Schrödinger’s Rainbow: The Renaissance in Quantum Optical Interferometry

Jonathan P. Dowling Quantum Science & Technologies (QST) Group Hearne Institute for Theoretical Physics Louisiana State University http://quantum.phys.lsu.edu Table of Contents

• Quantum Technologies

• Schrödinger’s Cat and All That

• Quantum Light—Over the Rainbow

• Putting Entangled Light to Work

• The Yellow-Brick Roadmap Quantum Technology: The Second Quantum Revolution JP Dowling & GJ Milburn, Phil. Transactions of the Royal Soc. of London

Ion Traps Quantum Quantum Bose-Einstein Cavity QED Optics Atomics Atomic Coherence Linear Optics Quantum Ion Traps Information Processing Coherent Quantum Quantum Mechanical Electronics Systems

Superconductors Pendulums Excitons Cantilevers Spintronics Phonons Schrödinger’s Cat and All That Schrödinger’s Cat Revisited Quantum Kitty Review

A sealed and insulated box (A) contains a radioactive source (B) which has a 50% chance during the course of the "experiment" of triggering Geiger counter (C) which activates a mechanism (D) causing a hammer to smash a flask of prussic acid (E) and killing the cat (F). An observer (G) must open the box in order to collapse the state vector of the system into one of the two possible states. A second observer (H) may be needed to collapse the state vector of the larger system containing the first observer (G) and the apparatus (A-F). And so on ... Paradox? What Paradox!?

(1.) The State of the Cat is “Entangled” with That of the Atom.

(2.) The Cat is in a Simultaneous Superposition of Dead & Alive.

(3.) Observers are Required to “Collapse” the Cat to Dead or Alive Quantum Entanglement

“Quantum entanglement is the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.”

— Erwin Schrödinger Conservation of Classical Angular Momentum

A B Conservation of Quantum Spin

David Bohm

Entangled A B Einstein, Podolsky, Rosen (EPR) Paradox

Albert Einstein Boris Podolsky Nathan Rosen

“If, without in any way disturbing a system, we can predict with certainty ... the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity." Hidden Variable Theory

+ A B A B Can the Spooky, Action-at-a-distance Predictions (Entanglement) of Quantum Mechanics…

+ A B A B

…Be Replaced by Some Sort of Local, Statistical, Classical (Hidden Variable) Theory? NO!—Bell’s Inequality

John Bell

The physical predictions of quantum theory disagree with those of any local (classical) hidden-variable theory! Clauser (1978) & Aspect (1982) Experiments

H V Two-Photon Atomic A B Decay V H

Alain Aspect

H V V H A B + A B

John Clauser

V= Vertical Polarization H = Horizontal Polarization Quantum Light—Over the Rainbow Parametric Downconversion: Type I Parametric Downconversion: Type I

Photon Pairs

Signal B

UV

Pump Idler A Type I

Degenerate (Entangled) Case: ωs=ωi

ωs , ϕ s , ks A ωi, ϕ i , ks B + ωi , ϕ i , ki A ω s , ϕ s , k s B Parametric Downconversion: Type I Parametric Downconversion: Type II

Degenerate (Entangled) Case: ωs=ωi

H V V H A B + A B

B A

Putting Entangled Light to Work Tests of Bell’s Inequalities at Innsbruck

Type II Downcoversion

Anton Zeilinger Alice Bob Quantum Teleportation

Teleportation Experiment at Innsbruck

EPR Source

Bell State Analysis

Experiment NIST Heralded Photon Absolute Light Source

Output characteristics : photon #  known photon timing  known wavelength  known direction  known polarization  known Alan Migdall Detector Quantum Efficiency Scheme

Detector to be Calibrated Absolute ! COUNTER Quantum 1 Efficiency

COINC N COUNTER !0

PARAMETRIC CRYSTAL !2 COUNTER Trigger or “Herald” Detector

N1=!1N N2=!2N NC=!1!2N

!1=NC/N2 No External Standards Needed! Characterizing Two-Photon Entanglement

Any two-photon tomography requires 16 of these measurements. V-polarized (from #2) Examples Arm 1 Arm 2 H V #2 H R Kwiat Super-Bright Source D D Detector PBS HWP QWP This setup allows Black Box measurement of an Generates arbitrary arbitrary polarization Entangled States state in each arm. QWP HWP Paul Kwiat PBS Detector U. Illinois Characterization of Entangled States

Bell States11 Impossible States

0.80.8 Maximally-Entangled Mixed States

0.60.6 Werner States 0.40.4

0.20.2

Product States00 00 0.1 0.20.2 0.3 0.40.4 0.5 0.60.6 0.7 0.80.8 0.9 11 Pure Mixed Linear entropy, S states L states Quantum Cryptography at University of Geneva

System Under Lake Geneva

Bob and “Charly” Share Random Crypto Key Nicolas Gisin New York Times ORIGINThe OFHong-Ou-Mandel THE LITHO EFFECT Effect SHOMI FOR N=2

Parametric Downcoversion Phase Shifter A ! C Coincidence 1 A 1 B 0 A 2 B + 2 A 0 B Counter 2 D B

phase oscillates twice as fast

2i! 0 A 2 B + 2 A 0 B 0 A 2 B + e 2 A 0 B 2 2

Leonard Mandel Quantum Optical Lithography

Quantum Peak Is Narrower and Spacing is HALVED!

D 2

1.5

1 Classical One-Photon Absorption — Classical Two-Photon Absorption — 0.5 Quantum Two-Photon Absorption — j - p 0 p Displacement Measurements and Gravity Waves

" " !xclassical = ", !xshotnoise = , !xHeisenberg = Image of the wave plate N N plane with waist=300µm

33cm 3.3cm

coherent beam R=0.92

0.08 + 0.92

wave plate lens f=3cm

squeezed vacuum : OPA Hans Bachor Australian National University Quantum Clock Synchronization

Entangled Photons Can Synchronize Past the Turbulent Atmosphere!

Seth Lloyd MIT

A B Quantum Computing

Entangled Photons are a Resource for Scalable Quantum Computation!

E. Knill, R. Laflamme and G. Milburn, Nature 409, 46, (2001)

Gerard Milburn University Of Quantum Controlled-NOT Gate Queensland using and Entangled-Light Source, Beam Splitters, and Detectors.

The Yellow-Brick Roadmap

Imaging Communications Clock Synchronization

Metrology Sensors Computing