Quantum Optical Computing, Imaging, and Metrology

Transcription

1 Quantum Optical Computing, Imaging, and Metrology Ionatán Jönåthán Pádraig Påtrîck O Dúnlaing 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): (2008).

2 Quantum (Optical) Sensors Ballroom I: WED 12:00N & 8:50PM 12:00 Christoph Wildfeuer & A. Migdall NIST & Louisiana State University Techniques for enhancing the precision of measurements with photon number resolving detectors 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! 12:40 E. E. Mikhailov & I. Novikova College of William and Mary Generation of squeezed vacuum with hot and ultra-cold Rb atoms 20:50 Geoff Pryde Griffith University, AUS Optimal multiphoton phase sensing and measurement 21:10 J. C. F. Matthews & J. L. O Brien University of Bristol, UK Entangled Multi-Photon States in Waveguide for Quantum Metrology 21:30 Kevin McCusker & Paul Kwiat University of Illinois Efficient Quantum Optical State Engineering 21:50 Xi Wang Texas A&M University Self-Implemented Heterodyne CARS by Using Its Intrinsic Background

3 Hearne Institute for Theoretical Physics Quantum Science & 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 Inset C. Brignac, R.Cross, B.Gard, D.J.Lum, Keith Motes, G.M.Raterman, C.Sabottke,

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

5 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 7. Super-Duper Sensitivity Beats Heisenberg! 8. A Parody on Parity

6 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 χ (3) R is a π/2 polarization rotation, followed by a polarization dependent phase shift π. R pol σ z PBS Unfortunately, the interaction χ (3) is extremely weak*: at the single photon level This is not practical! *R.W. Boyd, J. Mod. Opt. 46, 367 (1999).

7 Two Roads to Optical Quantum Computing I. Enhance Nonlinear Interaction with a Cavity or EIT Kimble, Walther, Lukin, et al. Cavity QED 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: # 0 + " 1 +! 2 # 0 + " 1 $! 2 Milburn Knill E, Laflamme R, Milburn GJ NATURE 409 (6816): JAN Franson JD, Donegan MM, Fitch MJ, et al. PRL 89 (13): Art. No SEP

9 WHY IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT? LOQC KLM Photon-Photon XOR Gate Photon-Photon Nonlinearity Cavity QED EIT Projective Measurement Kerr Material

10 Projective Measurement Yields Effective Nonlinearity! G. G. Lapaire, P. Kok, JPD, J. E. Sipe, PRA 68 (2003) 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

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

12 Sub-Shot-Noise Interferometric Measurements With Two-Photon N00N States A Kuzmich and L Mandel; Quantum Semiclass. Opt. 10 (1998) SNL Low!N00N e i2! 0 2 HL

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

14 Quantum Lithography Experiment Low!N00N e i2! >+ 02> 10>+ 01>

15 Quantum Imaging: Super-Resolution λ/ν N=1 (classical) N=5 (N00N) λ

16 Quantum Metrology: Super-Sensitivity!!" = ˆP dp /dϕ d ˆP / d" N N=1 (classical) N=5 (N00N) Shotnoise Limit: Δϕ 1 = 1/ N dp 1 /dϕ Heisenberg Limit: Δϕ N = 1/N

17 Showdown at High-N00N! How do we make High-N00N!? N,0 + 0,N With a large cross-kerr nonlinearity!* H = κ a a b b 1 0 N 0 N,0 + 0,N This is not practical! need κ = π but κ = 10 22! *C Gerry, and RA Campos, Phys. Rev. A 64, (2001).

18 FIRST LINEAR-OPTICS BASED HIGH-N00N GENERATOR PROPOSAL Success probability approximately 5% for 4-photon output. mode a Scheme conditions on the detection of one photon at each detector 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, (2002). J.C.F.Matthews, A.Politi, Damien Bonneau, J.L.O'Brien, arxiv:

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

20 Quantum LIDAR Winning LSU Proposal Noise DARPA Eyes Quantum Mechanics for Sensor Applications Jane s Defence Weekly Target Nonclassical Light Source Detection Delay Line INPUT find min( )!" N: photon number loss A loss B! in = N # i= 0 c i N " i, i inverse problem solver forward problem solver!" = f ( # in, " ; loss A, loss B)!" FEEDBACK LOOP: Genetic Algorithm OUTPUT min(!") ; # in (OPT ) N % = c i (OPT ) N $ i, i, " OPT i= 0

21 Loss in Quantum Sensors SD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # DEC 2008 N00N! Generator Visibility:! = (10,0 + 0,10 ) 2! L a L b Detector Lost photons Lost photons Sensitivity:! = (10,0 + 0,10 ) 2 N00N 3dB Loss --- N00N No Loss SNL--- 3/28/11 21 HL

22 Super-Lossitivity Gilbert, G; Hamrick, M; Weinstein, YS; JOSA B 25 (8): AUG 2008!" =! ˆP d ˆP / d" dp N /d! N=1 (classical) N=5 (N00N) e i! " e in! e #$ L " e # N$ L dp 1 /d! 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 # DEC 2008 N00N! Generator A B! L a Detector Lost photons L b Lost photons Gremlin Q: Why do N00N States Suck 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

24 Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # DEC 2008 Try other detection scheme and states! M&M state: M&M! Generator M&M Visibility N00N Visibility! = ( 20, ,20 ) 2! = (10,0 + 0,10 ) 2!! = ( m,m' + m',m ) 2 L a L b Detector Lost photons Lost photons M&M Adds Decoy Photons

25 Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # DEC 2008 Lost photons M&M!! L a Detector M&M state: Generator! = ( m,m' + m',m ) 2 L b Lost photons N00N State --- M&M State N00N SNL --- M&M SNL --- M&M HL N00N HL A Few Photons Lost Does Not Give Complete Which Path

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. Parity Detector! Quantum Classical

27 Quantum Metrology with Two-Mode Squeezed Vacuum: Parity Detection Beats the Heisenberg Limit PRL 104, (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/ ˆn HL! 1 / ˆn TMSV! 1 / ˆn ˆn + 2 HofL! 1/ ˆn 2 SNL HL TMSV & QCRB HofL

28 New Journal of Physics 12 (2010) , /10/ $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 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 7. Super-Duper Sensitivity Beats Heisenberg! 8. A Parody on Parity