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Distinction Between Entanglement
and Coherence in Many Photon
States and Impact on SuperResolution
Jonathan P. Dowling
Hearne Institute for Theoretical Physics
Quantum Science and Technologies Group
Louisiana State University
Baton Rouge, Louisiana USA
quantum.phys.lsu.edu
ONR SCE Program Review
San Diego, 28 JAN 13
Outline
1. Super-Resolution vs. Super-Sensitivity
2. High N00N States of Light
3. Efficient N00N Generators
4. The Role of Photon Loss
5. Mitigating Photon Loss with M&M States
6. Super-Resolving Detection with Coherent States
7. Super-Resolving Radar Ranging at Shotnoise
Quantum Metrology
H.Lee, P.Kok, JPD,
J Mod Opt 49,
(2002) 2325
Shot noise
Heisenberg
Sub-Shot-Noise Interferometric Measurements
With Two-Photon N00N States
A Kuzmich and L Mandel; Quantum Semiclass. Opt. 10 (1998) 493–500.
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Low N00N
2 0  ei 2  0 2
HL
SNL
AN Boto, DS Abrams,
CP Williams, JPD,
PRL 85 (2000) 2733
Super-Resolution
a† N a N
Sub-Rayleigh
New York Times
Discovery
Could Mean
Faster
Computer
Chips
Quantum Lithography Experiment
Low N00N
2 0  ei 2  0 2
|20>+|02
>
|10>+|01
>
Canonical Metrology
Suppose we have an ensemble of N states | = (|0 + ei |1)/2,
and we measure the following observable: A = |0 1| + |1 0|


The expectation value is given by: |A| = N cos 
and the variance (A)2 is given by: N(1cos2)

The unknown phase can be estimated with accuracy:
A
1
 =
=
| d A/d | N

This is the standard shot-noise limit.
note the
square-root
P Kok, SL Braunstein, and JP Dowling, Journal of Optics B 6, (2004) S811
Quantum
Lithography & Metrology
 N   N,0  0,N
Now we consider the state
AN  0,N N,0  N,0 0,N
Quantum Lithography*:

Quantum Metrology:
N |AN|N = cos N
High-Frequency
Lithography
Effect
AN
1
H =
=
| d AN/d |
N



and we measure

Heisenberg Limit:
No Square Root!
P. Kok, H. Lee, and J.P. Dowling, Phys. Rev. A 65, 052104 (2002).
 
Super-Sensitivity: Beats Shotnoise
P̂
d P̂ / d
dPN/d
 
1
N
dP1/d
N=1 (classical)
N=5 (N00N)
Super-Resolution: Beat Rayleigh Limit

N=1 (classical)
N=5 (N00N)

Showdown at High-N00N!
How do we make High-N00N!?
|N,0 + |0,N
With a large cross-Kerr
nonlinearity!* H =  a†a b†b
|1
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|0
|N
|0
This is not practical! —
need  = p but  = 10–22 !
N00N States
In Chapter 11
*C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001).
Measurement-Induced Nonlinearities
G. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314
First linear-optics based High-N00N generator proposal:
Success probability approximately 5% for 4-photon output.
Scheme conditions on the detection
of one photon at each detector
mode a
e.g.
component of
light from an
optical
parametric
oscillator
mode b
H Lee, P Kok, NJ Cerf and JP Dowling, PRA 65, 030101 (2002).
JCF Matthews, A Politi, D Bonneau, JL O'Brien, PRL 107, 163602 (2011)
|10::01>
|10::01>
|20::02>
|20::02>
|30::03>
|40::04>
|30::03>
N00N State Experiments
1990
2-photon
Rarity, (1990)
Ou, et al. (1990)
Shih, Alley (1990)
….
Mitchell,…,Steinberg
Nature (13 MAY)
Toronto
2004
3, 4-photon
Super6-photon
resolution
Super-resolution
only
Only!
Resch,…,White
PRL (2007)
Queensland
2007
4-photon
Super-sensitivity
&
Super-resolution
Walther,…,Zeilinger
Nature (13 MAY)
Vienna
Nagata,…,Takeuchi,
Science (04 MAY)
Hokkaido & Bristol
Efficient Schemes for
Generating N00N States!
|N>|0>
Constrained
|1,1,1>
|N0::0N>
Desired
Number
Resolving
Detectors
Question: Do there exist operators “U” that produce “N00N” States Efficiently?
Answer: YES!
Phys. Rev. Lett. 99, 163604 (2007)
Linear Optical N00N Generator II




2
2
2
0
U
0.03
( 50  05 )
2
1
0



This example disproves the
N00N Conjecture: “That it
Takes At Least N Modes to
Make N00N.”
The upper bound on the resources scales quadratically!
Upper bound theorem:
The maximal size of a
N00N state generated in
m modes via single
photon detection in m-2
modes is O(m2).
HIGH FLUX 2-PHOTON NOON STATES
From a High-Gain OPA (Theory)
We present a theoretical analysis of the properties of an unseeded
optical parametric amplifier (OPA) used as the source of
entangled photons.
OPA Scheme
The idea is to take known bright sources of
entangled photons coupled to number resolving
detectors and see if this can be used in LOQC,
while we wait for the single photon sources.
G.S.Agarwal, et al., J. Opt. Soc. Am. B 24, 270 (2007).
Quantum States of Light
From a High-Gain OPA (Experiment)
HIGH FLUX 2PHOTON N00N
EXPERIMENT
State Before Projection
Visibility Saturates
at 20% with
105 Counts Per
Second!
F.Sciarrino, et al., Phys. Rev. A 77, 012324 (2008)
HIGH N00N STATES FROM STRONG KERR
NONLINEARITIES
Kapale, KT; Dowling, JP, PRL, 99 (5): Art. No. 053602 AUG 3 2007.
Ramsey Interferometry
for atom initially in state b.
Dispersive coupling between the atom and cavity gives
required conditional phase shift
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Quantum States of Light For Remote Sensing
“DARPA Eyes Quantum
Mechanics for Sensor
Applications”
— Jane’s Defense
Weekly
Winning
LSU Proposal
Loss
Target
Entangled
Light
Source
Delay
Line
Detection
Super-Sensitive &
Resolving Ranging
Computational Optimization of
Quantum LIDAR
Noise
Target
INPUT
Nonclassical
Light
Source
inverse problem solver
“find
min(
)“

Delay
Line
Detection
forward problem solver
N: photon
number

in 
N
loss A
c
loss B
i
N  i, i
  f ( in ,  ; loss A, loss B)

i 0


FEEDBACK LOOP:

Genetic Algorithm
OUTPUT
min(  ) ;
N
)
in(OPT )   c (OPT
N  i, i , OPT
i
i 0

Lee, TW; Huver, SD; Lee, H; et al.
PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009
Loss in Quantum Sensors
SD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # 063828 DEC 2008
La

N00N

Detector
Generator

Lb
Visibility:
  ( 10,0  0,10 )
Lost
photons
2

Lost
photons
Sensitivity:   ( 10,0  0,10 )
2
N00N 3dB
Loss ---


N00N No
Loss —
SNL--5/24/2017
25
HL—
Super-Lossitivity
Gilbert, G; Hamrick, M; Weinstein, YS; JOSA B 25 (8): 1336-1340 AUG 2008
 
i
P̂
d P̂ / d
e e
e
 L
dPN /d
N=1 (classical)
N=5 (N00N)

iN 
e
 N L
dP1 /d
3dB Loss, Visibility & Slope — Super Beer’s Law!
Loss in Quantum Sensors
S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008
A
N00N

Lost
photons
La

Detector
B
Generator
Lb

Lost
photons

Gremlin
Q: Why do N00N States Do Poorly in the Presence of Loss?
A: Single Photon Loss = Complete “Which Path” Information!
N
A
0
B
e
iN
0
A
N
B
0
A
N 1 B
Towards A Realistic Quantum Sensor
S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008
Lost
photons
Try other detection scheme and states!
M&M
La


Detector
Generator
M&M state:
  ( m,m'  m',m )
M&M Visibility
  ( 20,10  10,20 )

Lb
N00N Visibility
  ( 10,0  0,10 )
2

0.3
Lost
photons
2

0.05
2
M&M’ Adds Decoy Photons
Towards A Realistic Quantum Sensor
S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008
Try other detection scheme and states!
M&M
La


Detector
Generator
M&M state:
  ( m,m'  m',m )


Lost
photons
Lb
2
Lost
photons
N00N State --M&M State —
N00N SNL --M&M SNL --M&M HL —
M&M HL —
A Few
Photons
Lost
Does Not
Give
Complete
“Which Path”
Optimization of Quantum Interferometric Metrological Sensors In the
Presence of Photon Loss
PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009
Tae-Woo Lee, Sean D. Huver, Hwang Lee, Lev Kaplan, Steven B. McCracken,
Changjun Min, Dmitry B. Uskov, Christoph F. Wildfeuer, Georgios Veronis,
Jonathan P. Dowling
We optimize two-mode, entangled, number states of light in the presence of
loss in order to maximize the extraction of the available phase information in an
interferometer. Our approach optimizes over the entire available input Hilbert
space with no constraints, other than fixed total initial photon number.
INPUT
inverse problem solver
“find
min(
)“

forward problem solver
N: photon
number

in 
N
loss A
c
loss B
i
N  i, i
  f ( in ,  ; loss A, loss B)

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i 0


FEEDBACK LOOP:

Genetic Algorithm
OUTPUT
min(  ) ;
N
)
in(OPT )   c (OPT
N  i, i , OPT
i
i 0
Lossy State Comparison
PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009
Here we take the optimal state, outputted by the code, at
each loss level and project it on to one of three know
states, NOON, M&M, and Generalized Coherent.
The conclusion from this plot is that
The optimal states found by the
computer code are N00N states for
very low loss, M&M states for
intermediate loss, and generalized
coherent states for high loss.
This graph supports the assertion
that a Type-II sensor with coherent
light but a non-classical
detection scheme is optimal for
very high loss.
Super-Resolution at the Shot-Noise Limit with Coherent States
and Photon-Number-Resolving Detectors
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 27 (6): A170-A174
Yang Gao, Christoph F. Wildfeuer, Petr M. Anisimov, Hwang Lee, Jonathan P. Dowling
We show that coherent light coupled with a quantum
detection scheme — parity measurement! — can provide a
super-resolution much below the Rayleigh diffraction
limit, with sensitivity at the shot-noise limit in terms of the
detected photon power.
Parity Measurement!
Quantum
Classical
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Quantum
Detector!
Waves are Coherent!
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
WHY? THERE’S N0ON IN THEM-THERE HILLS!
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Super-Resolution at the Shot-Noise Limit with Coherent States
and Photon-Number-Resolving Detectors
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 27 (6): A170-A174
Yang Gao, Christoph F. Wildfeuer, Petr M. Anisimov, Hwang Lee, Jonathan P. Dowling
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
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For coherent states
parity detection can be
implemented with a
“quantum inspired”
homodyne detection
scheme.
Super Resolution with Classical Light at the Quantum Limit
Emanuele Distante, Miroslav Jezek, and Ulrik L. Andersen

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Super Resolution @ Shotnoise Limit
Eisenberg Group, Israel

Super-Resolving Coherent Radar System
Loss
Target
Coherent
Microwave
Source
Delay
Line
Quantum
Homodyne Detection
Super-Resolving
Shotnoise Limited
Radar Ranging
Super-Resolving Quantum Radar
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Objective
• Coherent Radar at Low Power
• Sub-Rayleigh Resolution Ranging
• Operates at Shotnoise Limit
Objective Approach
Status
• Confirmed Super-resolution
• RADAR with Super Resolution
• Proof-of-Principle in Visible & IR
• Standard RADAR Source
• Loss Analysis in Microwave Needed
• Quantum Detection Scheme
• Atmospheric Modelling Needed
Outline
1. Super-Resolution vs. Super-Sensitivity
2. High N00N States of Light
3. Efficient N00N Generators
4. The Role of Photon Loss
5. Mitigating Photon Loss with M&M States
6. Super-Resolving Detection with Coherent States
7. Super-Resolving Radar Ranging at Shotnoise