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Quantum Interferometric Sensors

Jonathan P. Dowling Quantum Science & Technologies Group Hearne Institute for Theoretical Physics Department of Physics & Astronomy Louisiana State University, Baton Rouge. Quantum Interferometric Sensors. http://quantum.phys.lsu.edu/.

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Quantum Interferometric Sensors

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  1. Jonathan P. Dowling QuantumScience & Technologies Group Hearne Institute for Theoretical Physics Department of Physics & Astronomy Louisiana State University, Baton Rouge Quantum Interferometric Sensors http://quantum.phys.lsu.edu/ JP Dowling, “Quantum Optical Metrology — The Lowdown On High-N00N States,” Contemporary Physics 49 (2): 125-143 (2008). 22 APR 09, NIST, Gaithersburg

  2. K.Jacobs H.Lee T.Lee G.Veronis P.Anisimov H.Cable G.Durkin M.Florescu L.Florescu A.Guillaume P.Lougovski K.Kapale S.Thanvanthri D.Uskov A.Chiruvelli A.DaSilva Z.Deng Y.Gao R.Glasser M.Han S.Huver B.McCracken S.Olson W.Plick G.Selvaraj S.Vinjamanpathy Z.Wu Quantum Science & Technologies GroupHearne Institute for Theoretical Physics

  3. Quantum Control Theory

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

  5. $ You Are Here! $Quantum$ $Metrology$ $Quantum$ $Computing$ 1995 2000 2005 2010 2015 2020 … Predictions are Hard to Make — Especially About the Future!

  6. Overview — N00N states, properties, applications and experiments. • Fully scalable N00N-state generators — from linear-optical quantum computing. • Characterizing and engineering N00N states • What’s New with N00N? • Coherent Manipulation of BECs and Ultrastable Gyroscopes Outline

  7. Path-entangled state . High-N00N state if N > 2. • Super-Sensitivity – improving SNR for detecting small phase(path-length) shifts . Attains Heisenberg limit . • Super-Resolution – effective photon wavelength = /N. Properties of N00N states N00N state Schrödinger cat defined by relative optical phase Schrödinger cat defined by relative photon number Sanders, PRA 40, 2417 (1989). Boto,…,Dowling, PRL 85, 2733 (2000). Lee,…,Dowling, JMO 49, 2325 (2002).

  8. 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. Phase Estimation Prepare correlations between probes Probe-system interaction Detector N single particles Kok, Braunstein, Dowling, Journal of Optics B 6, (27 July 2004) S811

  9. independent trials/shot-noise limit Theorem: Quantum Cramer-Rao bound optimal POVM, optimal statistical estimator Phase Estimation Strategies to improve sensitivity: 1. Increase — sequential (multi-round) protocol. 2. Probes in entangled N-party state and one trial To make 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)

  10. Optical N00N states in modes a and b , Unknown phase shift on mode b so . Cramer-Rao bound “Heisenberg Limit!”. Phase Estimation parity measurement phase shift mode b mode a Super-sensitivity: beating the shotnoise limit.

  11. mirror a source of two-mode correlated light N-photon absorbing substrate NOON Generator b Quantum Interferometric Lithography phase difference along substrate Deposition rate: Classical input : N00N input : Super-resolution, beating the classical diffraction limit. Boto, Kok, Abrams, Braunstein, Williams, and Dowling PRL 85, 2733(2000)

  12. Super-Resolution á la N00N N=1 (classical) N=5 (N00N)

  13. N=1 (classical) N=5 (N00N) Super-Sensitivity For Many Sensor Applications — LIGO, Gyro, etc., — We Don’t CARE Which Fringe We’re On! The Question for Us is IF any Given Fringe Moves, With What Resolution Can We Tell This!?

  14. Outline • Overview — N00N states, properties, applications and experiments. • Fully scalable N00N-state generators — from linear-optical quantum computing. • Characterizing and engineering N00N states • What’s New with N00N? • Coherent Manipulation of BECs and Ultrastable Gyroscopes

  15. Road to Entangled- Particle Interferometry:Early Example of Remote Entanglement Generation by Erasure of Which-Path Information Followed by Detection!

  16. For proposals* to exploit a non-linear photon-photon interaction e.g. cross-Kerr interaction , the required optical non-linearity not readily accessible. N00N & Linear Optical Quantum Computing Nature 409, page 46, (2001). *C. Gerry, and R.A. Campos, Phys. Rev. A64, 063814 (2001).

  17. WHEN IS A KERR NONLINEARITY LIKE A PROJECTIVE MEASUREMENT? Photon-Photon XOR Gate Linear Opt KLM/Franson Cavity QED Kimble Photon-Photon Nonlinearity ??? Kerr Material Projective Measurement

  18. Projective Measurement Yields Effective Kerr! KLM CSIGN Hamiltonian Franson CNOT Hamiltonian G. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314 We are no longer limited by the nonlinearities we find in Nature! NON-Unitary Gates  Effective Unitary Gates

  19. |N,0 + |0,N How do we make: With a large Kerr non-linearity*: |1 |0 |N |N,0 + |0,N |0 But this is not practical…need  = 1! High NOON States *C. Gerry, and R.A. Campos, Phys. Rev. A64, 063814 (2001).

  20. First linear-optics based High-N00N generator proposal: Success probability approximately 5% for 4-photon output. Measurement-Induced NonlinearitiesG. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314 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).

  21. Implemented in Experiments!

  22. Mitchell,…,Steinberg Nature (13 MAY) Toronto Walther,…,Zeilinger Nature (13 MAY)Vienna 2004 3, 4-photon Super- resolution Nagata,…,Takeuchi, Science (04 MAY) Hokkaido & Bristol 2007 4-photon Super-sensitivity & Super-resolution 1990 2-photon Rarity, (1990) Ou, et al. (1990) Shih, Alley (1990) …. SuperQuantumPhaseRealisticallyExtractedálaPhotons! 6-photon Super-Resolution Resch,…,White PRL (2007) Queensland

  23. Outline • Overview — N00N states, properties, applications and experiments. • Fully scalable N00N-state generators — from linear-optical quantum computing. • Characterizing and engineering N00N states • What’s New with N00N? • Coherent Manipulation of BECs With Orbital Angular Momentum Beams of Light

  24. N00N

  25. Yes, Jeff and Anton, N00N States Are Really Entangled!

  26. U Physical Review A 76, 063808 (2007)

  27. Outline • Overview — N00N states, properties, applications and experiments. • Fully scalable N00N-state generators — from linear-optical quantum computing. • Characterizing and engineering N00N states • What’s New with N00N? • Coherent Manipulation of BECs With Orbital Angular Momentum Beams of Light

  28. “DARPA Eyes Quantum Mechanics for Sensor Applications” — Jane’s Defence Weekly Winning LSU Proposal Loss Target Entangled Light Source Delay Line Detection Who in Their Right Mind Would Think Quantum States Could be Used in Remote Sensing!?

  29. Loss in Quantum Sensors SD Huver, CF Wildfeuer, JP Dowling, PRA 063828 (2008). Lost photons La N00N Detector Lb Lost photons Generator Visibility: Sensitivity: N00N 3dB Loss --- N00N No Loss — SNL--- HL—

  30. Super-Lossitivity N=1 (classical) N=5 (N00N) Gilbert, Hamrick, Weinstein, JOSA B, 25 (8): 1336-1340 AUG 2008 3dB Loss, Visibility & Slope — Super Beer’s Law!

  31. Loss in Quantum Sensors S. Huver, C. F. Wildfeuer, J.P. Dowling, PRA 063828 (2008). Lost photons La N00N Detector Lb Lost photons Generator A B Gremlin Q: Why do N00N States “Suck” in the Presence of Loss? A: Single Photon Loss = Complete “Which Path” Information!

  32. Lost photons La M&M Detector Lb Lost photons Generator Towards A Realistic Quantum Sensor Try other detection scheme and states! M&M state: N00N Visibility M&M Visibility M&M’ Adds Decoy Photons 0.3 0.05

  33. Lost photons La M&M Detector Lb Lost photons Generator Mitigating Loss in Quantum Sensors Try other detection scheme and states! 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 —

  34. Outline • Overview — N00N states, properties, applications and experiments. • Fully scalable N00N-state generators — from linear-optical quantum computing. • Characterizing and engineering N00N states • What’s New with N00N? • Coherent Manipulation of BECs and Ultrastable Gyroscopes

  35. Sagnac Effect in Gyroscopy Sagnac effect is used to measure rotation rates using interference Atom interferometers are in principle more sensitive that light-based ones.

  36. Orbital Angular Momentum of Light Wavefront contains azimuthal phase singularities. Each photon carries of orbital angular momentum. [1] K.T. Kapale and J.P. Dowling, PRL 95, 173601 (2005). [2] N. Gonzalez et. al, Opt. Exp. 14, 9093 (2006)

  37. STIRAP* Makes BEC Vortex Superpositions Counterintuitive pulse sequence *Stimulated Rapid Adiabatic Passage

  38. Mexican Hat Trap with Thomas-Fermi Wave function

  39. General state of the BEC at time ‘t’ Measure of vortex transfer [3] S. Thanvanthri, K. T. Kapale and J.P. Dowling, PRA 77, 053825 (2008)

  40. Sagnac effect in vortex BEC superpositions For a vortex superposition rotating at angular velocity , the vortex interference pattern rotates by an angle

  41. Detection using Phase Contrast Imaging Advantage: Non destructive detection, increased phase accumulation with time. Sensitivity State of the art

  42. Stability? Noise from Atomic drift: Over 8 hours accumulation Current atom gyros, over 4 hours, D. S. Durfee, Y. K. Shaham and M. A. Kasevich, PRL 97, 240801 (2006).

  43. An ultra-stable, compact atom gyroscope. • Better imaging techniques directly improve sensitivity. • Atom drift can further be controlled using trap geometry.

  44. You Are Here! Quantum Meteorology! “Quantum Metrology has Rejuvenated My Career!” — Carlton M. Caves (Oct 07) Not to be Confused with....

  45. Outline • Overview — N00N states, properties, applications and experiments. • Fully scalable N00N-state generators — from linear-optical quantum computing. • Characterizing and engineering N00N states • What’s New with N00N? • Coherent Manipulation of BECs and Ultrastable Gyroscopes

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