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Jonathan P. Dowling

Distinction Between Entanglement and Coherence in Many Photon States and Impact on Super-Resolution. Jonathan P. Dowling. Hearne Institute for Theoretical Physics Quantum Science and Technologies Group Louisiana State University Baton Rouge, Louisiana USA. quantum.phys.lsu.edu.

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Jonathan P. Dowling

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  1. Distinction Between Entanglement and Coherence in Many Photon States and Impact on Super-Resolution Jonathan P. Dowling Hearne Institute for Theoretical Physics Quantum Science and Technologies Group Louisiana State University Baton Rouge, Louisiana USA quantum.phys.lsu.edu ONR SCE Program Review San Diego, 28 JAN 13

  2. Outline Super-Resolution vs. Super-Sensitivity High N00N States of Light Efficient N00N Generators The Role of Photon Loss Mitigating Photon Loss with M&M States 6. Super-Resolving Detection with Coherent States 7. Super-Resolving Radar Ranging at Shotnoise Limit

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

  4. Sub-Shot-Noise Interferometric Measurements With Two-Photon N00N States A Kuzmich and L Mandel; Quantum Semiclass. Opt. 10 (1998) 493–500. SNL HL

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

  6. New York Times Discovery Could Mean Faster Computer Chips

  7. Quantum Lithography Experiment |20>+|02> |10>+|01>

  8. note the square-root Canonical Metrology Suppose we have an ensemble of N states | = (|0 + ei|1)/2,  and we measure the following observable: A = |01| + |10|  |A| = N cos  The expectation value is given by: and the variance (A)2 is given by: N(1cos2) The unknown phase can be estimated with accuracy: A 1  = =  |dA/d | N This is the standard shot-noise limit. P Kok, SL Braunstein, and JP Dowling, Journal of Optics B 6, (2004) S811

  9. Quantum Lithography & Metrology High-Frequency Lithography Effect 1 N Heisenberg Limit: No Square Root! Now we consider the state and we measure N |AN|N = cos N QuantumLithography*:  AN H = = QuantumMetrology: |dAN/d |  P. Kok, H. Lee, and J.P. Dowling, Phys. Rev. A 65, 052104 (2002).

  10. Super-Sensitivity: Beats Shotnoise dPN/d dP1/d N=1 (classical) N=5 (N00N)

  11. Super-Resolution: Beat Rayleigh Limit  N=1 (classical) N=5 (N00N) 

  12. N00N States In Chapter 11 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 |N,0 + |0,N |0 This is not practical! — need  = p but  = 10–22 ! *C Gerry, and RA Campos, Phys. Rev. A64, 063814 (2001).

  13. First linear-optics based High-N00N generator proposal: Measurement-Induced NonlinearitiesG. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314 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, NJ Cerf and JP Dowling, PRA 65, 030101 (2002). JCF Matthews, A Politi, D Bonneau, JL O'Brien, PRL 107, 163602 (2011)

  14. |10::01> |10::01> |20::02> |20::02> |30::03> |30::03> |40::04>

  15. Mitchell,…,Steinberg Nature (13 MAY) Toronto Walther,…,Zeilinger Nature (13 MAY)Vienna 2004 3, 4-photon Super- resolution only Nagata,…,Takeuchi, Science (04 MAY) Hokkaido & Bristol 2007 4-photon Super-sensitivity & Super-resolution 1990 2-photon N00N State Experiments Rarity, (1990) Ou, et al. (1990) Shih, Alley (1990) …. 6-photon Super-resolution Only! Resch,…,White PRL (2007) Queensland

  16. Efficient Schemes for Generating N00N States! |N>|0> |N0::0N> Constrained Desired Number Resolving Detectors |1,1,1> Question: Do there exist operators “U” that produce “N00N” States Efficiently? Answer: YES!

  17. Phys. Rev. Lett. 99, 163604 (2007)

  18. Linear Optical N00N Generator II This example disproves the N00N Conjecture: “That it Takes At Least N Modes to Make N00N.” U The upper bound on the resources scales quadratically! Upper bound theorem: The maximal size of a N00N state generated in m modes via single photon detection in m-2 modes is O(m2).

  19. HIGH FLUX 2-PHOTON NOON STATES From a High-Gain OPA (Theory) We present a theoretical analysis of the properties of an unseeded optical parametric amplifier (OPA) used as the source of entangled photons. OPA Scheme The idea is to take known bright sources of entangled photons coupled to number resolving detectors and see if this can be used in LOQC, while we wait for the single photon sources. G.S.Agarwal, et al., J. Opt. Soc. Am. B 24, 270 (2007).

  20. Quantum States of Light From a High-Gain OPA (Experiment) HIGH FLUX 2-PHOTON N00N EXPERIMENT State Before Projection Visibility Saturates at 20% with 105 Counts Per Second! F.Sciarrino, et al., Phys. Rev. A 77, 012324 (2008)

  21. HIGH N00N STATES FROM STRONG KERR NONLINEARITIESKapale, KT; Dowling, JP, PRL, 99 (5): Art. No. 053602 AUG 3 2007. Ramsey Interferometry for atom initially in state b. Dispersive coupling between the atom and cavity gives required conditional phase shift

  22. “DARPA Eyes Quantum Mechanics for Sensor Applications” — Jane’s Defense Weekly Winning LSU Proposal Loss Target Entangled Light Source Delay Line Detection Quantum States of Light For Remote Sensing Super-Sensitive & Resolving Ranging

  23. Noise Target Nonclassical Light Source Delay Line Detection Computational Optimization of Quantum LIDAR INPUT inverse problem solver “find min( )“ forward problem solver N: photon number loss A loss B FEEDBACK LOOP: Genetic Algorithm OUTPUT Lee, TW; Huver, SD; Lee, H; et al. PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009

  24. Loss in Quantum Sensors SD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Lost photons La N00N Detector Lb Lost photons Generator Visibility: Sensitivity: N00N 3dB Loss --- N00N No Loss — SNL--- HL— 1/4/2020 25

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

  26. Loss in Quantum Sensors S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Lost photons La N00N Detector Lb Lost photons Generator A B Gremlin Q: Why do N00N States Do Poorly in the Presence of Loss? A: Single Photon Loss = Complete “Which Path” Information!

  27. Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Lost photons La M&M Detector Lb Lost photons Generator Try other detection scheme and states! M&M state: N00N Visibility M&M Visibility M&M’ Adds Decoy Photons 0.3 0.05

  28. Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Lost photons La M&M Detector Lb Lost photons Generator 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 —

  29. Optimization of Quantum Interferometric Metrological Sensors In the Presence of Photon Loss PHYSICAL REVIEW A, 80 (6): Art. No. 063803 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. INPUT inverse problem solver “find min( )“ forward problem solver N: photon number loss A loss B FEEDBACK LOOP: Genetic Algorithm OUTPUT

  30. Lossy State Comparison PHYSICAL REVIEW A, 80 (6): Art. No. 063803 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 Generalized 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 generalized coherent states for high loss. This graph supports the assertion that a Type-II sensor with coherent light but a non-classical detection scheme is optimal for very high loss.

  31. Super-Resolution at the Shot-Noise Limit with Coherent States and Photon-Number-Resolving Detectors JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 27 (6): A170-A174 Yang Gao, Christoph F. Wildfeuer, Petr M. Anisimov, Hwang Lee, Jonathan P. Dowling We show that coherent light coupled with a quantum detection scheme — parity measurement! — can provide a super-resolution much below the Rayleigh diffraction limit, with sensitivity at the shot-noise limit in terms of the detected photon power. Parity Measurement! Quantum Classical Quantum Detector!  Waves are Coherent!

  32. WHY? THERE’S N0ON IN THEM-THERE HILLS!

  33. Super-Resolution at the Shot-Noise Limit with Coherent States and Photon-Number-Resolving Detectors JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 27 (6): A170-A174 Yang Gao, Christoph F. Wildfeuer, Petr M. Anisimov, Hwang Lee, Jonathan P. Dowling 

  34. For coherent states parity detection can be implemented with a “quantum inspired” homodyne detection scheme.

  35. Super Resolution with Classical Light at the Quantum Limit Emanuele Distante, Miroslav Jezek, and Ulrik L. Andersen 

  36. Super Resolution @ Shotnoise Limit Eisenberg Group, Israel 

  37. Super-Resolving Coherent Radar System Loss Target Coherent Microwave Source Super-Resolving Shotnoise Limited Radar Ranging Delay Line Quantum Homodyne Detection

  38. Super-Resolving Quantum Radar Objective • Coherent Radar at Low Power • Sub-Rayleigh Resolution Ranging • Operates at Shotnoise Limit Objective Approach Status • RADAR with Super Resolution • Standard RADAR Source • Quantum Detection Scheme • Confirmed Super-resolution • Proof-of-Principle in Visible & IR • Loss Analysis in Microwave Needed • Atmospheric Modelling Needed

  39. Outline Super-Resolution vs. Super-Sensitivity High N00N States of Light Efficient N00N Generators The Role of Photon Loss Mitigating Photon Loss with M&M States 6. Super-Resolving Detection with Coherent States 7. Super-Resolving Radar Ranging at Shotnoise Limit

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