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