Jonathan P. Dowling Distinction Between Entanglement and Coherence in Many Photon States and Impact on Super-Resolution quantum.phys.lsu.eduHearne Institute for Theoretical PhysicsQuantum Science and Technologies GroupLouisiana State UniversityBaton Rouge, Louisiana USAONR SCE Program ReviewSan Diego, 28 JAN 13

OutlineSuper-Resolution vs. Super-SensitivityHigh N00N States of LightEfficient N00N Generators The Role of Photon LossMitigating Photon Loss with M&M States6. Super-Resolving Detection with Coherent States7. Super-Resolving Radar Ranging at Shotnoise Limit

Quantum MetrologyH.Lee, P.Kok, JPD, J Mod Opt 49, (2002) 2325Shot noiseHeisenberg

Sub-Shot-Noise Interferometric Measurements With Two-Photon N00N StatesA Kuzmich and L Mandel; Quantum Semiclass. Opt. 10 (1998) 493500.SNLHL

a N a NAN Boto, DS Abrams, CP Williams, JPD, PRL 85 (2000) 2733Super-ResolutionSub-Rayleigh

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

Canonical MetrologyP Kok, SL Braunstein, and JP Dowling, Journal of Optics B 6, (2004) S811Suppose we have an ensemble of N states | = (|0 + ei |1)/2,

and we measure the following observable:The expectation value is given by: and the variance (A)2 is given by: N(1cos2)A = |0 1| + |1 0||A| = N cos The unknown phase can be estimated with accuracy:This is the standard shot-noise limit. = = A| d A/d |N1

Quantum Lithography & Metrology Now we consider the state

and we measureP. Kok, H. Lee, and J.P. Dowling, Phys. Rev. A 65, 052104 (2002).Quantum Lithography*:Quantum Metrology: N |AN|N = cos NH = = AN| d AN/d |

Super-Sensitivity: Beats ShotnoisedP1/ddPN/dN=1 (classical)N=5 (N00N)

Super-Resolution: Beat Rayleigh LimitN=1 (classical)N=5 (N00N)

Showdown at High-N00N!|N,0 + |0,NHow do we make High-N00N!?*C Gerry, and RA Campos, Phys. Rev. A 64, 063814 (2001).With a large cross-Kerr nonlinearity!* H=aabbThis is not practical! need =p but =1022 !|1|N|0|0|N,0 + |0,N

Measurement-Induced NonlinearitiesG. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 042314First linear-optics based High-N00N generator proposal:Success probability approximately 5% for 4-photon output.e.g. component oflight from anoptical parametric oscillator Scheme conditions on the detection of one photon at each detectormode amode bH 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>|20::02>|40::04>|10::01>|20::02>|30::03>|30::03>

N00N State ExperimentsRarity, (1990) Ou, et al. (1990)Shih, Alley (1990).6-photon Super-resolutionOnly!Resch,,WhitePRL (2007)Queensland19902-photon

Efficient Schemes for Generating N00N States!Question: Do there exist operators U that produce N00N States Efficiently?

Answer: YES!

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

UThis 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).Linear Optical N00N Generator II

HIGH FLUX 2-PHOTON NOON STATESFrom 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, 012324 (2008)State Before ProjectionVisibility Saturates at 20% with105 Counts Per Second!

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

Quantum States of Light For Remote SensingSuper-Sensitive & Resolving Ranging

Computational Optimization of Quantum LIDARLee, TW; Huver, SD; Lee, H; et al.PHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009

**Loss in Quantum SensorsSD Huver, CF Wildfeuer, JP Dowling, Phys. Rev. A 78 # 063828 DEC 2008Visibility:Sensitivity:SNL---HLN00N NoLoss N00N 3dB Loss ---

Super-LossitivityGilbert, G; Hamrick, M; Weinstein, YS; JOSA B 25 (8): 1336-1340 AUG 20083dB Loss, Visibility & Slope Super Beers Law!N=1 (classical)N=5 (N00N)

Loss in Quantum SensorsS. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008Q: Why do N00N States Do Poorly in the Presence of Loss?A: Single Photon Loss = Complete Which Path Information!ABGremlin

Towards A Realistic Quantum SensorS. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008

Try other detection scheme and states!M&M VisibilityM&M state:N00N Visibility0.050.3M&M Adds Decoy Photons

Try other detection scheme and states!M&M state:M&M State N00N State ---M&M HL M&M HL M&M SNL ---N00N SNL ---A FewPhotonsLostDoes NotGiveCompleteWhich PathTowards A Realistic Quantum SensorS. Huver, C. F. Wildfeuer, J.P. Dowling, Phys. Rev. A 78 # 063828 DEC 2008

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.

Lossy State ComparisonPHYSICAL REVIEW A, 80 (6): Art. No. 063803 DEC 2009Here 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 thatThe 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-A174Yang 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. ClassicalQuantumWaves are Coherent!QuantumDetector!Parity Measurement!

WHY? THERES 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-A174Yang 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 LimitEmanuele Distante, Miroslav Jezek, and Ulrik L. Andersen

Super Resolution @ Shotnoise LimitEisenberg Group, Israel

Super-Resolving Coherent Radar SystemCoherent MicrowaveSourceDelayLineQuantumHomodyne DetectionTargetLossSuper-ResolvingShotnoise LimitedRadar Ranging

Super-Resolving Quantum RadarObjectiveObjective ApproachStatus

Coherent Radar at Low Power Sub-Rayleigh Resolution Ranging

Operates at Shotnoise Limit

RADAR with Super Resolution

Standard RADAR Source

Quantum Detection SchemeConfirmed Super-resolution

Proof-of-Principle in Visible & IR

Loss Analysis in Microwave Needed

Atmospheric Modelling Needed

OutlineSuper-Resolution vs. Super-SensitivityHigh N00N States of LightEfficient N00N Generators The Role of Photon LossMitigating Photon Loss with M&M States6. Super-Resolving Detection with Coherent States7. Super-Resolving Radar Ranging at Shotnoise Limit

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