Jonathan P. Dowling Distinction Between Entanglement and Coherence in Many Photon States and Impact on Super-Resolution quantum.phys.lsu.edu Hearne Institute for Theoretical Physics Quantum Science and Technologies Group Louisiana State University Baton Rouge, Louisiana USA ONR SCE Program Review San Diego, 28 JAN 13
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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.”
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)
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