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QuantumInterferometric 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-N00NStates,” Contemporary Physics 49 (2): 125-143 (2008).
Quantum Science & Technologies GroupHearne 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
You Are Here!
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 — fromlinear-optical quantum computing.
Characterizing and engineering N00N states
What’s New with N00N?
Coherent Manipulation of BECs andUltrastable Gyroscopes
Schrödinger catdefined 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 = 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
!H
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
Super-sensitivity: beating the shotnoise limit.
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 classical diffraction limit.
!N"( ) = a
†+ e
# i"b†( )
N
a + e+ i"b( )
N
!N"( ) = cos2N " / 2( )
!N"( ) = cos2 N" / 2( )
NOONGenerator
a
b
Super-Resolution á la N00N
N=1 (classical)N=5 (N00N)
!
! /N
Super-Sensitivity!" =
!P
d P / d"
N=1 (classical)N=5 (N00N)
dP1/d!
dPN/d!
For Many SensorApplications —
LIGO, Gyro, etc., —We Don’t CARE
Which Fringe We’reOn!
The Question forUs is IF any Given
Fringe Moves, WithWhat Resolution
Can We Tell This!?
Outline
Overview — N00N states, properties,applications and experiments.
Fully scalable N00N-state generators — fromlinear-optical quantum computing.
Characterizing and engineering N00N states
What’s New with N00N?
Coherent Manipulation of BECs andUltrastable Gyroscopes
Road toEntangled-Particle
Interferometry:
Early Example ofRemote
EntanglementGeneration by
Erasure ofWhich-PathInformationFollowed byDetection!
N00N & Linear Optical Quantum Computing
For proposals* to exploit a non-linear photon-photon interactione.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 = !! a†ab
†b
Photon-PhotonXOR Gate
Photon-PhotonNonlinearity
Kerr Material
Cavity QEDKimble
ProjectiveMeasurement
Linear OptKLM/Franson
WHEN IS A KERR NONLINEARITY LIKE APROJECTIVE MEASUREMENT?
G. G. Lapaire, Pieter Kok,JPD, J. E. Sipe, PRA 68
(2003) 042314
KLM CSIGN Hamiltonian Franson CNOT Hamiltonian
NON-Unitary Gates → Effective Unitary Gates
We are no longer limited by the nonlinearities we find in Nature!
Projective MeasurementYields Effective Kerr!
High NOON States
|N,0〉 + |0,N〉How 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 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).
Implemented in Experiments!
SuperQuantumPhaseRealisticallyExtractedálaPhotons!
Rarity, (1990)Ou, et al. (1990)Shih, Alley (1990)
….
6-photonSuper-Resolution
Resch,…,WhitePRL (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
Walther,…,ZeilingerNature (13 MAY)
Vienna
Outline
Overview — N00N states, properties,applications and experiments.
Fully scalable N00N-state generators — fromlinear-optical quantum computing.
Characterizing and engineering N00N states
What’s New with N00N?
Coherent Manipulation of BECs With OrbitalAngular Momentum Beams of Light
N00N
Yes, Jeff andAnton, N00N
States Are ReallyEntangled!
Physical Review A 76, 063808 (2007)
U
2
2
2
0
1
0
0.03
2( 50 + 05 )
Outline
Overview — N00N states, properties,applications and experiments.
Fully scalable N00N-state generators — fromlinear-optical quantum computing.
Characterizing and engineering N00N states
What’s New with N00N?
Coherent Manipulation of BECs With OrbitalAngular Momentum Beams of Light
Who in Their Right Mind Would Think Quantum States Could be Used in Remote Sensing!?
“DARPA Eyes QuantumMechanics for Sensor
Applications”— Jane’s Defence Weekly
EntangledLightSource
DelayLine
Detection
Target
Loss
WinningLSU Proposal
4/21/09 34
Loss in Quantum SensorsSD Huver, CF Wildfeuer, JP Dowling, PRA 063828 (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-Lossitivity
!" =!P
d P / d"
3dB Loss, Visibility & Slope — Super Beer’s Law!
Gilbert, Hamrick, Weinstein,JOSA B, 25 (8): 1336-1340AUG 2008
N=1 (classical)N=5 (N00N)
dP1/d!
dPN/d!
e!"L
# e!N"L
Loss in Quantum SensorsS. Huver, C. F. Wildfeuer, J.P. Dowling, PRA 063828 (2008).
!
N00N
Generator
Detector
Lostphotons
Lostphotons
La
Lb
!
Q: Why do N00N States “Suck” in the Presence of Loss?
A: Single Photon Loss = Complete “Which Path” Information!
NA0
B+ e
iN!0
AN
B" 0
AN #1
B
A
B
Gremlin
Towards A Realistic Quantum SensorTry 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
Mitigating Loss in Quantum SensorsTry 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”
Outline
Overview — N00N states, properties,applications and experiments.
Fully scalable N00N-state generators — fromlinear-optical quantum computing.
Characterizing and engineering N00N states
What’s New with N00N?
Coherent Manipulation of BECs andUltrastable 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.
!Sagnac = 4"#A
$v
mc2/!! ~ 10
10
Orbital Angular Momentum of Light
1. Wavefront contains azimuthal phase singularities.
2. Each photon carries of orbital angular momentum.
a! !l + ei"a+ +l( ) 2
l
l!
[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
!c
!±
!±(",#, z,t) = a
±!0(t)
"w
$%&
'()|l |
eil#
LG0l(",#)
! "# $#
eikz;!
c(t) = !
0(t)
*Stimulated Rapid AdiabaticPassage
Mexican Hat Trap with
Thomas-Fermi Wave function
! r !(t) = "(t)#g (
! r ) + $(t)#
+(! r ) + %(t)#&(
! r )
!g (! r ) = LG
0
0(",#);!
±(! r ) = LG
0
±2(",#)
F(t) =|!(t) |2 " |#(t) |2 " | $(t) |2
General state of the BEC at time ‘t’
Measure of vortex transfer
[3] S. Thanvanthri, K. T. Kapale and J.P. Dowling, PRA 77, 053825 (2008)
Sagnac effect in vortex BEC superpositionsFor a vortex superposition rotating at angular velocity ,
the vortex interference pattern rotates by an angle
!
!r !(t," ) = (e
i#Sagnac$+(!r ) + e
% i#Sagnac$% (!r )) / 2
!Sagnac = N(t)4" R
2m
!#
!Sagnac
Detection using Phase Contrast Imaging
Advantage: Non destructive detection, increasedphase accumulation with time.
SNR = !"Sagnac / !"noise !"noise
# 1 / Nsc
Sensitivity
State of the art
!min~ 1.25 "10
#5rads
–1Hz
–1/2
!min~ 10
"10rads
–1Hz
–1/2
!Sagnac (",t) = N(t)4# "2m
!$
Stability? Noise from Atomic drift:
! = R
! =1.5 R
! = 0.5 R
!" = "Sagnac (1.5 R ,t) #"Sagnac (0.5 R ,t)
!" # 68µdeg/hr
Over 8 hours accumulationCurrent atom gyros, over 4 hours,
!" # 0.2µdeg/hr
D. S. Durfee, Y. K. Shaham and M. A. Kasevich, PRL 97, 240801 (2006).
• An ultra-stable, compact atomgyroscope.
• Better imaging techniquesdirectly improve sensitivity.
• Atom drift can further becontrolled 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 — fromlinear-optical quantum computing.
Characterizing and engineering N00N states
What’s New with N00N?
Coherent Manipulation of BECs andUltrastable Gyroscopes
