Quantum Optical Computing, Imaging, and Metrology

Transcription

1 Quantum Optical Computing, Imaging, and Metrology Jonathan P. Dowling Hearne Institute for Theoretical Physics Quantum Science and Technologies Group Louisiana State University Baton Rouge, Louisiana USA quantum.phys.lsu.edu AQIS, 31 AUG 10, University of Tokyo Dowling JP, Quantum Optical Metrology The Lowdown On High-N00N States, Contemporary Physics 49 (2): (2008).

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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 Inset: P.M.Anisimov, B.R.Bardhan, A.Chiruvelli, L.Florescu, M.Florescu, Y.Gao, K.Jiang, K.T.Kapale, T.W.Lee, D.J.Lum, S.B.McCracken, C.J.Min, S.J.Olsen, R.Singh, K.P.Seshadreesan, S.Thanvanthri, G.Veronis. Not Shown: R.Cross, B.Gard, D.J.Lum, G.M.Raterman, C.Sabottke,

4 Nano-Technology There's Plenty of Room at the Bottom. Richard Feynman (1960) Quantum Technology There's Plenty More Room in the Quantum! Si - SILICON 1.0 cm { } Classical: All The Information in Every Computer in the World Can Be Stored in a Centimeter-Size Chunk of (1,000,000,000,000,000,000,000) Silicon Atoms at One Bit Per Atom. two nanometers > Quantum: All The Information in Every Computer in the World Can Be Stored in Seventy (70) Silicon Atoms at One Quantum Bit Per Atom!

5 IN 3-SPACE 1060 versus POWERS OF 2 IN HILBERT-SPACE A.D. 21,000,000 = , A.D.

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

7 The Most Important Outcome of the Race to Build A Quantum Computer will Certainly NOT be a Quantum Computer! $ You Are Here! $Funding Quantum Computing$ $Funding Quantum Metrology$

8 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!

9 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).

10 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.

11 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

12 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

13 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

14 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!

15 Properties of N00N states Path-entangled state large.. High N00N state if N Super-Sensitivity improving SNR for detecting small phase (path-length) shifts. Attains Heisenberg limit. Super-Resolution effective photon wavelength = λ/n. Schrödinger cat defined by relative photon number N00N state Schrödinger cat defined by relative optical phase Sanders, PRA 40, 2417 (1989). Boto,,Dowling, PRL 85, 2733 (2000). Lee,,Dowling, JMO 49, 2325 (2002).

16 Phase Estimation The Abstract Phase-Estimation Problem Estimate, e.g. path-length, field strength, etc. with maximum sensitivity given samplings with a total of N probe particles. N single particles Prepare correlations between probes Probe-system interaction Detector Kok, Braunstein, Dowling, Journal of Optics B 6, (27 July 2004) S811

17 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 (2006)

18 Phase Estimation Optical N00N states in modes a and b, Unknown phase shift on mode b so. Cramer-Rao bound mode b phase shift Heisenberg Limit!. parity measurement mode a

19 Quantum Interferometric Lithography source of two-mode correlated light NOON Generator mirror a b N-photon absorbing substrate phase difference along substrate Deposition rate: Classical input :! N (" ) = ( â + e #i" ) ˆb N ( â + e +i" ˆb ) N! N (" ) = cos 2 N (" / 2) N00N input :! N (" ) = cos 2 ( N" / 2) Super-resolution, beating the single-photon diffraction limit. Boto, Kok, Abrams, Braunstein, Williams, and Dowling PRL 85, 2733 (2000)

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

21 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

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

23 New York Times Discovery Could Mean Faster Computer Chips

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

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

26 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

27 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!

28 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).

29 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:

30 Implemented in Experiments!

31 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

32 N00N

33 Physical Review 76, (2007)

34 PRL 99, (2007)

35 Physical Review A 76, (2007) U ( ) 2

36 Entangled Superconducting Qubit Magnetometer A Guillaume & JPD, Physical Review A 73 (4): Art. No APR Objectives Develop theoretical techniques to enable Heisenberg-limited magnetic and electric field measurements with superconducting circuits. Exploit ideas from quantum optics and superconducting quantum computing! Approach Use quantum Optics techniques to create, manipulate and measure the collective state of an assembly of superconducting qubits. cavity QED approach Adapt techniques used in ion trap experiments to evaluate the uncertainty on the energy estimation (spectrometry). Status Established the first relation between the uncertainty on the electric charge Q g (or magnetic flux F x ) estimation and the number N of qubits: # Q g! #" x!1/ N

37 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!

38 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

39 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 39 HL

40 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!

41 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 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

42 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

43 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 M&M HL A Few Photons Lost Does Not Give Complete Which Path

44 Optimization of Quantum Interferometric Metrological Sensors In the Presence of Photon Loss PHYSICAL REVIEW A, 80 (6): Art. No 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.

45 Lossy State Comparison PHYSICAL REVIEW A, 80 (6): Art. No 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.

46 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!

47 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

48 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!

49 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

50 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!