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Distinction Between Entanglement and Coherence in Many Photon States and Impact on SuperResolution 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 Outline 1. Super-Resolution vs. Super-Sensitivity 2. High N00N States of Light 3. Efficient N00N Generators 4. The Role of Photon Loss 5. Mitigating Photon Loss with M&M States 6. Super-Resolving Detection with Coherent States 7. Super-Resolving Radar Ranging at Shotnoise Quantum Metrology H.Lee, P.Kok, JPD, J Mod Opt 49, (2002) 2325 Shot noise Heisenberg Sub-Shot-Noise Interferometric Measurements With Two-Photon N00N States A Kuzmich and L Mandel; Quantum Semiclass. Opt. 10 (1998) 493–500. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. Low N00N 2 0 ei 2 0 2 HL SNL AN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733 Super-Resolution a† N a N Sub-Rayleigh New York Times Discovery Could Mean Faster Computer Chips Quantum Lithography Experiment Low N00N 2 0 ei 2 0 2 |20>+|02 > |10>+|01 > 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| The expectation value is given by: |A| = N cos and the variance (A)2 is given by: N(1cos2) The unknown phase can be estimated with accuracy: A 1 = = | d A/d | N This is the standard shot-noise limit. note the square-root P Kok, SL Braunstein, and JP Dowling, Journal of Optics B 6, (2004) S811 Quantum Lithography & Metrology N N,0 0,N Now we consider the state AN 0,N N,0 N,0 0,N Quantum Lithography*: Quantum Metrology: N |AN|N = cos N High-Frequency Lithography Effect AN 1 H = = | d AN/d | N and we measure Heisenberg Limit: No Square Root! P. Kok, H. Lee, and J.P. Dowling, Phys. Rev. A 65, 052104 (2002). Super-Sensitivity: Beats Shotnoise P̂ d P̂ / d dPN/d 1 N dP1/d N=1 (classical) N=5 (N00N) Super-Resolution: Beat Rayleigh Limit N=1 (classical) N=5 (N00N) 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 QuickTime™ and a decompressor are needed to see this picture. |0 |N |0 This is not practical! — need = p but = 10–22 ! N00N States In Chapter 11 *C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001). 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. 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) |10::01> |10::01> |20::02> |20::02> |30::03> |40::04> |30::03> N00N State Experiments 1990 2-photon Rarity, (1990) Ou, et al. (1990) Shih, Alley (1990) …. Mitchell,…,Steinberg Nature (13 MAY) Toronto 2004 3, 4-photon Super6-photon resolution Super-resolution only Only! Resch,…,White PRL (2007) Queensland 2007 4-photon Super-sensitivity & Super-resolution Walther,…,Zeilinger Nature (13 MAY) Vienna Nagata,…,Takeuchi, Science (04 MAY) Hokkaido & Bristol Efficient Schemes for Generating N00N States! |N>|0> Constrained |1,1,1> |N0::0N> Desired Number Resolving Detectors Question: Do there exist operators “U” that produce “N00N” States Efficiently? Answer: YES! Phys. Rev. Lett. 99, 163604 (2007) Linear Optical N00N Generator II 2 2 2 0 U 0.03 ( 50 05 ) 2 1 0 This example disproves the N00N Conjecture: “That it Takes At Least N Modes to Make N00N.” 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). 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). Quantum States of Light From a High-Gain OPA (Experiment) HIGH FLUX 2PHOTON N00N EXPERIMENT State Before Projection Visibility Saturates at 20% with 105 Counts Per Second! F.Sciarrino, et al., Phys. Rev. A 77, 012324 (2008) HIGH N00N STATES FROM STRONG KERR NONLINEARITIES Kapale, 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 QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. Quantum States of Light For Remote Sensing “DARPA Eyes Quantum Mechanics for Sensor Applications” — Jane’s Defense Weekly Winning LSU Proposal Loss Target Entangled Light Source Delay Line Detection Super-Sensitive & Resolving Ranging Computational Optimization of Quantum LIDAR Noise Target INPUT Nonclassical Light Source inverse problem solver “find min( )“ Delay Line Detection forward problem solver N: photon number in N loss A c loss B i N i, i f ( in , ; loss A, loss B) i 0 FEEDBACK LOOP: Genetic Algorithm OUTPUT min( ) ; N ) in(OPT ) c (OPT N i, i , OPT i i 0 Lee, TW; Huver, SD; Lee, H; et al. PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009 Loss in Quantum Sensors SD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # 063828 DEC 2008 La N00N Detector Generator Lb Visibility: ( 10,0 0,10 ) Lost photons 2 Lost photons Sensitivity: ( 10,0 0,10 ) 2 N00N 3dB Loss --- N00N No Loss — SNL--5/24/2017 25 HL— Super-Lossitivity Gilbert, G; Hamrick, M; Weinstein, YS; JOSA B 25 (8): 1336-1340 AUG 2008 i P̂ d P̂ / d e e e L dPN /d N=1 (classical) N=5 (N00N) iN e N L dP1 /d 3dB Loss, Visibility & Slope — Super Beer’s Law! Loss in Quantum Sensors S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 A N00N Lost photons La Detector B Generator Lb 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 Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Lost photons Try other detection scheme and states! M&M La Detector Generator M&M state: ( m,m' m',m ) M&M Visibility ( 20,10 10,20 ) Lb N00N Visibility ( 10,0 0,10 ) 2 0.3 Lost photons 2 0.05 2 M&M’ Adds Decoy Photons Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008 Try other detection scheme and states! M&M La Detector Generator M&M state: ( m,m' m',m ) Lost photons Lb 2 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” 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 in N loss A c loss B i N i, i f ( in , ; loss A, loss B) QuickTime™ and a decompressor are needed to see this picture. i 0 FEEDBACK LOOP: Genetic Algorithm OUTPUT min( ) ; N ) in(OPT ) c (OPT N i, i , OPT i i 0 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. 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 QuickTime™ and a decompressor are needed to see this picture. Quantum Detector! Waves are Coherent! QuickTime™ and a decompressor are needed to see this picture. WHY? THERE’S N0ON IN THEM-THERE HILLS! QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. 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 QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. For coherent states parity detection can be implemented with a “quantum inspired” homodyne detection scheme. Super Resolution with Classical Light at the Quantum Limit Emanuele Distante, Miroslav Jezek, and Ulrik L. Andersen QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. Super Resolution @ Shotnoise Limit Eisenberg Group, Israel Super-Resolving Coherent Radar System Loss Target Coherent Microwave Source Delay Line Quantum Homodyne Detection Super-Resolving Shotnoise Limited Radar Ranging Super-Resolving Quantum Radar QuickTime™ and a decompressor are needed to see this picture. Objective • Coherent Radar at Low Power • Sub-Rayleigh Resolution Ranging • Operates at Shotnoise Limit Objective Approach Status • Confirmed Super-resolution • RADAR with Super Resolution • Proof-of-Principle in Visible & IR • Standard RADAR Source • Loss Analysis in Microwave Needed • Quantum Detection Scheme • Atmospheric Modelling Needed Outline 1. Super-Resolution vs. Super-Sensitivity 2. High N00N States of Light 3. Efficient N00N Generators 4. The Role of Photon Loss 5. Mitigating Photon Loss with M&M States 6. Super-Resolving Detection with Coherent States 7. Super-Resolving Radar Ranging at Shotnoise