /so
object-plane and the image-plane
Point-point relationship between the
is the result of constructive interference of the fields.


Diffraction-limited Classical Imaging
1 1 1
 
so si f
Gaussian thin lens
equation
o
F(i ) 

 i
 d A( ) somb(   /m)
o
o
o

i
m  si /so
somb(x) = 2J1(x) / x
Point-“spot” relationship between the object plane and the image plane
 is the result of constructive superposition: adiffraction pattern.
Biphoton Ghost Imaging
Biphoton “ghost” Imaging
So
Si
1 1 1
 
S0 Si f
“Ghost” Image: an EPR Experiment in momentum and position correlation.

PRA, 52, R3429 (1995); PRL, 74, 3600 (1995).
What is so special about entangled two-photon state?
“Can quantum mechanical physical reality be
considered complete?”
Einstein, Poldosky, Rosen, Phys. Rev. 47, 777 (1935).
Proposed the entangled two-particle state according to the
principle of quantum superposition:
x1, x 2  

 p1, p2  

dp  p x 2  u p x1   (x1  x 2  x 0 )

dx  x  p2 v x p1    ( p1  p2 )
(x1  x2 )  0 (p1  p2 )  0
Although: x1  , x2  , p1  , p2  .
What is so special about entangled two-photon states?
   ( s   i   p )  (k s  k i  k p ) aˆ s aˆ i 0
s,i

A typical EPR state:
(s  i )  (s  i )
In EPR’s language, the signal and the idler may come out
from any point of the
object plane; however, if the signal
(idler) is found in a certain position, the idler (signal) must
be found in the same position, with 100% certainty.
Biphoton “ghost” Imaging
(s  i )
&
(s  i )


Photon #1 stop at a
point on object plane

(O  I)
Photon #2 stop at a unique
point on image plane
??

Result of a constructive superposition of two-photon amplitudes, a
nonclassical entity corresponding to different yet indistinguishable
alternative ways of triggering a joint-detection event.
Biphoton Ghost Imaging
G ( O, I )  (O , I )
(2)
RC ( I ) 
 d

O
A( O ) (O , I )
2
2
R 2
  dO A(O ) somb(
O  I /m )
so  /2

 d
O
A(O )  ( O  I /m)
2
2
Chaotic light Ghost Imaging
Lens-less ghost Imaging
D2
S.C
X2
X2
Thermal light
(Near-field)
C.C
D1
S.C
X2
X2
Ghost Image with chaotic light
Thermal light
source
Correlator
Photon Counting
Correlation
Measurement
Near-field
  10 / d
Recent Experiment
In collaboration with ARL
Ghost image of
an Army soldier
A photon counting detector, D1, is used to collect and to count all the photons
that are randomly scattered-reflected from the soldier. A CCD array (2D) was
facing the light source instead of the object. An image of the soldier was observed
in the joint-detection of D1 and the CCD.
Chaotic light Ghost Imaging
RC (I )   dO A2 (O ) G(2) (O, I )
(1) 2
12
G ( O, I )  G G  G
(2)
(1)
11
(1)
22
 G0   (O  I )


Constant
Background
Image
Chaotic light ghost Imaging
(1) 2
12
G ( O, I )  G G  G
(2)
(1)
11
(1)
22
 G0   (O  I )
N
(1)
G12
  g1 j (O ) g2 j (I )
j1
  (O  I )
Superposition of two-photon amplitudes
 
() 
() 
G ( x2 ; x1 )   0 E ( x2 ) E ( x1 ) 1q ,1q '
( 2)
2
 
q ,q '
  g2 (x 2 ,q)g1(x1,q ')  g2 (x 2,q ')g1 (x1,q)
2
q ,q '
2
  g1 (x1,q)
2
 g2 (x 2,q) 
q
2
q

g
 1 (x1,q)g2 (x 2,q)
q
Source


q'
D1

q'

q

q
D2
Superposition of classical fields?
(1) 2
12
G G G
(1)
11
(1)
22
N
  E j (1 )
j1

 E k (2 ) 
2
k1
N
E
2
N
j
2
N

E
 j (1)E j (2 )
j1
(1 )E k (2 )  E j ( 2 )E k ( 1)
2
j,k1

Does it make any sense in Maxwell theory of light?
HBT and Ghost Imaging
k-k
Momentum-Momentum
Correlation
Imaging
x-x
Position-Position
Correlation
  10 / d
HBT
Thermal light ghost imaging
Far-field
Near-field
1956
2006
50 years
We cannot but stop to ask: What has been preventing this
simple move for 50 years (1956-2006)? Something must be
terribly misleading to give us such misled confidence not to
even try the near-field measurement in half a century.
Statistical correlation of
intensity fluctuation ?
I1 I2  I1 I2  I1 I2

???
Mode 1
k1
Mode 2
k2
Far-field
(Fourier transform Plane)
Identical modes:
I1 I2  I1 I2  I1 I2
Different modes:
I1 I2  I1 I2
The HBT experiment was successfully interpreted as statistical

correlation of intensity
fluctuations. In HBT, the measurement is in
far-field (Fouriertransform plane). The measured two intensities
have the same fluctuations while the two photodetectors receive the
same mode and thus yield maximum correlation. When the two
photodetector receive different modes, however, the intensities
have different fluctuations, and thus no correlation is observable.
Statistical correlation of intensity fluctuation ???
It does not work for near field !!!
Identical modes:
Different modes:
I1 I2  I1 I2  I1 I2
I1 I2  I1 I2  0


Near-field
Chanceof receivingidentical mod es N
1
 2
Chanceof receiving different mod es N
N
The physics of chaotic light ghost imaging?
“Can Two-photon Correlation of Chaotic Light Be Considered
as Correlation of Intensity Fluctuations?” PRL, 96, 063602
(2006) (G. Scarcelli,V. Berardi, and Y.H. Shih).
“A New Type of Ghost Imaging Experiment”, submitted to
Phys. Rev. Lett., (2007) (R. Meyers, K.S. Deacon, and Y.H.
Shih).
“Quantum Imaging”, IEEE J. of Selected Topic in Quantum
Electronics, 13, 1016 (2007) (Y.H. Shih).
The Physics
*
The nonlocal behavior observed in biphoton ghost imaging is due
to the superposition of two-photon amplitudes, a nonclassical entity
corresponding to different yet indistinguish-able alternative ways of
triggering a joint-detection event.
*
The lens-less ghost imaging of thermal light is an interference
phenomenon involving the superposition indistinguishable twophoton alternatives, rather than statistical correlation of intensity
fluctuation.
*
Ghost imaging: a quantum phenomenon of light.
Part II: The Theory
Lensless imaging with a classical statistical source
SPDC
Klyshko Picture
Incoherent
source
The current-current correlation is given by
iA iB  k  constant+  d  A C AB 
2
2
where
r r
r r
r r
CAB   d s d sg ( j , s )gA ( j , s )(s, s )
2
2
*
B
This are derived using
r r
r
E j   d s g j (  j , s )S( s )
r r
r
r
( s, s )  S( s )S( s )
2
In the paraxial approximation
i eikd
g A (  A , S ) 
AA
 dA
r
r
 ( , kP)  e
A
r
r
r
k
A A  t(  A ) (  A  S , )
dA
1
i kP  2
2
i eikd
g B (  B , S ) 
AB
 dB
r
r
B
r
r
k
A B   (  B  S , )
dB
ik (d d )
r
r
r
r
r
r
i
e


C AB   d 2 s d 2 sgB* (  j , s )gA (  j , s )( s , s )   
A *B A A
   dA dB
r
r k
r
r k
r r
*
2
2
* r
A B A A  t(  A )  d sd s (  B  S , ) (  A  S , )( S , S )
dB
dA
Let us assume the source is large so we can take
2
r r
r
r
d 2 q % r iqr g( r   r
( S , S )  ( S  S )  
(q)e
2
(2 )
S
S
)
A
B
2
d
q iqr g( r A  r B )
dB  dA % r
*
2
A B A A  t(  A ) d A d B 
e
 (q,
)(q)
2
(2 )
k
r
r
r
*
2
A B A A d d  t(  A ) d A d B (  A   B )
Point spread
r
A
B
function
q
dA
S
dB
All the rays from the point at A coherently add at in
the region  centered at B . One can say the same
thing in terms of the wave vectors.
The correlation function is then given by
r
r
 d A C AB   d A t 0 ( A )( A  B )
r
r
r
r
2
 t 0 ( B ) if ( A  B )   ( A  B )
2
2
2
2
If we change the detection scheme, we get a different result.
In the paraxial approximation:
Now each point of the detector A acts like the source of a
spherical wave that illuminates the entire object;
consequently,
for dA=dB
r
r
 d  A C AB   d 0 t 0 ( O )( O   B )
r
r
r
r
2
 t 0 (  B ) if (  A   B )   (  A   B )
2
2
2
2
We see that although the two results are the same for completely
incoherent sources, they differ in the more realistic case. When
looked at in the Klyshko picture, allowing for the phase conjugate
nature of the source, the last case looks like coherent imaging,
while the previous case looks like incoherent imaging.
Part III: The Detector
Range Finder, Stand Off Detection, and 3-D Lidar (APD
Arrays) Applications
DIfferential SCattering/DIfferential Absorption Lidar (DISC/DIAL)
IR LASER
TRANSMITTER
AND RECEIVER
... .
.
. ..
High Performance Photon Counting Detectors
and Arrays
Space Optical Communications
Quantum Communication & Image Applications
Guard-Ring
Mesa
Mesa vs. Guard-Ring
•
Potential issues with mesa APDS for space applications:
– Short lifetime from early breakdown (reliability)
– Dark current increases over time (stability)
Reliability of Guard-Ring APDS
-6
Dark current at M~10 (A)
10
Mesa APDs*
-7
10
-8
10
Goddard/AdTech guard ring APDs
-9
10
0
10
1
10
2
10
3
10
4
10
5
10
Time (hour)
Aging test condition: 200oC/I=100A Testing method: measure dark current
at M~10 periodically * S. Tanaka et al on OFC 2003
Key Issues for Photon Counting (PC)
1. Low Dark Counts:
Dark current is caused by surface leakage, tunneling, defects assisted tunneling.
Can be reduced by decrease the electrical field in the active (absorption) region.
2. High Gain and High Differential Gain
High gain can be obtained with high bias voltage. However, with high bias, a
high dark current will also be produced. High differential gain relies on high
rising slope of APD (dG/dV). An ideal PC APD will have a straight angle I-V
curve, which can be achieved with better device designs.
3. Designing and Fabricating Materials with Reduced AfterPulse Dark Current (AFDC) Amplitude and Duration
AFDC comes from traps in the avalanche regions and trapped carriers in the
hetero-interface. Interstitial Zn atoms created during the diffusion processes are
source of traps and can be activated and converted to substitutional dopants by
appropriate annealing procedures. More steps of InGaAsP quaternary layers
(1.1Q, 1.2Q, 1.3Q, 1.5Q, ..etc.) can added to the InP/InGaAs interface to reduce
hole trapping.
Geiger Mode Operations-I
1. Passive Quenching – Biased above breakdown voltage ( Vop-Vb< ~2V),
rely on a series resistance to reduce voltage drop on the APD when avalanche
is taking place. Advantages: simple circuits, disadvantages: long recovery
time.
I
+Vop
Iop
Vout
VB
Vop
V
Geiger Mode Operations-II
2. Active Quenching – Normally biased above breakdown voltage ( VopVb< ~2V). Once sensed that an avalanche process is taking place, immediately
reduce the bias below Vb. Advantages: relatively short recovery time (still
limited by afterpulse dark counts). Disadvantages: more complex circuits.
+Vop
I
Control Voltage
supplier
Iop
Avalanche Sensing
And trigger circuits
Vout
VB
Vop
V
Geiger Mode Operations-III
3. Gated Operations – Normally biased below or around Vb. A short
electrical pulse is applied to the APD terminal to raise the bias voltage above
Vb and gain when photons are coming. Advantages : simpler ckt and very high
gain. Disadvantages: can only work with periodic signals and
synchronization is an issue.
+Vop
I
Vout
Vac
Idc
VB
Vdc
V
Optimize Design To Achieve High Differential
Gain and Low Dark Current
Vp
10000
1000
Dark current
10
Gain
100
10
1
1
0.1
-100
Electrical Field (kV/cm)
Gain
0
Dark Current (nA)
100
-200
-300
-400
-500
0.1
0
10
20
30
Voltage (V)
40
50
VB
-600
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Distant from Front (micrometer)
Reducing the distance between the punch through voltage
and the breakdown voltage will help to reduce the voltage
drop falling on the small bandgap absorption region
Dark Current I-V Characteristics
Changing with Temperature
Dark Current variation with Temperature
* The dark current is
reduced
• The gain is increased
• A sharp rising gain with
the bias voltage will
help to choose good
operating points.
-7
10
-9
10
-11
10
-13
10
Current (A) @ 294 K
Current (A) @ 260 K
Current (A) @ 230 K
Current (A) @ 200 K
Current (A) @ 140 K
-15
10
-17
10
-10
0
10
20
Voltage (V)
30
40
50
16x16 Arrays and Vbr Color
Map
55
52.5
50
47.5
45
42.5
40
37.5
14 12
10 8
6 4
2 0
0
2
4
6
14
12
10
8
55
44
54
43
53
42
52
41
51
40
50
39
49
38
48
37
47
36
46
35
45
44
64x64 Arrays and Vbr
Breakdown Voltage
Distribution
Innovative Current Bias Scheme
Current bias mode resolves
several common difficult
problems from conventional
voltage biasing mode in arrays.
•
•
•
•
•
No need to know the
breakdown voltage
Less sensitive to the
temperature fluctuation
Much easier to control
the bias point.
Ideal for APD arrays
operations
Partially solved the
after-pulsing problem.
Photon Counting Testing Setup
Operating temperature
Dependence II
0
10
Dark Count Probability
(b)
-1
10
I
=100 nA, V =1 V
I
=100 nA, V =1.5V
I
=100 nA, V =2 V
DC
DC
-2
10
-100
-90
f a = 1k Hz, FWHM=20 ns
-80
-70
-60
o
Operating Temperature ( C)
DC
-50
ac
ac
ac
-40
-30
Dark Count Probability Versus Vac at
Different Temperatures
1
o
at -70 C, I
o
0.8
at -90 C, I
o
=100 nA
DC
at -100 C, I
Dark Count Probability
(c)
=100 nA
DC
=100 nA
DC
0.6
0.4
0.2
0
1
1.5
2
V
ac
(V)
2.5
3
Dark Count Probability Versus the Combination of
IDC and Vac at Fixed Temperatures
1
1
o
o
at -90 C, V =1 V
0.9
at -90 C, I =100 nA
ac
o
at -90 C, V =2 V
ac
o
o
0.9
o
at -90 C, V =3 V
DC
0.8
0.8
0.7
0.7
Dark Count Probability
Dark Count Probability
DC
at -90 C, I =500 nA
ac
0.6
0.5
0.4
0.3
0.2
0.6
0.5
0.4
0.3
0.2
0.1
0
100
DC
at -90 C, I =300 nA
0.1
200
300
400
500
600
I (nA)
DC
700
800
900
1000
0
1
1.2
1.4
1.6
1.8
2
V (V)
ac
2.2
2.4
2.6
2.8
3
Detection Efficiency ~25% Achieved
Under Gated Mode Operations
30
25
o
at -70 C, I =100 nA
20
o
25
at -70 C, I =300 nA
o
o
DC
DC
15
10
5
1.5
DC
at -50 C, I =500 nA
DC
at -70 C, I =500 nA
0
1
DC
at -50 C, I =300 nA
DC
Single Photon Detection Efficiency (%)
Single Photon Detection Efficiency (%)
o
(b)
at -50 C, I =100 nA
(b)
o
2
VB-VP=22V
V (V)
ac
2.5
3
20
15
10
5
0
1
1.2
1.4
2.2
2
1.8
VB-V
=14V
(V)
V
P
1.6
p
2.4
2.6
2.8
3
After Pulsing Problems
1. NASA lidar group did studies on one of the best reported commercial
InGaAs photon counting APD product and found that within the
claimed 10% DE, the portion of total counts caused by after-pulsing is
600% of that of the light count.
2. A test of after-pulsing duration can be done by increasing the gating
pulse repetition rate (reducing time duration between gating pulse) and
observe the increase of DCR.
3. As long as a few micro-seconds after-pulsing duration (equivalently the
blind period) can usually be observed and that can put show stoppers to
many timing sensitive applications.
4. After –pulsing is a material problem and need long term plan of
improvement. However, it can be dealt with short term methods.
Suppression of After-Pulsing
1. The “Current Mode” operation will only allow one avalanche event to
take place and prevent any possible after-pulsing for each gating
period. This is achieved by limiting the DC supply current and the
value of the gating capacitor.
2. During the avalanche process, the APD is switching on and the gating
capacitor is discharged. The APD bias drops below the breakdown
voltage. Limited by the set current of the DC current source and the
capacitance value of the gating capacitor, the charging time to reach
breakdown can never happen until the gating period is passed.
3. On the other hand using the voltage mode to operate the APD, the
gating capacitor is quickly charged up to above breakdown and the
APD is not soon ready to be fired again. At that moment if there still
plenty residue carriers in the avalanche region, after-pulses will be
generated.
Increasing The DC Source Current Can
Reduce The Charging Time.
1
Dark Count Probability (%)
0.8
0.6
0.4
I
=100 nA, V
I
=100 nA, V
I
=500 nA, V
I
=500 nA, V
DC
0.2
DC
DC
DC
0
2
10
ac
ac
ac
ac
=2 V at -30 C
=2 V at room temperature
=2 V at -30 C
=2 V at room temperature
3
4
10
10
Frequency (Hz)
5
10
More on Bias Current Effects
1
Dark Count Probability (%)
0.8
0.6
I
=10 nA
I
=50 nA
I
=100 nA
I
=200 nA
I
=300 nA
I
=400 nA
I
=500 nA
DC
0.4
DC
DC
DC
0.2
DC
DC
DC
0
2
10
3
4
10
10
Frequency (Hz)
5
10
Quantum Imaging - UMBC
Objective
• Study the physics of multi-photon imaging for
entangled state, coherent state and chaotic
thermal state: distinguish their quantum and
classical nature, in particular, the necessary
and/or unnecessary role of quantum entanglement in quantum imaging and lithography.
• Study the “magic mirror” for “ghost” imaging.
New type of
ghost imaging
experiment: a
successful
collaboration
with ARL.
• Muti-photon sources and measurement devices.
Approach
Accomplishments
• Using entangled two-photon and three-photon
states created via optical nonlinear interaction in
spontaneous and stimulated modes for multiphoton spatial correlation study and imaging;
*The physics: Y.H. Shih, “Quantum Imaging”,
IEEE Journal of Selected Topics in Quantum
Electronics, (2007).
*The experiment: R. Meyers, K.S. Deacon, and
Y.H. Shih, “A new type of ghost imaging experiment”, submitted to Phys. Rev. Lett., (2007).
*The photon source: J.M. Wen, P. Xu, M.H.
Rubin, Y.H. Shih, “Transverse correlations in
triphoton entanglement: geometrical and physical
optics, Phys. Rev. A76, 023828 (2007).
• Using chaotic light source, coherent light source
for two-photon spatial correlation study and ghost
imaging;
• Using photon counting and classical currentcurrent correlation circuit to explore the nature of
two-photon correlation.
* The detector: High uniformity, stability, and
reliability large-format InGaAs APD arrays.