Quantum Interferometric

Sensors

22 APR 09, NIST, Gaithersburg

Jonathan P. Dowling

Quantum Science & Technologies Group Hearne Institute for Theoretical Physics

Department of Physics & AstronomyLouisiana State University, Baton Rouge

http://quantum.phys.lsu.edu/JP Dowling, “Quantum Optical Metrology — The Lowdown On High-N00N States,” Contemporary Physics 49 (2):

125-143 (2008).

Quantum Science & Technologies Group

Hearne Institute for Theoretical Physics

K.JacobsH.LeeT.LeeG.VeronisP.AnisimovH.CableG.DurkinM.FlorescuL.FlorescuA.GuillaumeP.LougovskiK.KapaleS.ThanvanthriD.UskovA.ChiruvelliA.DaSilvaZ.DengY.GaoR.GlasserM.HanS.HuverB.McCrackenS.OlsonW.PlickG.SelvarajS.VinjamanpathyZ.Wu

Quantum Control Theory

Quantum Metrology

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QuantumSensing

QuantumImaging

Quantum Computing

Predictions are Hard to Make — Especially About the Future!

You Are Here!

$Quantum$ $Computing$

$Quantum$ $Metrology$

$

1995 2000 2005 2010 2015 2020 …

Outline

Overview — N00N states, properties, applications and experiments.

Fully scalable N00N-state generators — from linear-optical quantum computing.

Characterizing and engineering N00N states

What’s New with N00N?

Coherent Manipulation of BECs and Ultrastable Gyroscopes

Schrödinger cat defined by relative

photon number

Path-entangled state . High-N00N state if N > 2.

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

Super-Resolution – effective photon wavelength = /N.

Properties of N00N states

N00N state

Schrödinger cat defined 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. with maximum sensitivity given samplings with a total of N probe particles.

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

Phase Estimation

Prepare correlationsbetween probes

Probe-system

interactionDetectorN 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

ΔH

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

parity measurement

Super-sensitivity: beating the shotnoise limit.

Super-sensitivity: beating the shotnoise limit.

Deposition rate:

Classical input :

N00N input :

Quantum Interferometric Lithography

source of two-mode

correlated light

mirror

N-photonabsorbingsubstrate

phase difference along substrate

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

Super-resolution, beating the classical diffraction limit.Super-resolution, beating the classical diffraction limit.

ΔN ϕ( ) = a† + e−iϕ b†( )

N

a + e+iϕ b( )N

ΔN ϕ( ) = cos2 N ϕ / 2( )

ΔN ϕ( ) = cos2 Nϕ / 2( )

NOONGenerator

a

b

Super-Resolution á la N00N

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

€

€

/N

Super-SensitivityΔϕ =

ΔP

d P / dϕ

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

€

dP1 /dϕ

€

dPN /dϕ

For Many Sensor Applications — LIGO, Gyro,

etc., — We Don’t CARE Which

Fringe We’re On!

The Question for Us is IF any Given Fringe

Moves, With What Resolution Can We Tell This!?

Outline

Overview — N00N states, properties, applications and experiments.

Fully scalable N00N-state generators — from linear-optical quantum computing.

Characterizing and engineering N00N states

What’s New with N00N?

Coherent Manipulation of BECs and Ultrastable Gyroscopes

Road to Entangled- Particle

Interferometry:

Early Example of Remote

Entanglement Generation by Erasure of Which-Path Information Followed by Detection!

Road to Entangled- Particle

Interferometry:

Early Example of Remote

Entanglement Generation by Erasure of Which-Path Information Followed by Detection!

N00N & Linear Optical Quantum Computing

For proposals* to exploit a non-linear photon-photon interaction

e.g. cross-Kerr interaction ,the required optical non-linearity not readily

accessible.

*C. Gerry, and R.A. Campos, Phys. Rev. A 64, 063814 (2001).

Nature 409,page 46,(2001).

H =hκ a†ab†b

Photon-PhotonXOR Gate

Photon-PhotonNonlinearity

Kerr Material

Cavity QEDKimble

Cavity QEDKimble

ProjectiveMeasurement

Linear OptKLM/FransonLinear OptKLM/Franson

WHEN IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT?

G. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314

G. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314

KLM CSIGN Hamiltonian Franson CNOT Hamiltonian

NON-Unitary Gates Effective Unitary GatesNON-Unitary Gates Effective Unitary Gates

We are no longer limited by the nonlinearities we find in Nature!We are no longer limited by the nonlinearities we find in Nature!

Projective Measurement Yields Effective Kerr!

High NOON States

|N,0 + |0,NHow do we make:

*C. Gerry, and R.A. Campos, Phys. Rev. A 64, 063814 (2001).

With a large Kerr non-linearity*:

But this is not practical…need κ = 1!

|1

|N

|0

|0|N,0 + |0,N

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

anoptical

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).

Implemented in Experiments!

SuperQuantumPhaseRealisticallyExtractedálaPhotons!

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

Shih, Alley (1990)….

6-photon Super-

ResolutionResch,…,WhitePRL (2007)Queensland

19902-photon

Nagata,…,Takeuchi, Science (04

MAY)Hokkaido & Bristol

20074-photon

Super-sensitivity&

Super-resolution

Mitchell,…,Steinberg

Nature (13 MAY)Toronto

20043, 4-photon

Super-resolution

Walther,…,Zeilinger

Nature (13 MAY)Vienna

Outline

Overview — N00N states, properties, applications and experiments.

Fully scalable N00N-state generators — from linear-optical quantum computing.

Characterizing and engineering N00N states

What’s New with N00N?

Coherent Manipulation of BECs With Orbital Angular Momentum Beams of Light

N00N

Yes, Jeff and Anton, N00N States Are

Really Entangled!

Yes, Jeff and Anton, N00N States Are

Really Entangled!

Physical Review A 76, 063808 (2007)

U

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2

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2

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2

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0

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1

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0

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0.03

2( 50 + 05 )

Outline

Overview — N00N states, properties, applications and experiments.

Fully scalable N00N-state generators — from linear-optical quantum computing.

Characterizing and engineering N00N states

What’s New with N00N?

Coherent Manipulation of BECs With Orbital Angular Momentum Beams of Light

Who in Their Right Mind Would Think Quantum States Could be Used in Remote Sensing!?“DARPA Eyes Quantum

Mechanics for Sensor

Applications”— Jane’s Defence

Weekly

“DARPA Eyes Quantum Mechanics for

Sensor Applications”

— Jane’s Defence Weekly

EntangledLightSource

DelayLine

Detection

Target

Loss

Winning LSU Proposal

04/21/23 34

Loss in Quantum SensorsSD Huver, CF Wildfeuer, JP Dowling, PRA 063828 (2008).

€

ψN00N

Generator

Detector

Lost photons

Lost photons

La

Lb

Visibility:

Sensitivity:

€

ψ =(10,0 + 0,10 ) 2

€

ψ =(10,0 + 0,10 ) 2

€

ϕ

SNL---

HL—

N00N NoLoss —

N00N 3dB Loss ---

Super-Lossitivity

Δϕ =ΔP

d P / dϕ

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

Gilbert, Hamrick, Weinstein, JOSA B, 25 (8): 1336-1340 AUG 2008

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

€

dP1 /dϕ

€

dPN /dϕ

€

e−γL → e−NγL

Loss in Quantum SensorsS. Huver, C. F. Wildfeuer, J.P. Dowling, PRA 063828 (2008).

€

ψN00N

Generator

Detector

Lost photons

Lost photons

La

Lb

€

ϕ

Q: Why do N00N States “Suck” in the Presence of Loss?A: Single Photon Loss = Complete “Which Path” Information!

€

N A 0 B + e iNϕ 0 A N B → 0 A N −1 B

A

B

Gremlin

Towards A Realistic Quantum SensorTry other detection scheme

and states!

M&M Visibility

€

ψM&M

Generator

Detector

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

0.05

0.3

M&M’ Adds Decoy Photons

Mitigating Loss in Quantum SensorsTry other detection scheme

and states!

€

ψM&M

Generator

Detector

Lost photons

Lost photons

La

Lb

€

ψ =( m,m' + m',m ) 2M&M state:

€

ϕ

M&M State —

N00N State ---

M&M HL —

M&M HL —

M&M SNL ---

N00N SNL ---

A FewPhotonsLost

Does NotGive

Complete“Which Path”

Outline

Overview — N00N states, properties, applications and experiments.

Fully scalable N00N-state generators — from linear-optical quantum computing.

Characterizing and engineering N00N states

What’s New with N00N?

Coherent Manipulation of BECs and Ultrastable Gyroscopes

Sagnac Effect in GyroscopySagnac effect is used to measure rotation rates using

interference

Atom interferometers are in principle more sensitive that light-based ones.

€

φSagnac = 4πΩA

λv

€

mc 2 /hω ~ 1010

Orbital Angular Momentum of Light

1. Wavefront contains azimuthal phase singularities.

2. Each photon carries of orbital angular momentum.

€

a− −l + e iφa+ +l( ) 2€

l

€

lh

[1] K.T. Kapale and J.P. Dowling, PRL 95, 173601 (2005).

[2] N. Gonzalez et. al, Opt. Exp. 14, 9093 (2006)

STIRAP* Makes BEC Vortex Superpositions

Counterintuitive

pulse sequence

€

Ωc

€

Ω±

Ω±(ρ ,φ, z, t) = a±Ω0 (t)ρ

w⎛⎝⎜

⎞⎠⎟

|l |

eilφ

LG0l (ρ ,φ)

1 24 34eikz;Ωc (t) = Ω0 (t)

*Stimulated Rapid AdiabaticPassage

Mexican Hat Trap with

Thomas-Fermi Wave function

€

rr Ψ(t) = α (t)ψ g (

r r ) + β (t)ψ +(

r r ) + γ (t)ψ−(

r r )

€

ψg (r r ) = LG0

0(ρ,φ);ψ ±(r r ) = LG0

±2(ρ,φ)

€

F(t) =|α (t) |2 − | β (t) |2 − | γ(t) |2

General state of the BEC at time ‘t’

Measure of vortex transfer

[3] S. Thanvanthri, K. T. Kapale and J.P. Dowling, PRA 77, 053825 (2008)

Sagnac effect in vortex BEC superpositions

For a vortex superposition rotating at angular velocity ,

the vortex interference pattern rotates by an angle €

Ω

rr Ψ(t,ω ) =(eiφSagnacψ +(

rr ) + e−iφSagnacψ −(

rr )) / 2

€

φSagnac

Detection using Phase Contrast Imaging

Advantage: Non destructive detection, increased phase accumulation with time.

SNR =ΔφSagnac / Δφnoise Δφnoise ≈ 1 / Nsc

Sensitivity

State of the art

Ωmin ~ 1.25 ×10−5 rads–1Hz–1/2

Ωmin ~ 10−10 rads–1 Hz–1/2

Stability? Noise from Atomic drift:

€

ρ = R

€

ρ =1.5 R

€

ρ =0.5 R

€

Δφ=φSagnac (1.5 R , t) − φSagnac (0.5 R , t)

€

Δφ ≈68μ deg/hr

Over 8 hours accumulation Current atom gyros, over 4 hours,

€

Δφ ≈0.2μ deg/hr

D. S. Durfee, Y. K. Shaham and M. A. Kasevich, PRL 97, 240801 (2006).

• An ultra-stable, compact atom gyroscope.

• Better imaging techniques directly improve sensitivity.

• Atom drift can further be controlled using trap geometry.

“Quantum Metrology has Rejuvenated My Career!” — Carlton M. Caves (Oct 07)

You Are Here!

Outline

Overview — N00N states, properties, applications and experiments.

Fully scalable N00N-state generators — from linear-optical quantum computing.

Characterizing and engineering N00N states

What’s New with N00N?

Coherent Manipulation of BECs and Ultrastable Gyroscopes