quantum interferometric sensors 22 apr 09, nist, gaithersburg jonathan p. dowling quantum science...
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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
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-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).
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
Yes, Jeff and Anton, N00N States Are
Really Entangled!
Yes, Jeff and Anton, N00N States Are
Really Entangled!
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
€
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.
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