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Quantum Optical Metrology,
Imaging, and Computing
Jonathan P. Dowling
Hearne Institute for Theoretical Physics
Quantum Science and Technologies Group
Louisiana State University
Baton Rouge, Louisiana USA
quantum.phys.lsu.edu
Frontiers of Nonlinear Physics, 19 July 2010
On The «Georgy Zhukov» Between Valaam and St. Petersburg, Russia
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Dowling JP, “Quantum Metrology,”
Contemporary Physics 49 (2): 125-143 (2008)
Hearne Institute for Theoretical Physics
Quantum Science & Technologies Group
H.Cable, C.Wildfeuer, H.Lee, S.D.Huver, W.N.Plick, G.Deng, R.Glasser, S.Vinjanampathy,
K.Jacobs, D.Uskov, J.P.Dowling, P.Lougovski, N.M.VanMeter, M.Wilde, G.Selvaraj, A.DaSilva
Not Shown: P.M.Anisimov, B.R.Bardhan, A.Chiruvelli, R.Cross, G.A.Durkin, M.Florescu, Y.Gao, B.Gard,
K.Jiang, K.T.Kapale, T.W.Lee, D.J.Lum, S.B.McCracken, C.J.Min, S.J.Olsen, G.M.Raterman, C.Sabottke,
R.Singh, K.P.Seshadreesan, S.Thanvanthri, G.Veronis
Outline
1. Nonlinear Optics vs. Projective
Measurements
2. Quantum Imaging vs. Precision
Measurements
3. Showdown at High N00N!
4. Mitigating Photon Loss
6. Super Resolution with Classical Light
Optical Quantum Computing:
Two-Photon CNOT with Kerr Nonlinearity
The Controlled-NOT can be implemented using a Kerr medium:
|0= |H Polarization
|1= |V Qubits
(3)
PBS
R is a /2 polarization rotation,
followed by a polarization dependent
phase shift .
Rpol
z
Unfortunately, the interaction (3) is extremely weak*:
10-22 at the single photon level — This is not practical!
*R.W. Boyd, J. Mod. Opt. 46, 367 (1999).
Two Roads to
Optical Quantum Computing
I. Enhance Nonlinear
Interaction with a
Cavity or EIT —
Kimble, Walther,
Lukin, et al.
II. Exploit
Nonlinearity of
Measurement —
Knill, LaFlamme,
Milburn, Franson, et
al.
Cavity QED
Linear Optical Quantum Computing
Linear Optics can be Used to Construct
2 X CSIGN = CNOT Gate and a Quantum Computer:
 0   1  2
Knill E, Laflamme R, Milburn GJ
NATURE 409 (6816): 46-52 JAN 4 2001
 0   1  2
Milburn
Franson JD, Donegan MM, Fitch MJ, et al.
PRL 89 (13): Art. No. 137901 SEP 23 2002
WHY IS A KERR NONLINEARITY LIKE
A PROJECTIVE MEASUREMENT?
LOQC
KLM
Photon-Photon
XOR Gate
Cavity QED
EIT
Photon-Photon
Nonlinearity
Projective
Measurement
Kerr Material
Projective Measurement
Yields Effective Nonlinearity!
G. G. Lapaire, P. Kok,
JPD, J. E. Sipe, PRA 68
(2003) 042314
A Revolution in Nonlinear Optics at the Few Photon Level:
No Longer Limited by the Nonlinearities We Find in Nature!
NON-Unitary Gates 
KLM CSIGN: Self Kerr
Effective Nonlinear Gates
Franson CNOT: Cross Kerr
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
>
Quantum Imaging: Super-Resolution

N=1 (classical)
N=5 (N00N)

Quantum Metrology: Super-Sensitivity
P̂
 
d P̂ / d
N
N=1 (classical)
N=5 (N00N)
dP /d
Shotnoise
Limit:
1 = 1/√N
dP1/d
Heisenberg
Limit:
N = 1/N
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
|0
|N
|0
This is not practical! —
need  =  but  = 10–22 !
*C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001).
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, N. J. Cerf and J. P. Dowling, PRA 65, 030101 (2002).
Implemented in Experiments!
N00N State Experiments
1990’s
2-photon
Rarity, (1990)
Ou, et al. (1990)
Shih (1990)
Kuzmich (1998)
Shih (2001)
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
Quantum LIDAR
“DARPA Eyes Quantum
Mechanics for Sensor
Applications”
— Jane’s Defence
Weekly
Winning
LSU Proposal
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
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
22
HL—
Super-Lossitivity
Gilbert, G; Hamrick, M; Weinstein, YS; JOSA B 25 (8): 1336-1340 AUG 2008
 
P̂

i
e e
e
dPN /d
d P̂ / d
N=1 (classical)
N=5 (N00N)
 L
iN 
e
Κ
 N L
Κ
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
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.
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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 “Spin” 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
“spin” coherent states for
high loss.
Super-Resolution at the Shot-Noise Limit with Coherent States
and Photon-Number-Resolving Detectors
J. Opt. Soc. Am. B/Vol. 27, No. 6/June 2010
Y. Gao, C.F. Wildfeuer, P.M. Anisimov, H. Lee, J.P. Dowling
We show that coherent light coupled with photon number
resolving detectors — implementing parity detection —
produces super-resolution much below the Rayleigh
diffraction limit, with sensitivity at the shot-noise limit.
Quantum
Classical
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Parity
Detector!
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Quantum Metrology with Two-Mode Squeezed Vacuum:
Parity Detection Beats the Heisenberg Limit
PRL 104, 103602 (2010)
PM Anisimov, GM Raterman, A Chiruvelli, WN Plick, SD Huver, H Lee, JP Dowling
We show that super-resolution and sub-Heisenberg sensitivity is obtained
with parity detection. In particular, in our setup, dependence of the signal on
the phase evolves <n> times faster than in traditional schemes, and
uncertainty in the phase estimation is better than 1/<n>.
SNL  1 /
nφ ΚΚΚΚΚΚHL  1 / nφ ΚΚΚΚΚΚTMSV  1 /
nφ nφ 2 ΚΚΚΚΚΚHofL  1 /
SNL
nφ2
HL
TMSV
& QCRB
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HofL
Outline
1. Nonlinear Optics vs. Projective
Measurements
2. Quantum Imaging vs. Precision
Measurements
3. Showdown at High N00N!
4. Mitigating Photon Loss
6. Super Resolution with Classical Light