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J ö nåth á n Påtr î ck Døwl î ng

Quantum Optical Computing, Imaging, and Metrology. Ionatán Pádraig O’D únlaing. J ö nåth á n Påtr î ck Døwl î ng. Hearne Institute for Theoretical Physics Quantum Science and Technologies Group Louisiana State University Baton Rouge, Louisiana USA. quantum.phys.lsu.edu.

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J ö nåth á n Påtr î ck Døwl î ng

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  1. Quantum Optical Computing, Imaging, and Metrology Ionatán Pádraig O’Dúnlaing Jönåthán Påtrîck Døwlîng Hearne Institute for Theoretical Physics Quantum Science and Technologies Group Louisiana State University Baton Rouge, Louisiana USA quantum.phys.lsu.edu PQE 05 JAN 2011, Snowbird, UT Dowling JP, “Quantum Optical Metrology — The Lowdown On High-N00N States,” Contemporary Physics 49 (2): 125-143 (2008).

  2. Quantum (Optical) Sensors Ballroom I: WED 12:00N & 8:50PM 20:50 Geoff Pryde Griffith University, AUS ‘‘Optimal multiphoton phase sensing and measurement’’ 12:00 Christoph Wildfeuer & A. Migdall NIST & Louisiana State University ‘‘Techniques for enhancing the precision of measurements with photon number resolving detectors’’ 21:10 J. C. F. Matthews & J. L. O’Brien University of Bristol, UK ‘‘Entangled Multi-Photon States in Waveguide for Quantum Metrology’’ 12:20 Petr M. Anisimov Louisiana State University ‘‘Squeezing the Vacuum and beating Heisenberg: Limits? Where we’re going we do not need any limits!’’ 21:30 Kevin McCusker & Paul Kwiat University of Illinois ‘‘Efficient Quantum Optical State Engineering’’ 12:40 E. E. Mikhailov & I. Novikova College of William and Mary ‘‘Generation of squeezed vacuum with hot and ultra-cold Rb atoms’’ 21:50 Xi Wang Texas A&M University ‘‘Self-Implemented Heterodyne CARS by Using Its Intrinsic Background’’

  3. Hearne Institute for Theoretical Physics QuantumScience & Technologies Group 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 Top Inset: P.M.Anisimov,B.R.Bardhan,A.Chiruvelli,L.Florescu, M.Florescu, Y.Gao, K.Jiang,K.T.Kapale,T.W.Lee,S.B.McCracken, C.J.Min, S.J.Olsen, R.Singh,K.P.Seshadreesan,S.Thanvanthri, G.Veronis. Bottom InsetC. Brignac,R.Cross,B.Gard,D.J.Lum, Keith Motes, G.M.Raterman,C.Sabottke,

  4. Quantum Imaging Quantum Sensing Quantum Computing You Are Here! Quantum Metrology

  5. Outline Nonlinear Optics vs. Projective Measurements Quantum Imaging vs. Precision Measurements Showdown at High N00N! Mitigating Photon Loss 6. Super Resolution with Classical Light 7. Super-Duper Sensitivity Beats Heisenberg! 8. A Parody on Parity

  6. (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). Optical Quantum Computing: Two-Photon CNOT with Kerr 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 .

  7. Cavity QED Two Roads to Optical Quantum Computing I. Enhance Nonlinear Interaction with a Cavity or EIT — Kimble, Walther, Lukin, et al. II. Exploit Nonlinearity of Measurement — Knill, LaFlamme, Milburn, Nemoto, et al.

  8. Linear Optical Quantum Computing Linear Optics can be Used to Construct 2 X CSIGN = CNOT Gate and a 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

  9. 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

  10. Projective Measurement Yields Effective Nonlinearity! G. G. Lapaire, P. Kok, JPD, J. E. 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 Nonlinear Gates Franson CNOT: Cross Kerr KLM CSIGN: Self Kerr

  11. H.Lee, P.Kok, JPD, J Mod Opt 49, (2002) 2325 Quantum Metrology Shot noise Heisenberg

  12. Sub-Shot-Noise Interferometric Measurements With Two-Photon N00N States A Kuzmich and L Mandel; Quantum Semiclass. Opt. 10 (1998) 493–500. SNL HL

  13. AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733 a† N a N Super-Resolution Sub-Rayleigh

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

  15. Quantum Imaging: Super-Resolution  N=1 (classical) N=5 (N00N) 

  16. Quantum Metrology: Super-Sensitivity N=1 (classical) N=5 (N00N) dPN/d Shotnoise Limit: 1 = 1/√N Heisenberg Limit: N = 1/N dP1/d

  17. 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).

  18. FIRST LINEAR-OPTICS BASED HIGH-N00N GENERATOR PROPOSAL Success probability approximately 5% for 4-photon output. Scheme conditions on the detection of one photon at each detector mode a e.g. component of light from an optical parametric oscillator 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

  19. Mitchell,…,Steinberg Nature (13 MAY) Toronto Walther,…,Zeilinger Nature (13 MAY)Vienna 2004 3, 4-photon Super- resolution only Nagata,…,Takeuchi, Science (04 MAY) Hokkaido & Bristol; J.C.F.Matthews, A.Politi, Damien Bonneau, J.L.O'Brien, arXiv:1005.5119 2007–2010 4-photon Super-sensitivity & Super-resolution 1990’s 2-photon N00N State Experiments Rarity, (1990) Ou, et al. (1990) Shih (1990) Kuzmich (1998) Shih (2001) 6-photon Super-resolution Only! Resch,…,White PRL (2007) Queensland

  20. Noise Target Nonclassical Light Source Delay Line Detection Quantum LIDAR “DARPA Eyes Quantum Mechanics for Sensor Applications” — Jane’s Defence Weekly Winning LSU Proposal INPUT inverse problem solver “find min( )“ forward problem solver N: photon number loss A loss B FEEDBACK LOOP: Genetic Algorithm OUTPUT

  21. Loss in Quantum Sensors SD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Lost photons La N00N Detector Lb Lost photons Generator Visibility: Sensitivity: N00N 3dB Loss --- N00N No Loss — SNL--- HL— 8/20/2014 21

  22. Super-Lossitivity Gilbert, G; Hamrick, M; Weinstein, YS; JOSA B 25 (8): 1336-1340 AUG 2008 N=1 (classical) N=5 (N00N) 3dB Loss, Visibility & Slope — Super Beer’s Law!

  23. Loss in Quantum Sensors S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Lost photons La N00N Detector Lb Lost photons Generator A B Gremlin Q: Why do N00N States “Suck” in the Presence of Loss? A: Single Photon Loss = Complete “Which Path” Information!

  24. Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Lost photons La M&M Detector Lb Lost photons Generator Try other detection scheme and states! M&M state: N00N Visibility M&M Visibility M&M’ Adds Decoy Photons 0.3 0.05

  25. Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Lost photons La M&M Detector Lb Lost photons Generator M&M state: N00N State --- M&M State — A Few Photons Lost Does Not Give Complete “Which Path” N00N SNL --- M&M SNL --- M&M HL — N00N HL —

  26. Super-Resolution at the Shot-Noise Limit with Coherent States and 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 number resolving detectors — implementing parity detection — produces super-resolution much below the Rayleigh diffraction limit, with sensitivity at the shot-noise limit. Quantum Classical Parity Detector!

  27. 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 is obtained with parity detection. In particular, in our setup, dependence of the signal on the phase evolves <n> times faster than in traditional schemes, and uncertainty in the phase estimation is better than 1/<n>. SNL HL TMSV & QCRB HofL

  28. New Journal of Physics 12 (2010) 113025, 1367-2630/10/113025+12$30.00 Parity detection in quantum optical metrology without number-resolving detectors William N Plick, Petr M Anisimov, Jönåthán P Døwlîng, Hwang Lee, and Girish S Agarwal Abstract. We present a method for directly obtaining the parity of a Gaussian state of light without recourse to photon-number counting. The scheme uses only a simple balanced homodyne technique and intensity correlation. Thus interferometric schemes utilizing coherent or squeezed light and parity detection may be practically implemented for an arbitrary photon flux.

  29. Outline Nonlinear Optics vs. Projective Measurements Quantum Imaging vs. Precision Measurements Showdown at High N00N! Mitigating Photon Loss 6. Super Resolution with Classical Light 7. Super-Duper Sensitivity Beats Heisenberg! 8. A Parody on Parity

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