distinction between entanglement and coherence in many
TRANSCRIPT
Jonathan P. Dowling
Distinction BetweenEntanglement and Coherence inMany Photon States and Impact
on Super-Resolution
quantum.phys.lsu.edu
Hearne Institute for Theoretical PhysicsQuantum Science and Technologies Group
Louisiana State UniversityBaton Rouge, Louisiana USA
ONR SCE Program ReviewSan Diego, 28 JAN 13
Schrödinger's Killer App — Race to Build the World's First Quantum Computer
By Jonathan P. Dowling
To Be Published May 6th 2013 by Taylor & Francis – 480 pages
“Told from a government insider's pointof view, this volume is the fascinatingstory of the quest to develop a quantumcomputer. Using non-technicallanguage, amusing personal anecdotes,and easy-to-follow analogies, the bookleads us from the beginnings ofquantum information technology to thepresent time.”
Outline
1.1. Super-Resolution Super-Resolution vsvs. Super-Sensitivity. Super-Sensitivity
2.2. High N00N States of LightHigh N00N States of Light
3.3. Efficient N00N GeneratorsEfficient N00N Generators
4.4. The Role of Photon LossThe Role of Photon Loss
5.5. Mitigating Photon Loss with M&M StatesMitigating Photon Loss with M&M States
6.6. Super-Resolving Detection with Coherent StatesSuper-Resolving Detection with Coherent States
7.7. Super-Resolving Radar Ranging at Shotnoise LimitSuper-Resolving Radar Ranging at Shotnoise Limit
Quantum MetrologyH.Lee, P.Kok, JPD,J Mod Opt 49,(2002) 2325
Shot noise
Heisenberg
Sub-Shot-Noise Interferometric MeasurementsWith Two-Photon N00N States
A Kuzmich and L Mandel; Quantum Semiclass. Opt. 10 (1998) 493–500.
Low!N00N2 0 + ei2! 0 2
SNL
HL
a† N a N
AN Boto, DS Abrams,CP Williams, JPD, PRL85 (2000) 2733
Super-Resolution
Sub-Rayleigh
New York Times
DiscoveryCould MeanFasterComputerChips
Quantum Lithography Experiment
|20>+|02>
|10>+|01>
Low!N00N2 0 + ei2! 0 2
Canonical Metrology
note the square-root
P Kok, SL Braunstein, and JP Dowling, Journal of Optics B 6, (2004) S811
Suppose we have an ensemble of N states |ϕ〉 = (|0〉 + eiϕ |1〉)/√2,and we measure the following observable:
The expectation value is given by: and the variance (ΔA)2 is given by: N(1−cos2ϕ)
A = |0〉 1| + |1〉 0|〉 〉
ϕ|A|ϕ〉 = N cos ϕ〉The unknown phase can be estimated with accuracy:
This is the standard shot-noise limit.
Δϕ = = ΔA
| d A〉/dϕ |〉
√N1
QuantumLithography & Metrology
Now we consider the state
and we measureHigh-FrequencyLithographyEffect
Heisenberg Limit:No Square Root!
P. Kok, H. Lee, and J.P. Dowling, Phys. Rev. A 65, 052104 (2002).
Quantum Lithography*:
Quantum Metrology:
ϕN |AN|ϕN〉 = cos Nϕ〉
ΔϕH = = ΔAN
| d AN〉/dϕ |〉
N1
AN = 0,N N,0 + N,0 0,N
!N = N,0 + 0,N( )
Super-Sensitivity: Beats Shotnoise
dP1/dϕ
dPN/dϕ!" =!P̂
d P̂ / d"
N=1 (classical)N=5 (N00N)
!" <
1N
Super-Resolution: Beat Rayleigh Limit
λ
λ/Ν
N=1 (classical)N=5 (N00N)
Showdown at High-N00N!
|N,0〉 + |0,N〉How do we make High-N00N!?
*C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001).
With a large cross-Kerrnonlinearity!* H = κ a†a b†b
This is not practical! — need κ = π but κ = 10–22 !
|1〉
|N〉
|0〉
|0〉|N,0〉 + |0,N〉
N00N StatesIn Chapter 11
Measurement-Induced NonlinearitiesG. 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.
e.g.component oflight from an
opticalparametricoscillator
Scheme conditions on the detection of one photon at each detector
mode a
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>
|20::02>
|40::04>
|10::01>
|20::02>
|30::03>
|30::03>
N00N State Experiments
Rarity, (1990)Ou, et al. (1990)Shih, Alley (1990)
….
6-photonSuper-resolution
Only!Resch,…,White
PRL (2007)Queensland
19902-photon
Nagata,…,Takeuchi,Science (04 MAY)Hokkaido & Bristol
20074-photon
Super-sensitivity&
Super-resolution
Mitchell,…,SteinbergNature (13 MAY)
Toronto
20043, 4-photon
Super-resolution
only
Walther,…,ZeilingerNature (13 MAY)
Vienna
Efficient Schemes forGenerating N00N States!
Question: Do there exist operators “U” that produce “N00N” States Efficiently?
Answer: YES!
Constrained Desired
|N>|0> |N0::0N>
|1,1,1> NumberResolvingDetectors
Phys. Rev. Lett. 99, 163604 (2007)
U
2
2
2
0
1
0
0.032( 50 + 05 ) This example disproves the
N00N Conjecture: “That itTakes At Least N Modes toMake N00N.”
The upper bound on the resources scales quadratically!
Upper bound theorem:The maximal size of aN00N state generatedin m modes via singlephoton detection in m-2modes is O(m2).
Linear Optical N00N Generator II
HIGH FLUX 2-PHOTON NOON STATESFrom a High-Gain OPA (Theory)
G.S.Agarwal, et al., J. Opt. Soc. Am. B 24, 270 (2007).
We present a theoretical analysis of the properties of an unseededoptical parametric amplifier (OPA) used as the source ofentangled photons.
The idea is to take known bright sources ofentangled photons coupled to number resolvingdetectors and see if this can be used in LOQC,while we wait for the single photon sources.
OPA Scheme
Quantum States of Light From a High-Gain OPA (Experiment)
HIGH FLUX 2-PHOTON N00NEXPERIMENT
F.Sciarrino, et al., Phys. Rev. A 77, 012324 (2008)
State Before Projection
Visibility Saturatesat 20% with105 Counts PerSecond!
HIGH N00N STATES FROM STRONG KERR NONLINEARITIESKapale, KT; Dowling, JP, PRL, 99 (5): Art. No. 053602 AUG 3 2007.
Ramsey Interferometryfor atom initially in state b.
Dispersive coupling between the atom and cavity givesrequired conditional phase shift
Quantum States of Light For Remote Sensing
EntangledLightSource
DelayLine
Detection
Target
Loss
WinningLSU Proposal
“DARPA Eyes QuantumMechanics for Sensor
Applications”— Jane’s Defense Weekly
Super-Sensitive &Resolving Ranging
Computational Optimization ofQuantum LIDAR
!in =
ci N " i, ii= 0
N
#
!"
forward problem solver
!" = f ( #in , " ; loss A, loss B)
INPUT
“findmin( )“
!"
FEEDBACK LOOP:Genetic Algorithm
inverse problem solver
OUTPUT
min(!") ; #in(OPT ) = ci
(OPT ) N $ i, i , "OPTi= 0
N
%
N: photon number
loss Aloss B
Lee, TW; Huver, SD; Lee, H; et al.PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009
NonclassicalLight
Source
DelayLine
Detection
Target
Noise
1/28/13 25
Loss in Quantum SensorsSD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # 063828 DEC 2008
!N00N
Generator
Detector
Lostphotons
Lostphotons
La
Lb
Visibility:
Sensitivity:
! = (10,0 + 0,10 ) 2
! = (10,0 + 0,10 ) 2
!
SNL---
HL—
N00N NoLoss —
N00N 3dBLoss ---
Super-LossitivityGilbert, G; Hamrick, M; Weinstein, YS; JOSA B 25 (8): 1336-1340 AUG 2008
!" =!P̂
d P̂ / d"
3dB Loss, Visibility & Slope — Super Beer’s Law!
N=1 (classical)N=5 (N00N)
dP1 /d!
dPN /d!
ei! " eiN!
e#$ L " e#N$ L
Loss in Quantum SensorsS. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008
!N00N
Generator
Detector
Lostphotons
Lostphotons
La
Lb
!
Q: Why do N00N States Do Poorly in the Presence of Loss?
A: Single Photon Loss = Complete “Which Path” Information!
N A 0 B + eiN! 0 A N B " 0 A N #1 B
A
B
Gremlin
Towards A Realistic Quantum SensorS. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008
Try other detection scheme and states!
M&M Visibility
!M&M
Generator
Detector
Lostphotons
Lostphotons
La
Lb
! = ( m,m' + m',m ) 2M&M state:
! = ( 20,10 + 10,20 ) 2
! = (10,0 + 0,10 ) 2
!
N00N Visibility
0.05
0.3
M&M’ Adds Decoy Photons
Try other detection scheme and states!
!M&M
Generator
Detector
Lostphotons
Lostphotons
La
Lb
! = ( m,m' + m',m ) 2M&M state:
!
M&M State —N00N State ---
M&M HL —M&M HL —
M&M SNL ---
N00N SNL ---
A FewPhotons
LostDoes Not
GiveComplete
“Which Path”
Towards A Realistic Quantum SensorS. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008
Optimization of Quantum Interferometric Metrological Sensors In thePresence 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 ofloss in order to maximize the extraction of the available phase information in aninterferometer. Our approach optimizes over the entire available input Hilbertspace with no constraints, other than fixed total initial photon number.
!in =
ci N " i, ii= 0
N
#
!"
forward problem solver
!" = f ( #in , " ; loss A, loss B)
INPUT
“findmin( )“
!"
FEEDBACK LOOP:Genetic Algorithm
inverse problem solver
OUTPUT
min(!") ; #in(OPT ) = ci
(OPT ) N $ i, i , "OPTi= 0
N
%
N: photon number
loss Aloss B
Lossy State ComparisonPHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009
Here we take the optimal state, outputted by the code, ateach loss level and project it on to one of three knowstates, NOON, M&M, and Generalized Coherent.
The conclusion from this plot is thatThe optimal states found by thecomputer code are N00N states forvery low loss, M&M states forintermediate loss, and generalizedcoherent states for high loss.
This graph supports the assertionthat a Type-II sensor with coherentlight but a non-classicaldetection scheme is optimal forvery high loss.
Super-Resolution at the Shot-Noise Limit with Coherent Statesand Photon-Number-Resolving Detectors
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 27 (6): A170-A174Yang Gao, Christoph F. Wildfeuer, Petr M. Anisimov, Hwang Lee, Jonathan P. Dowling
We show that coherent light coupled with a quantumdetection scheme — parity measurement! — can provide asuper-resolution much below the Rayleigh diffractionlimit, with sensitivity at the shot-noise limit in terms of thedetected photon power.
ClassicalQuantum
µWaves are Coherent!
QuantumDetector!
λ
Parity Measurement!
WHY? THERE’S N0ON IN THEM-THERE HILLS!
Super-Resolution at the Shot-Noise Limit with Coherent Statesand Photon-Number-Resolving Detectors
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 27 (6): A170-A174Yang Gao, Christoph F. Wildfeuer, Petr M. Anisimov, Hwang Lee, Jonathan P. Dowling
λ/10
For coherent statesparity detection can beimplemented with a“quantum inspired”homodyne detectionscheme.
λ
Super Resolution with Classical Light at the Quantum LimitEmanuele Distante, Miroslav Jezek, and Ulrik L. Andersen
Super Resolution @ Shotnoise LimitEisenberg Group, Israel
λ
Super-Resolving Coherent Radar System
Coherent Microwave
Source
DelayLine
QuantumHomodyne Detection
Target
Loss
Super-ResolvingShotnoise LimitedRadar Ranging
Super-Resolving Quantum Radar
Objective
Objective Approach Status
• Coherent Radar at Low Power
• Sub-Rayleigh Resolution Ranging
• Operates at Shotnoise Limit
• RADAR with Super Resolution
• Standard RADAR Source
• Quantum Detection Scheme
• Confirmed Super-resolution
• Proof-of-Principle in Visible & IR
• Loss Analysis in Microwave Needed
• Atmospheric Modelling Needed
Outline
1.1. Super-Resolution Super-Resolution vsvs. Super-Sensitivity. Super-Sensitivity
2.2. High N00N States of LightHigh N00N States of Light
3.3. Efficient N00N GeneratorsEfficient N00N Generators
4.4. The Role of Photon LossThe Role of Photon Loss
5.5. Mitigating Photon Loss with M&M StatesMitigating Photon Loss with M&M States
6.6. Super-Resolving Detection with Coherent StatesSuper-Resolving Detection with Coherent States
7.7. Super-Resolving Radar Ranging at Shotnoise LimitSuper-Resolving Radar Ranging at Shotnoise Limit