Jonathan P. Dowling

1. Quantum Optical Metrology, Imaging, and Computing Jonathan P. Dowling Hearne Institute for Theoretical Physics Quantum Science and Technologies Group Louisiana State University Baton Rouge, Louisiana USA quantum.phys.lsu.edu Frontiers of Nonlinear Physics, 19 July 2010 On The «Georgy Zhukov» Between Valaam and St. Petersburg, Russia

2. Not to be confused with: Quantum Meteorology! Dowling JP, “Quantum Metrology,” Contemporary Physics 49 (2): 125-143 (2008)

3. Hearne Institute for Theoretical Physics QuantumScience & Technologies Group 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 Not Shown: P.M.Anisimov,B.R.Bardhan,A.Chiruvelli, R.Cross,G.A.Durkin, M.Florescu, Y.Gao, B.Gard, K.Jiang,K.T.Kapale,T.W.Lee,D.J.Lum,S.B.McCracken, C.J.Min, S.J.Olsen, G.M.Raterman,C.Sabottke,R.Singh,K.P.Seshadreesan,S.Thanvanthri, G.Veronis

4. 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!

5. (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 .

6. 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, Franson, et al.

7. 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

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 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

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

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

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

13. New York Times Discovery Could Mean Faster Computer Chips

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).

19. Implemented in Experiments!

20. 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 2007 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

21. 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

22. 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— 11/27/2014 22

23. 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!

24. 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 Do Poorly in the Presence of Loss? A: Single Photon Loss = Complete “Which Path” Information!

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 Try other detection scheme and states! M&M state: N00N Visibility M&M Visibility M&M’ Adds Decoy Photons 0.3 0.05

26. 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 — M&M HL —

27. Optimization of Quantum Interferometric Metrological Sensors In the Presence of Photon Loss PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009 Tae-Woo Lee, Sean D. Huver, Hwang Lee, Lev Kaplan, Steven B. McCracken, Changjun Min, Dmitry B. Uskov, Christoph F. Wildfeuer, Georgios Veronis, Jonathan P. Dowling We optimize two-mode, entangled, number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert space with no constraints, other than fixed total initial photon number.

28. Lossy State Comparison PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009 Here we take the optimal state, outputted by the code, at each loss level and project it on to one of three know states, NOON,M&M, and “Spin” Coherent. The conclusion from this plot is that the optimal states found by the computer code are N00N states for very low loss, M&M states for intermediate loss, and “spin” coherent states for high loss.

29. 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!

30. 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

31. 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!