Jonathan P. Dowling LINEAR OPTICAL QUANTUM INFORMATION PROCESSING, IMAGING, AND SENSING: WHAT’S NEW WITH N00N STATES? quantum.phys.lsu.edu Hearne Institute for Theoretical Physics Louisiana State University Baton Rouge, Louisiana 14 JUNE 2007 ICQI-07, Rochester
LINEAR OPTICAL QUANTUM INFORMATION PROCESSING, IMAGING, AND SENSING: WHAT’S NEW WITH N00N STATES?. Jonathan P. Dowling. Hearne Institute for Theoretical Physics Louisiana State University Baton Rouge, Louisiana. quantum.phys.lsu.edu. 14 JUNE 2007 ICQI-07, Rochester. - PowerPoint PPT Presentation
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Jonathan P. Dowling
LINEAR OPTICAL QUANTUM INFORMATION PROCESSING, IMAGING, AND SENSING:
WHAT’S NEW WITH N00N STATES?
quantum.phys.lsu.edu
Hearne Institute for Theoretical PhysicsLouisiana State UniversityBaton Rouge, Louisiana
A Revolution in Nonlinear Optics at the Few Photon Level:No Longer Limited by the Nonlinearities We Find in Nature!
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”!
Nonlinear Single-Photon Quantum Non-
DemolitionYou want to know if there is a single photon in mode b, without destroying it.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.
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.
H Lee, P Kok, JPD,
J Mod Opt 49, (2002) 2325.
Supersensitivity!
Shotnoise to Heisenberg
Limit
N Photons
N-PhotonDetectorϕ = kx+NA0BeiNϕ0ANB
1 + cos N ϕ
2
1 + cos ϕ
2
uncorrelatedcorrelatedOscillates in REAL Space!N-XOR Gatesmagic BSFROM QUANTUM INTERFEROMETRYTO QUANTUM LITHOGRAPHY
Mirror
N
2A
N
2B
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
AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733
Superresolution!
Quantum Lithography Experiment
|20>+|02>
|10>+|01>
Canonical Metrology
note the square-root
P Kok, SL Braunstein, and JP Dowling, Journal of Optics B 6, (2004) S811
P Kok, SL Braunstein, and JP Dowling, Journal of Optics B 6, (2004) S811
Suppose we have an ensemble of N states | = (|0 + ei |1)/2,and we measure the following observable:
The expectation value is given by: and the variance (A)2 is given by: N(1cos2)
A = |0 1| + |1 0|
|A| = N cos
The unknown phase can be estimated with accuracy:
This is the standard shot-noise limit.
= = A
| d A/d |
N1
Quantum Lithography & Metrology
Now we consider the state
and we measure
High-FrequencyLithographyEffect
Heisenberg Limit:No Square Root!
P. Kok, H. Lee, and J.P. Dowling, Phys. Rev. A 65, 052104 (2002).
P. Kok, H. Lee, and J.P. Dowling, Phys. Rev. A 65, 052104 (2002).
*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:
64
3 Best we found:
16
3
Solution: Replace the Kerr with Projective Measurements!
H Lee, P Kok, NJ Cerf, and JP Dowling, Phys. Rev. A 65, R030101 (2002).
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
These Ideas Implemented in Recent
Experiments!
|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!
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