1. Jonathan P. Dowling QUANTUM SENSORS: WHAT’S NEW WITH N00N STATES?
Hearne Institute for Theoretical Physics
Louisiana State University
Baton Rouge, Louisiana
quantum.phys.lsu.edu
SPIE F&N 23 May 2007

2. Statue Antiche di Firenze
(Ancient Statues of Florence)
Scully with Projector
Mother with Children

3. Hearne Institute for Theoretical Physics
Quantum Science & Technologies Group
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

4. Outline Quantum Computing & Projective Measurements
Quantum Imaging, Metrology, & Sensing
Showdown at High N00N!
Efficient N00N-State Generating Schemes
Conclusions

5. 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.

6. 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.

7. WHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT?
Photon-Photon
XOR Gate
  LOQC  
KLM
Cavity QED
EIT
Photon-Photon
Nonlinearity
???
Kerr Material
Projective
Measurement

8. Projective Measurement Yields Effective “Kerr”!
GG Lapaire, P Kok, JPD, JE Sipe, PRA 68 (2003)
A Revolution in Nonlinear Optics at the Few Photon Level:
No Longer Limited by the Nonlinearities We Find in Nature! 
NON-Unitary Gates  Effective Unitary Gates
Franson CNOT Hamiltonian
KLM CSIGN Hamiltonian

9. Single-Photon Quantum Non-Demolition
You want to know if there is a single photon in mode b, without destroying it.
Cross-Kerr Hamiltonian: HKerr =  a†a b†b
Again, with  = 10–22, this is impossible.
Kerr medium
“1” a b
|in
|1 D1 D2
*N Imoto, HA Haus, and Y Yamamoto, Phys. Rev. A. 32, 2287 (1985).

10. Quantum Non-Demolition  21 Orders of Magnitude Improvement!
Linear Single-Photon
Quantum 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 D1 D2 D0
 /2
|in = cn |n 
n = 0 2
|0
Effective  = 1/8
 21 Orders of Magnitude Improvement!
P Kok, H Lee, and JPD, PRA 66 (2003)

11. Quantum Metrology with N00N States
H Lee, P Kok, JPD, J Mod Opt 49, (2002) 2325.
Quantum Metrology with N00N States
Shotnoise to Heisenberg Limit
Supersensitivity!

12. a† N a N Superresolution!
AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733
a† N a N
Superresolution!

13. Showdown at High-N00N! |N,0 + |0,N N00N States In Chapter 11
How do we make High-N00N!?
N00N States
In Chapter 11
|N,0 + |0,N
With a large cross-Kerr nonlinearity!* H =  a†a b†b
|1
|0
|N
|N,0 + |0,N
|0
This is not practical! —
need  = p but  = 10–22 !
*C Gerry, and RA Campos, Phys. Rev. A 64, (2001).

14. Solution: Replace the Kerr with Projective Measurements!
single photon detection
at each detector a b a’ b’
OPO
Cascading
Not
Efficient!
Probability of success:
Best we found:
H Lee, P Kok, NJ Cerf, and JP Dowling, Phys. Rev. A 65, R (2002).

15. |10::01>
|10::01>
|20::02>
|20::02>
|30::03>
|40::04>
|30::03>

16. in Quantum Interferometry
Local and Global Distinguishability
in Quantum Interferometry
GA Durkin & JPD, quant-ph/
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

17. NOON-States Violate Bell’s Inequalities
CF Wildfeuer, AP Lund and JP Dowling, quant-ph/
Probabilities of correlated clicks and independent clicks
Building a Clauser-Horne Bell inequality from the expectation values
Bell Violation!
Shared Local Oscillator Acts As Common Reference Frame!

18. Efficient Schemes for Generating N00N States!
Constrained
Desired
|N>|0>
|N0::0N>
|1,1,1>
Number
Resolving
Detectors
Question: Do there exist operators “U” that produce “N00N” States Efficiently?
Answer: YES!
H Cable, R Glasser, & JPD, quant-ph/ Linear!
N VanMeter, P Lougovski, D Uskov, JPD, quant-ph/ Linear!
KT Kapale & JPD, quant-ph/ (Nonlinear.)

19. Quantum P00Per Scooper! Old Scheme OPO New Scheme χ 2-mode
H Cable, R Glasser, & JPD, quant-ph/
2-mode
squeezing process
linear
optical
processing
Old Scheme χ
OPO
beam
splitter
New Scheme
How to eliminate
the “POOP”?
quant-ph/
G. S. Agarwal, K. W. Chan,
R. W. Boyd, H. Cable
and JPD

20. Quantum P00Per Scoopers! “Pizza Pie” Phase Shifter
H Cable, R Glasser, & JPD, quant-ph/
“Pizza
Pie”
Phase
Shifter
Spinning glass wheel. Each segment a different thickness.
N00N is in Decoherence-Free Subspace!
Feed Forward based circuit
Generates and manipulates special
cat states for conversion to N00N states. First theoretical scheme scalable to
many particle experiments!

21. The upper bound on the resources scales quadratically!
Linear-Optical Quantum-State Generation: A N00N-State Example N VanMeter, D Uskov, P Lougovski, K Kieling, J Eisert, JPD, quant-ph/ U
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).

22. Conclusions Quantum Computing & Projective Measurements
Quantum Imaging & Metrology
Showdown at High N00N!
Efficient N00N-State Generating Schemes
Conclusions