Lecture 31: MON 30 MAR Review Session : Midterm 3 Physics 2113 Jonathan Dowling.
Jonathan P. Dowling
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Jonathan P. Dowling QUANTUM SENSORS: WHAT’S NEW WITH N00N STATES? quantum.phys.lsu.edu Hearne Institute for Theoretical Physics Louisiana State University Baton Rouge, Louisiana SPIE F&N 23 May 2007
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QUANTUM SENSORS: WHAT’S NEW WITH N00N STATES?. Jonathan P. Dowling. Hearne Institute for Theoretical Physics Louisiana State University Baton Rouge, Louisiana. quantum.phys.lsu.edu. SPIE F&N 23 May 2007. Mother with Children. Scully with Projector. Statue Antiche di Firenze - PowerPoint PPT Presentation
Transcript of Jonathan P. Dowling
Jonathan P. Dowling
QUANTUM SENSORS: WHAT’S NEW WITH N00N STATES?
quantum.phys.lsu.edu
Hearne Institute for Theoretical PhysicsLouisiana State UniversityBaton Rouge, Louisiana
SPIE F&N 23 May 2007
Statue Antiche di Firenze(Ancient Statues of Florence)
Mother with ChildrenScully with Projector
H.Cable, C.Wildfeuer, H.Lee, S.Huver, W.Plick, G.Deng, R.Glasser, S.Vinjanampathy, K.Jacobs, D.Uskov, JP.Dowling, P.Lougovski,
N.VanMeter, M.Wilde, G.Selvaraj, A.DaSilva
Not Shown: R.Beaird, M.A. Can, A.Chiruvelli, GA.Durkin, M.Erickson, L. Florescu,
M.Florescu, M.Han, KT.Kapale, SJ. Olsen, S.Thanvanthri, Z.Wu, J.Zuo
Hearne Institute for Theoretical Physics
Quantum Science & Technologies Group
Outline
1.1.Quantum Computing & Projective Quantum Computing & Projective
MeasurementsMeasurements
2.2.Quantum Imaging, Metrology, & Quantum Imaging, Metrology, &
SensingSensing
3.3.Showdown at High N00N!Showdown at High N00N!
4.4.Efficient N00N-State Generating Efficient N00N-State Generating
SchemesSchemes
5.5.ConclusionsConclusions
The objective of the DARPA Quantum Sensor Program is to develop practical sensors operating outside of a controlled laboratory environment that exploit non-classical photon states (e.g. entangled, squeezed, or cat) to surpass classical sensor resolution.
Two Roads to Optical CNOT
Cavity QED
I. Enhance Nonlinear Interaction with a Cavity or EIT — Kimble, Walther, Lukin, et al.II. Exploit Nonlinearity of Measurement — Knill, LaFlamme, Milburn, Franson, et al.
Photon-PhotonXOR Gate
Photon-PhotonNonlinearity
Kerr Material
Cavity QEDEIT
ProjectiveMeasurement
LOQC KLM
WHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT?
GG Lapaire, P Kok, JPD, JE Sipe, PRA 68 (2003) 042314
KLM CSIGN Hamiltonian Franson CNOT Hamiltonian
NON-Unitary Gates Effective Unitary Gates
A Revolution in Nonlinear Optics at the Few Photon Level:No Longer Limited by the Nonlinearities We Find in Nature!
Projective Measurement Yields Effective “Kerr”!
Single-Photon Quantum Non-Demolition
You want to know if there is a single photon in mode b, without destroying it.
*N Imoto, HA Haus, and Y Yamamoto, Phys. Rev. A. 32, 2287 (1985).
Cross-Kerr Hamiltonian: HKerr = a†a b†b
Again, with = 10–22, this is impossible.
Kerr medium
“1”
a
b|in|1
|1
D1
D2
Linear Single-PhotonQuantum Non-Demolition
The success probability is less than 1 (namely 1/8).
The input state is constrained to be a superposition of 0, 1, and 2 photons only.
Conditioned on a detector coincidence in D1 and D2.
|1
|1
|1D1
D2
D0
/2
/2
|in = cn |nn = 0
2
|0Effective = 1/8
21 Orders of Magnitude Improvement!
P Kok, H Lee, and JPD, PRA 66 (2003) 063814
+NA0BeiNϕ0ANB
1 + cos N ϕ
2
1 + cos ϕ
2
ABϕ|N⟩A |0⟩B N Photons
N-PhotonDetector
ϕ = kxΔϕ: 1/√N →1/ΝuncorrelatedcorrelatedOscillates N times as fast!N-XOR GatesN-XOR Gatesmagic BSMACH-ZEHNDER INTERFEROMETERApply the Quantum Rosetta Stone!
Quantum Metrology with N00N StatesH Lee, P Kok,
JPD, J Mod Opt 49, (2002) 2325.
Supersensitivity!
Shotnoise to Heisenberg
Limit
N Photons
N-PhotonDetectorϕ = x+NA0BeiNϕ0ANB
1 + cos N ϕ
2
1 + cos ϕ
2
uncorrelatedcorrelatedOscillates in REAL Space!N-XOR Gatesmagic BSFROM QUANTUM INTERFEROMETRYTO QUANTUM LITHOGRAPHY
Mirror
N
2 A
N
2 B
LithographicResist
ϕ →Νϕ λ →λ/Ν
ψ a†
a†
aa ψa† N a
N
AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733
Superresolution!
Showdown at High-N00N!
|N,0 + |0,NHow do we make High-N00N!?
*C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001).
With a large cross-Kerr nonlinearity!* H = a†a b†b
This is not practical! — need = but = 10–22 !
|1
|N
|0
|0|N,0 + |0,N
N00N StatesIn Chapter 11
ba33
a
b
a’
b’
ba06
ba24
ba42
ba60
Probability of success:643 Best we found:
163
Solution: Replace the Kerr with Projective Measurements!
H Lee, P Kok, NJ Cerf, and JP Dowling, Phys. Rev. A 65, R030101 (2002).
ba13
ba31
single photon detection at each detector
''''4004
baba−
CascadingNotEfficient!
OPO
|10::01>
|20::02>
|40::04>
|10::01>
|20::02>
|30::03>
|30::03>
A statistical distinguishability based on relative entropy characterizes the fitness of quantum states for phase estimation. This criterion is used to interpolate between two regimes, of local and global phase distinguishability.
The analysis demonstrates that, in a passive MZI, the Heisenberg limit is the true upper limit for local phase sensitivity — and Only N00N States Reach It!
N00N
Local and Global Distinguishability in Quantum InterferometryGA Durkin & JPD, quant-ph/0607088
NOON-States Violate Bell’s Inequalities
Building a Clauser-Horne Bell inequality from the expectation values
€
Pab (α ,β ),Pa (α ),Pb (β )
€
−1≤ Pab (α ,β ) − Pab (α , ′ β ) + Pab ( ′ α ,β ) + Pab ( ′ α , ′ β ) − Pa ( ′ α ) − Pb (β ) ≤ 0
Probabilities of correlated clicks and independent clicks
€
Pab (α ,β ),Pa (α ),Pb (β )
CF Wildfeuer, AP Lund and JP Dowling, quant-ph/0610180
Shared Local Oscillator Acts As Common Reference Frame!
Bell Violation!
Efficient Schemes for Generating N00N
States!
Question: Do there exist operators “U” that produce “N00N” States Efficiently?
Answer: YES!
H Cable, R Glasser, & JPD, quant-ph/0704.0678. Linear!N VanMeter, P Lougovski, D Uskov, JPD, quant-ph/0612154. Linear!KT Kapale & JPD, quant-ph/0612196. (Nonlinear.)
Constrained Desired
|N>|0> |N0::0N>
|1,1,1> NumberResolvingDetectors
linear optical processing
U(50:50)|4>|4>
0
0.05
0.1
0.15
0.2
0.25
0.3
|0>|8> |2>|6> |4>|4> |6>|2> |8>|0>
Fock basis state
|amplitude|^2
How to eliminate the “POOP”?
beamsplitter
quant-ph/0608170 G. S. Agarwal, K. W. Chan,
R. W. Boyd, H. Cable and JPD
Quantum P00Per Scooper!
χ
2-mode squeezing process
H Cable, R Glasser, & JPD, quant-ph/0704.0678.
OPO
Old Scheme
New Scheme
Spinning glass wheel. Each segment a different thickness. N00N is in Decoherence-Free
Subspace!
Generates and manipulates special
cat states for conversion to N00N states.
First theoretical scheme scalable to
many particle experiments!
“PizzaPie”Phase Shifter
Feed Forward based circuit
Quantum P00Per Scoopers!H Cable, R Glasser, & JPD, quant-ph/0704.0678.
Linear-Optical Quantum-State Generation: A N00N-State Example
N VanMeter, D Uskov, P Lougovski, K Kieling, J Eisert, JPD, quant-ph/0612154
U
€
2
€
2
€
2
€
0
€
1
€
0
€
0.032
( 50 + 05 )
This counter example disproves the N00N Conjecture: That N Modes Required for N00N.
The upper bound on the resources scales quadratically!
Upper bound theorem:
The maximal size of a N00N state generated in m modes via single photon detection in m–2 modes is O(m2).
Conclusions
1.1.Quantum Computing & Projective Quantum Computing & Projective
MeasurementsMeasurements
2.2.Quantum Imaging & MetrologyQuantum Imaging & Metrology
3.3.Showdown at High N00N!Showdown at High N00N!
4.4.Efficient N00N-State Generating Efficient N00N-State Generating
SchemesSchemes
5.5.ConclusionsConclusions
