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Jonathan P. Dowling

Optical Quantum Imaging, Computing, and Metrology: WHAT’S NEW WITH N00N STATES?. Jonathan P. Dowling. Hearne Institute for Theoretical Physics Louisiana State University Baton Rouge, Louisiana. quantum.phys.lsu.edu. 07 JUNE 2007 DAMOP-07, Calgary. Hearne Institute for Theoretical Physics

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Jonathan P. Dowling

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  1. Optical Quantum Imaging, Computing, and Metrology: WHAT’S NEW WITH N00N STATES? Jonathan P. Dowling Hearne Institute for Theoretical Physics Louisiana State University Baton Rouge, Louisiana quantum.phys.lsu.edu 07 JUNE 2007 DAMOP-07, Calgary

  2. Hearne Institute for Theoretical Physics QuantumScience & 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: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

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

  4. (3) PBS Rpol z Unfortunately, the interaction (3)is extremely weak*: 10-22 at the single photon level —This is not practical! *R.W. Boyd, J. Mod. Opt.46, 367 (1999). CNOT with Optical Nonlinearity The Controlled-NOT can be implemented using a Kerr medium: |0= |H Polarization |1= |V Qubits R is a /2 polarization rotation, followed by a polarization dependent phase shift .

  5. Cavity QED Two Roads to Optical CNOT I. Enhance Nonlinearity with Cavity, EIT — Kimble, Walther, Haroche, Lukin, Zubairy, et al. II. Exploit Nonlinearity of Measurement — Knill, LaFlamme, Milburn, Franson, et al.

  6. Linear Optical Quantum Computing Linear Optics can be Used to Construct CNOT and a Scaleable Quantum Computer: Milburn Franson JD, Donegan MM, Fitch MJ, et al. PRL 89 (13): Art. No. 137901 SEP 23 2002 Knill E, Laflamme R, Milburn GJ NATURE 409 (6816): 46-52 JAN 4 2001

  7. Road to Entangled- Particle Interferometry:First Example of Entanglement Generation by Erasure of Which-Path Information Followed by Detection!?

  8. 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

  9. Projective Measurement Yields Effective “Kerr”! GG Lapaire, P Kok, JPD, JE Sipe, PRA 68 (2003) 042314 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

  10. Nonlinear Single-Photon Quantum Non-Demolition Cross-Kerr Hamiltonian: HKerr=a†ab†b Kerr medium b |in |1 |1 a D2 D1 Again, with  = 10–22, this is impossible. “1” 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).

  11. D0 |1 D1 D2 /2 |1 /2 |0 |1 2 |in = cn |n  n = 0 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. Effective  = 1/8  21 Orders of Magnitude Improvement! P Kok, H Lee, and JPD, PRA 66 (2003) 063814

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

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

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

  15. Quantum Lithography Experiment |20>+|02> |10>+|01>

  16. note the square-root Canonical Metrology Suppose we have an ensemble of N states | = (|0 + ei|1)/2,  and we measure the following observable: A = |01| + |10|  |A| = N cos  The expectation value is given by: and the variance (A)2 is given by: N(1cos2) The unknown phase can be estimated with accuracy: A 1  = =  |dA/d | N This is the standard shot-noise limit. P Kok, SL Braunstein, and JP Dowling, Journal of Optics B 6, (2004) S811

  17. Quantum Lithography & Metrology High-Frequency Lithography Effect 1 N Heisenberg Limit: No Square Root! Now we consider the state and we measure N |AN|N = cos N QuantumLithography*:  AN H = = QuantumMetrology: |dAN/d |  P. Kok, H. Lee, and J.P. Dowling, Phys. Rev. A 65, 052104 (2002).

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

  19. Showdown at High-N00N! How do we make High-N00N!? |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. A64, 063814 (2001).

  20. single photon detection at each detector a a’ b b’ Cascading Not Efficient! Best we found: Probability of success: Solution: Replace the Kerr with Projective Measurements! OPO H Lee, P Kok, NJ Cerf, and JP Dowling, Phys. Rev. A 65, R030101 (2002).

  21. These Ideas Implemented in Recent Experiments!

  22. |10::01> |10::01> |20::02> |20::02> |30::03> |30::03> |40::04>

  23. Local and Global Distinguishability in Quantum Interferometry GA Durkin & JPD, quant-ph/0607088 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

  24. NOON-States Violate Bell’s Inequalities Probabilities of correlated clicks and independent clicks Building a Clauser-Horne Bell inequality from the expectation values CF Wildfeuer, AP Lund and JP Dowling, quant-ph/0610180 Bell Violation! Shared Local Oscillator Acts As Common Reference Frame!

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

  26. Efficient Schemes for Generating N00N States! |N>|0> |N0::0N> Constrained Desired Number Resolving Detectors |1,1,1> 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.)

  27. linear optical processing Quantum P00Per Scooper! H Cable, R Glasser, & JPD, quant-ph/0704.0678. 2-mode squeezing process Old Scheme χ OPO beam splitter New Scheme How to eliminate the “POOP”? quant-ph/0608170 G. S. Agarwal, K. W. Chan, R. W. Boyd, H. Cable and JPD

  28. Quantum P00Per Scoopers! H Cable, R Glasser, & JPD, quant-ph/0704.0678. “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!

  29. Linear-Optical Quantum-State Generation: A N00N-State ExampleN VanMeter, D Uskov, P Lougovski, K Kieling, J Eisert, JPD, quant-ph/0612154 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).

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

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