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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 QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this pict ure. Dowling JP, “Quantum Metrology,” Contemporary Physics 49 (2): 125-143 (2008) Hearne Institute for Theoretical Physics Quantum Science & 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 Outline 1. Nonlinear Optics vs. Projective Measurements 2. Quantum Imaging vs. Precision Measurements 3. Showdown at High N00N! 4. Mitigating Photon Loss 6. Super Resolution with Classical Light 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 (3) PBS R is a /2 polarization rotation, followed by a polarization dependent phase shift . 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). 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. Cavity QED Linear Optical Quantum Computing Linear Optics can be Used to Construct 2 X CSIGN = CNOT Gate and a Quantum Computer: 0 1 2 Knill E, Laflamme R, Milburn GJ NATURE 409 (6816): 46-52 JAN 4 2001 0 1 2 Milburn Franson JD, Donegan MM, Fitch MJ, et al. PRL 89 (13): Art. No. 137901 SEP 23 2002 WHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT? LOQC KLM Photon-Photon XOR Gate Cavity QED EIT Photon-Photon Nonlinearity Projective Measurement Kerr Material 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 KLM CSIGN: Self Kerr Effective Nonlinear Gates Franson CNOT: Cross Kerr Quantum Metrology H.Lee, P.Kok, JPD, J Mod Opt 49, (2002) 2325 Shot noise Heisenberg Sub-Shot-Noise Interferometric Measurements With Two-Photon N00N States A Kuzmich and L Mandel; Quantum Semiclass. Opt. 10 (1998) 493–500. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. Low N00N 2 0 ei 2 0 2 HL SNL AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733 Super-Resolution a† N a N Sub-Rayleigh New York Times Discovery Could Mean Faster Computer Chips Quantum Lithography Experiment Low N00N 2 0 ei 2 0 2 |20>+|02 > |10>+|01 > Quantum Imaging: Super-Resolution N=1 (classical) N=5 (N00N) Quantum Metrology: Super-Sensitivity P̂ d P̂ / d N N=1 (classical) N=5 (N00N) dP /d Shotnoise Limit: 1 = 1/√N dP1/d Heisenberg Limit: N = 1/N 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 |0 This is not practical! — need = but = 10–22 ! *C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001). 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). Implemented in Experiments! N00N State Experiments 1990’s 2-photon Rarity, (1990) Ou, et al. (1990) Shih (1990) Kuzmich (1998) Shih (2001) Mitchell,…,Steinberg Nature (13 MAY) Toronto 2004 3, 4-photon Super6-photon resolution Super-resolution only Only! Resch,…,White PRL (2007) Queensland 2007 4-photon Super-sensitivity & Super-resolution Walther,…,Zeilinger Nature (13 MAY) Vienna Nagata,…,Takeuchi, Science (04 MAY) Hokkaido & Bristol Quantum LIDAR “DARPA Eyes Quantum Mechanics for Sensor Applications” — Jane’s Defence Weekly Winning LSU Proposal Noise Target INPUT Nonclassical Light Source inverse problem solver “find min( )“ Delay Line Detection forward problem solver N: photon number in N loss A c loss B i N i, i f ( in , ; loss A, loss B) i 0 FEEDBACK LOOP: Genetic Algorithm OUTPUT min( ) ; N ) in(OPT ) c (OPT N i, i , OPT i i 0 Loss in Quantum Sensors SD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # 063828 DEC 2008 La N00N Detector Generator Lb Visibility: ( 10,0 0,10 ) Lost photons 2 Lost photons Sensitivity: ( 10,0 0,10 ) 2 N00N 3dB Loss --- N00N No Loss — SNL--5/24/2017 22 HL— Super-Lossitivity Gilbert, G; Hamrick, M; Weinstein, YS; JOSA B 25 (8): 1336-1340 AUG 2008 P̂ i e e e dPN /d d P̂ / d N=1 (classical) N=5 (N00N) L iN e Κ N L Κ dP1 /d 3dB Loss, Visibility & Slope — Super Beer’s Law! Loss in Quantum Sensors S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 A N00N Lost photons La Detector B Generator Lb Lost photons Gremlin Q: Why do N00N States Do Poorly in the Presence of Loss? A: Single Photon Loss = Complete “Which Path” Information! N A 0 B e iN 0 A N B 0 A N 1 B Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Lost photons Try other detection scheme and states! M&M La Detector Generator M&M state: ( m,m' m',m ) M&M Visibility ( 20,10 10,20 ) Lb N00N Visibility ( 10,0 0,10 ) 2 0.3 Lost photons 2 0.05 2 M&M’ Adds Decoy Photons Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 M&M La Detector Generator M&M state: ( m,m' m',m ) Lost photons Lb 2 Lost photons N00N State --M&M State — N00N SNL --M&M SNL --M&M HL — M&M HL — A Few Photons Lost Does Not Give Complete “Which Path” 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. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. 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. 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 QuickTime™ and a decompressor are needed to see this picture. Parity Detector! QuickTime™ and a decompressor are needed to see this picture. 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 1 / nφ ΚΚΚΚΚΚHL 1 / nφ ΚΚΚΚΚΚTMSV 1 / nφ nφ 2 ΚΚΚΚΚΚHofL 1 / SNL nφ2 HL TMSV & QCRB QuickTime™ and a decompressor are needed to see this picture. HofL Outline 1. Nonlinear Optics vs. Projective Measurements 2. Quantum Imaging vs. Precision Measurements 3. Showdown at High N00N! 4. Mitigating Photon Loss 6. Super Resolution with Classical Light