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 JP Dowling, “Quantum Optical Metrology — The Lowdown On High- N00N States,” Contemporary Physics 49 (2): (2008).

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

Quantum Control Theory

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

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

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

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).

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

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 (2006) independent trials/shot-noise limit

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.

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

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

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!?

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

Road to Entangled- Particle Interferometry: Early Example of Remote Entanglement Generation by Erasure of Which-Path Information Followed by Detection!

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, (2001). Nature 409, page 46, (2001).

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?

G. G. Lapaire, Pieter Kok, JPD, J. E. Sipe, PRA 68 (2003) 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!

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

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, N. J. Cerf and J. P. Dowling, PRA 65, (2002).

Implemented in Experiments!

SuperQuantumPhaseRealisticallyExtractedálaPhotons! Rarity, (1990) Ou, et al. (1990) Shih, Alley (1990) …. 6-photon Super-Resolution 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 Walther,…,Zeilinger Nature (13 MAY) Vienna

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

N00N

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

Physical Review A 76, (2007) U

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

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

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

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

Loss in Quantum Sensors S. Huver, C. F. Wildfeuer, J.P. Dowling, PRA (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

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 M&M’ Adds Decoy Photons

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”

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

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.

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, (2005). [2] N. Gonzalez et. al, Opt. Exp. 14, 9093 (2006)

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

Mexican Hat Trap with Thomas-Fermi Wave function

General state of the BEC at time ‘t’ Measure of vortex transfer [3] S. Thanvanthri, K. T. Kapale and J.P. Dowling, PRA 77, (2008)

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

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

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, (2006).

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

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

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