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

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. SNL HL

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

New York Times Discovery Could Mean Faster Computer Chips

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

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

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

Super-Sensitivity: Beats Shotnoise dP 1 /d  dP N /d  N=1 (classical) N=5 (N00N)

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

Showdown at High-N00N! |N,0  + |0,N  How do we make High-N00N!? *C Gerry, and RA Campos, Phys. Rev. A 64, (2001). With a large cross-Kerr nonlinearity!* H =  a † a b † b This is not practical! — need  =  but  = 10 –22 ! |1  |N|N |0  |N,0  + |0,N  N00N States In Chapter 11

Measurement-Induced Nonlinearities G. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 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, NJ Cerf and JP Dowling, PRA 65, (2002). JCF Matthews, A Politi, D Bonneau, JL O'Brien, PRL 107, (2011)

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

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

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

Phys. Rev. Lett. 99, (2007)

U 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(m 2 ). Upper bound theorem: The maximal size of a N00N state generated in m modes via single photon detection in m-2 modes is O(m 2 ). Linear Optical N00N Generator II

HIGH FLUX 2-PHOTON NOON STATES From a High-Gain OPA (Theory) G.S.Agarwal, et al., J. Opt. Soc. Am. B 24, 270 (2007). We present a theoretical analysis of the properties of an unseeded optical parametric amplifier (OPA) used as the source of entangled photons. 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. OPA Scheme

Quantum States of Light From a High-Gain OPA (Experiment) HIGH FLUX 2- PHOTON N00N EXPERIMENT F.Sciarrino, et al., Phys. Rev. A 77, (2008) State Before Projection Visibility Saturates at 20% with 10 5 Counts Per Second!

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

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

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

6/3/ Loss in Quantum Sensors SD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # DEC 2008 N00N Generator Detector Lost photons LaLa LbLb Visibility: Sensitivity: SNL--- HL— N00N No Loss — N00N 3dB Loss ---

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

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

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 Visibility M&M Generator Detector Lost photons LaLa LbLb M&M state: N00N Visibility M&M’ Adds Decoy Photons

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” Towards A Realistic Quantum Sensor S. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # DEC 2008

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. forward problem solver INPUT “find min( )“ FEEDBACK LOOP: Genetic Algorithm inverse problem solver OUTPUT N: photon number loss A loss B

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 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. Classical Quantum  Waves are Coherent! Quantum Detector! Parity Measurement!

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

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 

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

Super Shotnoise Limit Eisenberg Group, Israel

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

Super-Resolving Quantum Radar Objective Objective Approach Status Coherent Radar at Low Power Sub-Rayleigh Resolution Ranging Operates at Shotnoise Limit 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

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 Limit