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Quantum Optical Metrology, Imaging, and Computing “Spiritual Jian建道灵 Dow-Ling Jonathan P.Alliance” Dowling Hearne Institute for Theoretical Physics Quantum Science and Technologies Group Louisiana State University Baton Rouge, Louisiana USA quantum.phys.lsu.edu QONMIV, 26 JAN 2011, CSRC, Beijing Dowling JP, “Quantum Optical Metrology — The Lowdown On High-N00N States,” Contemporary Physics 49 (2): 125-143 (2008). QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this pict ure. Hearne Institute for Theoretical Physics Quantum Science & Technologies Group QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. QuickTi me™ and a decompressor are needed to see thi s pi ctur e. QuickTi me™ and a decompressor are needed to see thi s pi ctur e. QuickTi me™ and a decompressor are needed to see thi s pi ctur e. QuickTi me™ and a decompressor are needed to see thi s pi ctur e. QuickTi me™ and a decompressor are needed to see thi s pi ctur e. QuickTi me™ and a decompressor are needed to see thi s pi ctur e. QuickTi me™ and a decompressor are needed to see thi s pi ctur e. 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 Inset C. Brignac, R.Cross, B.Gard, D.J.Lum, Keith Motes, G.M.Raterman, C.Sabottke, Outline 1. Nonlinear Optics vs. Projective Measurements 2. Quantum Imaging vs. Precision Measurements 3. Showdown at High N00N! 6. Super Resolution with Classical Light 7. Super-Duper Sensitivity Beats Heisenberg! 8. A Parody on Parity 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, Nemoto, et al. Cavity QED 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 Effective Nonlinear Gates KLM CSIGN: Self Kerr Franson CNOT: Cross Kerr Phase Estimation Theorem: Quantum Cramer-Rao bound optimal POVM, optimal statistical estimator independent trials/shot-noise limit Strategies to improve sensitivity: 1. Increase — sequential (multi-round) protocol. 2. Probes in entangled N-party state and one trial To make Ĥ as large as possible —> N00N! S. L. Braunstein, C. M. Caves, and G. J. Milburn, Annals of Physics 247, page 135 (1996) V. Giovannetti, S. Lloyd, and L. Maccone, PRL 96 010401 (2006) 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 Quantum Lithography Experiment Low N00N 2 0 ei 2 0 2 |20>+|0 2> |10>+|0 1> 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 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 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! La M&M Detector Generator M&M state: ( m,m' m',m ) M&M Visibility ( 20,10 10,20 ) Lb N00N Visibility ( 10,0 0,10 ) 2 M&M: V=0.3 Lost photons 2 N00N: V=0.05 2 恶魔 M&M’ Adds Decoy Photons MZI with Coherent Light There’s N00N in Them There Hills — Partner! ? AB ei / 2 / 2 A B I. Coherent state input II. Beam splitter is adjusted to balance any possible loss Quantum Inspired Detection: 0NN0-N00N! Visibility is Very, Very Low! 0.0002 0.0001 1 2 3 4 5 6 - 0.0001 - 0.0002 K.J. Resch, …, A.G. White, Physical Review Letters 98, 223601 (2007) Quantum Inspired Detection: 0NN0-N00N! 5 5 4 4 3 3 2 2 1 1 00 Sensitivity is Much Worse Than Shot Noise! 11 22 33 44 55 66 1 ? n Quantum Inspired Detection: Sum O’ NooNs! Visibility is Very Low! 0.003 0.002 0.001 - 2 - 0.001 - 0.002 - 0.003 - 1 0 1 2 3 Quantum Inspired Detection: Sum O’ M&Ms! Every Photon is Precious! Signal: Sensitivity: / n SNL Sub-Rayleigh & Visibility is One! We Hit ShotNoise Limit! Recall single mode phase measurement by projection synthesis discussed in – Barnett&Pegg, PRL 76, 4148 (1996). We Have Re-Invented the Barnett & Pegg Phase Operator! B&P Op The Barnett & Pegg Phase Operator Transforms into the Parity Operator! Parity Op 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 / nφ2 SNL HL TMSV & QCRB QuickTime™ and a decompressor are needed to see this picture. |TMSV> HofL QuickTime™ and a decompressor are needed to see this picture. 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, JPD, 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 photonnumber 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. QuickTime™ and a decompressor are needed to see this picture. Outline 1. Nonlinear Optics vs. Projective Measurements 2. Quantum Imaging vs. Precision Measurements 3. Showdown at High N00N! 6. Super Resolution with Classical Light 7. Super-Duper Sensitivity Beats Heisenberg! 8. A Parody on Parity 非常感谢你!