1. 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

2. Not to be confused with: Quantum Meteorology!
Dowling JP, “Quantum Metrology,”
Contemporary Physics 49 (2): (2008)

3. 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

4. Outline Nonlinear Optics vs. Projective Measurements
Quantum Imaging vs. Precision Measurements
Showdown at High N00N!
Mitigating Photon Loss
6. Super Resolution with Classical Light
7. Super-Duper Sensitivity Beats Heisenberg!

5. Optical Quantum Computing: Two-Photon CNOT with Kerr Nonlinearity
The Controlled-NOT can be implemented using a Kerr medium:
(3)
Rpol
PBS z
|0= |H Polarization
|1= |V Qubits
R is a /2 polarization rotation,
followed by a polarization dependent
phase shift .
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).

6. Optical Quantum Computing
Two Roads to
Optical Quantum Computing
Cavity QED
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.

7. Linear Optical Quantum Computing
Linear Optics can be Used to Construct 2 X CSIGN = CNOT Gate and a Quantum Computer:
Milburn
Knill E, Laflamme R, Milburn GJ
NATURE 409 (6816): JAN
Franson JD, Donegan MM, Fitch MJ, et al.
PRL 89 (13): Art. No SEP

8. WHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT?
Photon-Photon
XOR Gate
  LOQC  
KLM
Cavity QED
EIT
Photon-Photon
Nonlinearity
???
Kerr Material
Projective
Measurement

9. Projective Measurement Yields Effective Nonlinearity!
G. G. Lapaire, P. Kok, JPD, J. E. Sipe, PRA 68 (2003)
A Revolution in Nonlinear Optics at the Few Photon Level:
No Longer Limited by the Nonlinearities We Find in Nature! 
NON-Unitary Gates  Effective Nonlinear Gates
Franson CNOT: Cross Kerr
KLM CSIGN: Self Kerr

10. Shot noise Heisenberg Quantum Metrology
H.Lee, P.Kok, JPD, J Mod Opt 49, (2002) 2325
Quantum Metrology
Shot noise
Heisenberg

11. Sub-Shot-Noise Interferometric Measurements
With Two-Photon N00N States
A Kuzmich and L Mandel; Quantum Semiclass. Opt. 10 (1998) 493–500.
SNL HL

12. a† N a N Super-Resolution Sub-Rayleigh
AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733
a† N a N
Super-Resolution
Sub-Rayleigh

13. New York Times
Discovery Could Mean Faster Computer Chips

14. Quantum Lithography Experiment
|20>+|02>
|10>+|01>

15. Quantum Imaging: Super-Resolution

N=1 (classical)
N=5 (N00N) 

16. Quantum Metrology: Super-Sensitivity
N=1 (classical)
N=5 (N00N)
dPN/d
Shotnoise
Limit:
1 = 1/√N
Heisenberg
Limit:
N = 1/N
dP1/d

17. Showdown at High-N00N! |N,0 + |0,N How do we make High-N00N!?
With a large cross-Kerr nonlinearity!* H =  a†a b†b
|1
|0
|N
|N,0 + |0,N
|0
This is not practical! —
need  = p but  = 10–22 !
*C Gerry, and RA Campos, Phys. Rev. A 64, (2001).

18. Success probability approximately 5% for 4-photon output.
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, (2002).

19. Implemented in Experiments!

20. N00N State Experiments 1990’s 2-photon 2004 3, 4-photon Super-
Mitchell,…,Steinberg
Nature (13 MAY)
Toronto
2004
3, 4-photon
Super-
resolution
only
Walther,…,Zeilinger
Nature (13 MAY) Vienna
Rarity, (1990)
Ou, et al. (1990)
Shih (1990)
Kuzmich (1998)
Shih (2001)
6-photon
Super-resolution
Only!
Resch,…,White
PRL (2007)
Queensland
Nagata,…,Takeuchi,
Science (04 MAY)
Hokkaido & Bristol
2007
4-photon
Super-sensitivity
&
Super-resolution

21. Quantum LIDAR “DARPA Eyes Quantum Mechanics for Sensor Applications”
— Jane’s Defence Weekly
Winning
LSU Proposal
Nonclassical
Light
Source
Delay
Line
Detection
Target
Noise
forward problem solver
INPUT
“find
min( )“
FEEDBACK LOOP:
Genetic Algorithm
inverse problem solver
OUTPUT
N: photon
number
loss A
loss B

22. Loss in Quantum Sensors
SD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # DEC 2008
N00N
Generator
Detector
Lost photons La Lb
Visibility:
Sensitivity:
N00N 3dB Loss ---
N00N No
Loss —
SNL---
HL—
4/26/2017 22 22

23. 3dB Loss, Visibility & Slope — Super Beer’s Law!
Super-Lossitivity
Gilbert, G; Hamrick, M; Weinstein, YS; JOSA B 25 (8): AUG 2008
N=1 (classical)
N=5 (N00N)
3dB Loss, Visibility & Slope — Super Beer’s Law! 23

24. Loss in Quantum Sensors
S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # DEC 2008
N00N
Generator
Detector
Lost photons La Lb A B
Gremlin
Q: Why do N00N States Do Poorly in the Presence of Loss?
A: Single Photon Loss = Complete “Which Path” Information! 24

25. Towards A Realistic Quantum Sensor
S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # DEC 2008
M&M
Generator
Detector
Lost photons La Lb
Try other detection scheme and states!
M&M state:
M&M Visibility
N00N Visibility
M&M’ Adds Decoy Photons
0.3
0.05 25

26. Towards A Realistic Quantum Sensor
S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # DEC 2008
M&M
Generator
Detector
Lost photons La Lb
M&M state:
N00N State ---
M&M State —
A Few
Photons
Lost
Does Not
Give
Complete
“Which Path”
N00N SNL ---
M&M SNL ---
M&M HL —
M&M HL — 26

27. Optimization of Quantum Interferometric Metrological Sensors In the
Presence of Photon Loss
PHYSICAL REVIEW A, 80 (6): Art. No 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.

28. Lossy State Comparison
PHYSICAL REVIEW A, 80 (6): Art. No 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.

29. 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
Parity
Detector!

30. Quantum Metrology with Two-Mode Squeezed Vacuum:
Parity Detection Beats the Heisenberg Limit
PRL 104, (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 HL
TMSV
& QCRB
HofL

31. Outline Nonlinear Optics vs. Projective Measurements
Quantum Imaging vs. Precision Measurements
Showdown at High N00N!
Mitigating Photon Loss
6. Super Resolution with Classical Light
7. Super-Duper Sensitivity Beats Heisenberg!