Physics 2113 Lecture: 15 FRI 20 FEB Electric Potential III Physics 2113 Jonathan Dowling.
Jonathan P. Dowling
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Jonathan P. Dowling Quantum Optical Metrology, Imaging, and Computing quantum.phys.lsu.edu Hearne Institute for Theoretical Physics Quantum Science and Technologies Group Louisiana State University Baton Rouge, Louisiana USA QONMIV, 26 JAN 2011, CSRC, Beijing QuickTime™ a decompresso are needed to se QuickTime™ and a decompressor are needed to see this picture. Dowling JP, “Quantum Optical Metrology — The Lowdown On High-N00N States,” Contemporary Physics 49 (2): 125-143 (2008). Jian Dow-Ling 建建建 “Spiritual Alliance”
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Quantum Optical Metrology, Imaging, and Computing. 建道灵. “Spiritual Alliance”. Jian Dow-Ling . Jonathan P. Dowling. Hearne Institute for Theoretical Physics Quantum Science and Technologies Group Louisiana State University Baton Rouge, Louisiana USA. quantum.phys.lsu.edu. - PowerPoint PPT Presentation
Transcript of Jonathan P. Dowling
Jonathan P. Dowling
Quantum Optical Metrology, Imaging, and
Computing
quantum.phys.lsu.edu
Hearne Institute for Theoretical PhysicsQuantum Science and Technologies Group
Louisiana State UniversityBaton Rouge, Louisiana USA
QONMIV, 26 JAN 2011, CSRC, Beijing
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Dowling JP, “Quantum Optical Metrology — The Lowdown On High-N00N States,” Contemporary Physics 49 (2): 125-143 (2008).
Jian Dow-Ling 建道灵“Spiritual Alliance”
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.DaSilvaTop 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,
Hearne Institute for Theoretical PhysicsQuantum Science & Technologies Group
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Outline
1.1. Nonlinear Optics vs. Projective Nonlinear Optics vs. Projective
MeasurementsMeasurements
2.2. Quantum Imaging vs. Precision Quantum Imaging vs. Precision
MeasurementsMeasurements
3.3. Showdown at High N00N!Showdown at High N00N!
6. Super Resolution with Classical Light6. Super Resolution with Classical Light
7. Super-Duper Sensitivity Beats 7. Super-Duper Sensitivity Beats
Heisenberg! Heisenberg!
8. A Parody on Parity8. A Parody on Parity
Optical Quantum Computing:Two-Photon CNOT with Kerr
NonlinearityThe Controlled-NOT can be implemented using a Kerr medium:
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).
R is a /2 polarization rotation,followed by a polarization dependentphase shift .
(3)
Rpol
PBS
z
|0= |H Polarization|1= |V Qubits
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, Nemoto, et al.
Photon-PhotonXOR Gate
Photon-PhotonNonlinearity
Kerr Material
Cavity QEDEIT
ProjectiveMeasurement
LOQC KLM
WHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT?
G. G. Lapaire, P. Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314
KLM CSIGN: Self Kerr Franson CNOT: Cross Kerr
NON-Unitary Gates Effective Nonlinear Gates
A Revolution in Nonlinear Optics at the Few Photon Level:No Longer Limited by the Nonlinearities We Find in Nature!
Projective Measurement Yields Effective Nonlinearity!
Strategies to improve sensitivity:1. Increase — sequential (multi-round) protocol.2. Probes in entangled N-party state and one trial
To make as large as possible —> N00N!
Theorem: Quantum Cramer-Rao bound
optimal POVM, optimal statistical estimator
Phase Estimation
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)
independent trials/shot-noise limit
ΔH
+NA0BeiNϕ0ANB
1 + cos N ϕ
2
1 + cos ϕ
2
ABϕ|N⟩A |0⟩B N Photons
N-PhotonDetector
ϕ = kxΔϕ: 1/√N →1/ΝuncorrelatedcorrelatedOscillates N times as fast!N-XOR GatesN-XOR Gatesmagic BSMACH-ZEHNDER INTERFEROMETERApply the Quantum Rosetta Stone!
Quantum MetrologyH.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 + ei2ϕ 0 2
SNL
HL
N Photons
N-PhotonDetectorϕ = kx+NA0BeiNϕ0ANB
1 + cos N ϕ
2
1 + cos ϕ
2
uncorrelatedcorrelatedOscillates in REAL Space!N-XOR Gatesmagic BSFROM QUANTUM INTERFEROMETRYTO QUANTUM LITHOGRAPHY
Mirror
N
2 A
N
2 B
LithographicResist
ϕ →Νϕ λ →λ/Ν
ψ a†
a†
aa ψa† N a N
AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733
Super-Resolution
Sub-Rayleigh
Quantum Lithography Experiment
|20>+|02>
|10>+|01>
Low N00N
2 0 + ei2ϕ 0 2
Showdown at High-N00N!
|N,0 + |0,NHow do we make High-N00N!?
*C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001).
With a large cross-Kerr nonlinearity!* H = k a†a b†b
This is not practical! — need k = but k = 10–22 !
|1
|N
|0
|0|N,0 + |0,N
FIRST LINEAR-OPTICS BASED HIGH-N00N GENERATOR
Success probability approximately 5% for 4-photon output.
e.g. component
oflight from an
optical parametric oscillator
Scheme conditions on the detection of one photon at each detector
mode a
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
Try other detection scheme and states!
M&M Visibility€
ψM&M
GeneratorDetector
Lost photons
Lost photons
La
Lb
€
ψ =( m,m' + m',m ) 2M&M state:
€
ψ =( 20,10 + 10,20 ) 2
€
ψ =(10,0 + 0,10 ) 2
€
ϕ
N00N Visibility
N00N: V=0.05
M&M: V=0.3
M&M’ Adds Decoy Photons
恶魔
MZI with Coherent Light
I. Coherent state inputII. Beam splitter is adjusted to balance any possible loss
? ψ
AB=αeiϕ / 2
Aα / 2
B
There’s N00N in Them There Hills —
Partner!
How can we make coherent state interferometry super-
resolving? – Gao, Anisimov, …, Dowling, JOSA B 27, A170 (2010)
Quantum Inspired Detection: 0NN0-N00N!
K.J. Resch, …, A.G. White, Physical Review Letters 98, 223601 (2007)
1 2 3 4 5 6
- 0.0002
- 0.0001
0.0001
0.0002Visibility is Very,
Very Low!
0 1 2 3 4 5 6
1
2
3
4
5
1 2 3 4 5 60
1
2
3
4
5
?
1n
Sensitivity is Much Worse Than Shot Noise!
Quantum Inspired Detection: 0NN0-N00N!
Quantum Inspired Detection: Sum O’ NooNs!
- 2 - 1 0 1 2 3
- 0.003
- 0.002
- 0.001
0.001
0.002
0.003Visibility is Very Low!
Quantum Inspired Detection: Sum O’ M&Ms!
Signal: Sensitivity:
Sub-Rayleigh & Visibility is
One!
We Hit Shot-Noise Limit!
SNL
Every Photon is Precious!
λ / n
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!
The Barnett & Pegg Phase Operator Transforms into the Parity Operator!
Parity OpB&P 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>.
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SNL HLTMSV& QCRB
HofL
SNL ≡1/ n HL≡1/ n TMSV ≡1/ n n + 2 HoϕL≡1/ n2
|TMSV>
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Parity detection in quantum optical metrologywithout number-resolving detectors
New Journal of Physics 12 (2010) 113025, 1367-2630/10/113025+12$30.00
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 photon-number 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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Outline1.1. Nonlinear Optics vs. Projective Nonlinear Optics vs. Projective
MeasurementsMeasurements
2.2. Quantum Imaging vs. Precision Quantum Imaging vs. Precision
MeasurementsMeasurements
3.3. Showdown at High N00N!Showdown at High N00N!
6. Super Resolution with Classical Light6. Super Resolution with Classical Light
7. Super-Duper Sensitivity Beats 7. Super-Duper Sensitivity Beats
Heisenberg! Heisenberg!
8. A Parody on Parity8. A Parody on Parity
非常感谢你！
