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Quantum Optical Metrology,
Imaging, and Computing
“Spiritual
Jian建道灵
Dow-Ling
Jonathan
P.Alliance”
Dowling
Hearne Institute for Theoretical Physics
Quantum Science and Technologies Group
Louisiana State University
Baton Rouge, Louisiana USA
quantum.phys.lsu.edu
QONMIV, 26 JAN 2011, CSRC, Beijing
Dowling JP, “Quantum Optical Metrology — The Lowdown On High-N00N
States,” Contemporary Physics 49 (2): 125-143 (2008).
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Hearne Institute for Theoretical Physics
Quantum Science & Technologies Group
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Photo: 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
Top Inset: P.M.Anisimov, B.R.Bardhan, A.Chiruvelli, L.Florescu, M.Florescu, Y.Gao, K.Jiang, K.T.Kapale,
T.W.Lee, S.B.McCracken, C.J.Min, S.J.Olsen, R.Singh, K.P.Seshadreesan, S.Thanvanthri, G.Veronis.
Bottom Inset C. Brignac, R.Cross, B.Gard, D.J.Lum, Keith Motes, G.M.Raterman, C.Sabottke,
Outline
1. Nonlinear Optics vs. Projective Measurements
2. Quantum Imaging vs. Precision Measurements
3. Showdown at High N00N!
6. Super Resolution with Classical Light
7. Super-Duper Sensitivity Beats Heisenberg!
8. A Parody on Parity
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, Nemoto, et
al.
Cavity QED
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 Effective Nonlinear Gates
KLM CSIGN: Self Kerr
Franson CNOT: Cross Kerr
Phase Estimation
Theorem: Quantum Cramer-Rao bound
optimal POVM, optimal statistical estimator
independent trials/shot-noise limit
Strategies to improve sensitivity:
1. Increase — sequential (multi-round) protocol.
2. Probes in entangled N-party state and one trial
To make Ĥ as large as possible —> N00N!
S. L. Braunstein, C. M. Caves, and G. J. Milburn, Annals of Physics 247, page 135 (1996)
V. Giovannetti, S. Lloyd, and L. Maccone, PRL 96 010401 (2006)
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
Quantum Lithography Experiment
Low N00N
2 0  ei 2  0 2
|20>+|0
2>
|10>+|0
1>
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
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).
J.C.F.Matthews, A.Politi, Damien Bonneau, J.L.O'Brien, arXiv:1005.5119
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!
La

M&M

Detector
Generator
M&M state:
  ( m,m'  m',m )

M&M Visibility
  ( 20,10  10,20 )
Lb
N00N Visibility
  ( 10,0  0,10 )
2

M&M:
V=0.3
Lost
photons
2

N00N:
V=0.05
2
恶魔
M&M’ Adds Decoy Photons
MZI with Coherent Light
There’s
N00N in
Them
There Hills
— Partner!
?

AB
  ei / 2
/ 2
A
B
I. Coherent state input
II. Beam splitter is adjusted to balance any possible loss
Quantum Inspired Detection: 0NN0-N00N!
Visibility is
Very, Very
Low!
0.0002
0.0001
1
2
3
4
5
6
- 0.0001
- 0.0002
K.J. Resch, …, A.G. White, Physical Review Letters 98, 223601 (2007)
Quantum Inspired Detection: 0NN0-N00N!
5
5
4
4
3
3
2
2
1
1
00
Sensitivity is
Much Worse
Than Shot
Noise!
11
22
33
44
55
66
1
?
n
Quantum Inspired Detection: Sum O’ NooNs!
Visibility is
Very Low!
0.003
0.002
0.001
- 2
- 0.001
- 0.002
- 0.003
- 1
0
1
2
3
Quantum Inspired Detection: Sum O’ M&Ms!
Every
Photon is
Precious!
Signal:
Sensitivity:
/ n
SNL
Sub-Rayleigh &
Visibility is One!
We Hit ShotNoise Limit!
Recall 
single mode phase measurement by projection synthesis
discussed in – Barnett&Pegg, PRL 76, 4148 (1996).
We Have Re-Invented the Barnett & Pegg Phase Operator!
B&P Op
The Barnett & Pegg Phase Operator
Transforms into the Parity Operator!
Parity Op
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 /
nφ2
SNL HL
TMSV
& QCRB
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|TMSV>
HofL
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New Journal of Physics 12 (2010) 113025, 1367-2630/10/113025+12$30.00
Parity detection in quantum optical metrology
without number-resolving detectors
William N Plick, Petr M Anisimov, JPD, Hwang Lee, and Girish S Agarwal
Abstract. We present a method for
directly obtaining the parity of a Gaussian
state of light without recourse to photonnumber counting.
The scheme uses only a simple balanced
homodyne technique and intensity
correlation. Thus interferometric schemes
utilizing coherent or squeezed light and
parity detection may be practically
implemented for an arbitrary photon flux.
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Outline
1. Nonlinear Optics vs. Projective Measurements
2. Quantum Imaging vs. Precision Measurements
3. Showdown at High N00N!
6. Super Resolution with Classical Light
7. Super-Duper Sensitivity Beats Heisenberg!
8. A Parody on Parity
非常感谢你！