Quantum Optical Computing, Imaging, and Metrologyphys.lsu.edu/~jdowling/talks/NRT10-AQIS.pdf · Imaging, and Metrology quantum.phys.lsu.edu Hearne Institute for Theoretical Physics

Jonathan P. Dowling

Quantum Optical Computing,Imaging, and Metrology

quantum.phys.lsu.edu

Hearne Institute for Theoretical PhysicsQuantum Science and Technologies Group

Louisiana State UniversityBaton Rouge, Louisiana USA

AQIS, 31 AUG 10, University of Tokyo

Dowling JP, “Quantum Optical Metrology — The Lowdown On High-N00NStates,” Contemporary Physics 49 (2): 125-143 (2008).

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

Inset: P.M.Anisimov, B.R.Bardhan, A.Chiruvelli, L.Florescu, M.Florescu, Y.Gao, K.Jiang, K.T.Kapale, T.W.Lee,D.J.Lum, S.B.McCracken, C.J.Min, S.J.Olsen, R.Singh, K.P.Seshadreesan, S.Thanvanthri, G.Veronis.

Not Shown: R.Cross, B.Gard, D.J.Lum, G.M.Raterman, C.Sabottke,

Hearne Institute for Theoretical PhysicsQuantum Science & Technologies Group

Nano-Technology

“There's Plenty of Room at the Bottom.”— Richard Feynman (1960)

{1010010100101101}

Classical: All The Information in EveryComputer in the World Can Be Stored

in a Centimeter-Size Chunk of 1021(1,000,000,000,000,000,000,000)

Silicon Atoms at One Bit Per Atom.

1.0 cm

Quantum TechnologyThere's Plenty More Room

in the Quantum!

Quantum: All The Information inEvery Computer in the World CanBe “Stored” in Seventy (70)

Silicon Atoms atOne Quantum Bit Per Atom!

|1010010100101101>

twonanometers

Si - SILICON

IN 3-SPACE POWERS OF 2 IN HILBERT-SPACE

210 21,000,000 = 10301,0301060 versus 10300 2010 A.D. 2060 A.D.

Quantum Metrology

QuantumSensing

QuantumImaging

Quantum Computing

You Are Here!

The Most Important Outcome of the Race to Build A QuantumComputer will Certainly NOT be a Quantum Computer!

$FundingQuantum

Computing$

$FundingQuantum

Metrology$

$

1995 2005 2015 2025 2035

You Are Here!

Outline

1.1. Nonlinear Optics Nonlinear Optics vsvs. Projective Measurements. Projective Measurements

2.2. Quantum Imaging Quantum Imaging vsvs. Precision Measurements. Precision Measurements

3.3. Showdown at High N00N!Showdown at High N00N!

4.4. Mitigating Photon LossMitigating Photon Loss

6.6. Super Resolution with Classical LightSuper Resolution with Classical Light

7. 7. Super-Duper Sensitivity Beats Heisenberg!Super-Duper Sensitivity Beats Heisenberg!

Optical Quantum Computing:Two-Photon CNOT with Kerr Nonlinearity

The Controlled-NOT can be implemented using a Kerr medium:

Unfortunately, the interaction χ(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 π/2 polarization rotation,followed by a polarization dependentphase shift π.

χ(3)

Rpol

PBS

σz

|0〉= |H〉 Polarization|1〉= |V〉 Qubits

Two Roads toOptical Quantum Computing

Cavity QED

I. Enhance NonlinearInteraction with aCavity or EIT —Kimble, Walther,Lukin, et al.

II. ExploitNonlinearity ofMeasurement — Knill,LaFlamme, Milburn,Nemoto, et al.

210 !"# ++ 210 !"# $+

Linear Optical Quantum Computing

Linear Optics can be Used to Construct2 X CSIGN = CNOT Gate and a Quantum Computer:

Knill E, Laflamme R, Milburn GJNATURE 409 (6816): 46-52 JAN 4 2001

Franson JD, Donegan MM, Fitch MJ, et al.PRL 89 (13): Art. No. 137901 SEP 23 2002

Milburn

Photon-PhotonXOR Gate

Photon-PhotonNonlinearity

Kerr Material

Cavity QEDEIT

ProjectiveMeasurement

LOQC KLM

WHY IS A KERR NONLINEARITY LIKE APROJECTIVE 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 YieldsEffective Nonlinearity!

Outline







Schrödinger catdefined by relative

photon number

Path-entangled state . High N00N state if Nlarge.

Super-Sensitivity – improving SNR for detecting small phase(path-length) shifts . Attains Heisenberg limit .

Super-Resolution – effective photon wavelength = λ/N.

Properties of N00N states

N00N state

Schrödinger catdefined by relative

optical phase

Sanders, PRA 40, 2417 (1989).Boto,…,Dowling, PRL 85, 2733 (2000).Lee,…,Dowling, JMO 49, 2325 (2002).

The Abstract Phase-Estimation ProblemEstimate , e.g. path-length, field strength, etc. withmaximum sensitivity given samplings with a total ofN probe particles.

Phase Estimation

Prepare correlationsbetween probes

Probe-systeminteraction DetectorN single

particles

Kok, Braunstein, Dowling, Journal of Optics B 6, (27 July 2004) S811

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

!Ĥ

Optical N00N states in modes a and b ,Unknown phase shift on mode b so .

Cramer-Rao bound “Heisenberg Limit!”.

Phase Estimation

mode a

mode b phaseshift

paritymeasurement

Deposition rate:

Classical input :

N00N input :

Quantum Interferometric Lithography

source of two-modecorrelated

light

mirror

N-photonabsorbingsubstrate

phase difference along substrate

Boto, Kok, Abrams, Braunstein, Williams, and Dowling PRL 85, 2733 (2000)

Super-resolution, beating the single-photon diffraction limit.

!N "( ) = â† + e# i"b̂†( )N â + e+ i"b̂( )N

!N "( ) = cos2N " / 2( )

!N "( ) = cos2 N" / 2( )

NOONGenerator

a

b

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

Quantum Imaging: Super-Resolution

λ

λ/Ν

N=1 (classical)N=5 (N00N)

Quantum Metrology: Super-Sensitivity

dP1/dϕ

dPN/dϕ!" =!P̂

d P̂ / d"


ShotnoiseLimit:Δϕ1 = 1/√N

HeisenbergLimit:ΔϕN = 1/N

Outline







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〉

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, 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

Implemented in Experiments!

N00N State Experiments

Rarity, (1990)Ou, et al. (1990)

Shih (1990)Kuzmich (1998)

Shih (2001)

6-photonSuper-resolution

Only!Resch,…,White

PRL (2007)Queensland

1990’s2-photon

Nagata,…,Takeuchi,Science (04 MAY)

Hokkaido & Bristol;J.C.F.Matthews,A.Politi, Damien

Bonneau, J.L.O'Brien,arXiv:1005.5119

20074-photon

Super-sensitivity&

Super-resolution

Mitchell,…,SteinbergNature (13 MAY)

Toronto

20043, 4-photon

Super-resolution

only

Walther,…,ZeilingerNature (13 MAY)

Vienna

Physical Review 76, 052101 (2007)

PRL 99, 163604 (2007)

Physical Review A 76, 063808 (2007)

U

2

2

2

0

1

0

0.032( 50 + 05 )

Objectives

Approach Status• Use quantum Optics techniques to create,manipulate and measure the collectivestate of an assembly of superconductingqubits.

• cavity QED approach• Adapt techniques used in ion trapexperiments to evaluate the uncertaintyon the energy estimation (spectrometry).

Established the first relation between theuncertainty on the electric charge Qg (ormagnetic flux Fx) estimation and the numberN of qubits:

NQ xg /1!"!##

Develop theoretical techniques toenable Heisenberg-limited magneticand electric field measurementswith superconducting circuits.

Exploit ideas from quantum opticsand superconducting quantumcomputing!

Entangled Superconducting Qubit MagnetometerA Guillaume & JPD, Physical Review A 73 (4): Art. No. 040304 APR 2006.

Outline







Quantum 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

NonclassicalLight

Source

DelayLine

Detection

Target

Noise

“DARPA Eyes QuantumMechanics for Sensor

Applications”— Jane’s Defence

Weekly

WinningLSU Proposal

3/28/11 39

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

!" = !P̂d P̂ / d"

3dB Loss, Visibility & Slope — Super Beer’s Law!


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

!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.

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 “Spin” Coherent.

The conclusion from thisplot is that the optimalstates found by thecomputer code are N00Nstates for very low loss,M&M states forintermediate loss, and“spin” coherent states forhigh loss.

Outline







Super-Resolution at the Shot-Noise Limit with Coherent Statesand Photon-Number-Resolving Detectors

J. Opt. Soc. Am. B/Vol. 27, No. 6/June 2010

Y. Gao, C.F. Wildfeuer, P.M. Anisimov, H. Lee, J.P. Dowling

We show that coherent light coupled with photon numberresolving detectors — implementing parity detection —produces super-resolution much below the Rayleighdiffraction limit, with sensitivity at the shot-noise limit.

ClassicalQuantum

ParityDetector!

Outline







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 isobtained with parity detection. In particular, in our setup, dependenceof the signal on the phase evolves times faster than in traditionalschemes, and uncertainty in the phase estimation is better than 1/.

SNL HL

TMSV& QCRB

HofL

SNL ! 1 / n̂ HL ! 1 / n̂ TMSV ! 1 / n̂ n̂ + 2 HofL ! 1 / n̂2

Outline1.1. Nonlinear Optics Nonlinear Optics vsvs. Projective Measurements. Projective Measurements






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Quantum Optical Computing, Imaging, and Metrologyphys.lsu.edu/~jdowling/talks/NRT10-AQIS.pdf · Imaging, and Metrology quantum.phys.lsu.edu Hearne Institute for Theoretical Physics