Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
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
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!
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 "( ) = ↠+ 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"
N=1 (classical)N=5 (N00N)
ShotnoiseLimit:Δϕ1 = 1/√N
HeisenbergLimit:ΔϕN = 1/N
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!
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
N00N
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
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!
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!
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
!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
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!
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
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!
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
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!
有難うございます!