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

2. Quantum Science & Technologies Group Hearne Institute for Theoretical Physics 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

3. Quantum Control Theory

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

5. Predictions are Hard to Make — Especially About the Future! You Are Here! $Quantum$ $Computing$ $Quantum$ $Metrology$ $ 199520002005201020152020 …

6. 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

7. Schrödinger cat defined by relative photon number  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 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. 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 interactionDetector N single particles Kok, Braunstein, Dowling, Journal of Optics B 6, (27 July 2004) S811

9. Strategies to improve sensitivity: 1. Increase — sequential (multi-round) protocol. 2. Probes in entangled N-party state and one trial To makeas large as possible —> N00N! Theorem: Quantum Cramer-Rao bound optimal POVM, optimal statistical estimator Phase Estimation 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) independent trials/shot-noise limit

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

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

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

13. Super-Sensitivity N=1 (classical) N=5 (N00N) 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. N00N & Linear Optical Quantum Computing For proposals* to exploit a non-linear photon-photon interaction e.g. cross-Kerr interaction, the required optical non-linearity not readily accessible. *C. Gerry, and R.A. Campos, Phys. Rev. A 64, 063814 (2001). Nature 409, page 46, (2001).

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

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

19. High NOON States |N,0  + |0,N  How do we make: *C. Gerry, and R.A. Campos, Phys. Rev. A 64, 063814 (2001). With a large Kerr non-linearity*: But this is not practical…need  = 1! |1  |N|N |0  |N,0  + |0,N 

20. Measurement-Induced Nonlinearities G. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314 First linear-optics based High-N00N generator proposal: Success probability approximately 5% for 4-photon output. e.g. component of light from an optical parametric oscillator Scheme conditions on the detection of one photon at each detector mode a mode b H. Lee, P. Kok, N. J. Cerf and J. P. Dowling, PRA 65, 030101 (2002).

21. Implemented in Experiments!

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

24. 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

25. N00N

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

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

32. 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

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

34. 10/8/201534 Loss in Quantum Sensors SD Huver, CF Wildfeuer, JP Dowling, PRA 063828 (2008). N00N Generator Detector Lost photons LaLa LbLb Visibility: Sensitivity: SNL--- HL— N00N No Loss — N00N 3dB Loss ---

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

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

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

38. Mitigating Loss in Quantum Sensors Try other detection scheme and states! M&M Generator Detector Lost photons LaLa LbLb M&M state: M&M State — N00N State --- M&M HL — M&M SNL --- N00N SNL --- A Few Photons Lost Does Not Give Complete “Which Path”

39. 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

40. 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.

41. Orbital Angular Momentum of Light 1.Wavefront contains azimuthal phase singularities. 2.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)

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

43. Mexican Hat Trap with Thomas-Fermi Wave function

44. 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)

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

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

47. 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).

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

49. “Quantum Metrology has Rejuvenated My Career!” — Carlton M. Caves (Oct 07) You Are Here!

50. 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