Schrödinger’s Rainbow: The Renaissance in Quantum Optical Interferometry

Jonathan P. DowlingQuantum Science & Technologies (QST) Group

Hearne Institute for Theoretical PhysicsLouisiana 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 RevolutionJP Dowling & GJ Milburn, Phil. Transactions of the Royal Soc. of London

QuantumMechanical

Systems

PendulumsCantileversPhonons

CoherentQuantumElectronics

SuperconductorsExcitonsSpintronics

Quantum Optics

Ion TrapsCavity QEDLinear Optics

QuantumAtomics

Bose-EinsteinAtomic CoherenceIon TrapsQuantum

InformationProcessing

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

Entangled

David Bohm

A B

Einstein, Podolsky, Rosen (EPR) Paradox

Albert Einstein

Boris Podolsky

“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."

Nathan Rosen

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

The physical predictions of quantum theory disagree with those of any local (classical) hidden-variable theory!

John Bell

Clauser (1978) & Aspect (1982) Experiments

John Clauser

Alain Aspect

V= Vertical Polarization

H = Horizontal Polarization

HAV

B VAH

B

A B

H

V H

VTwo-PhotonAtomicDecay

Quantum Light—Over the Rainbow

Parametric Downconversion: Type I

Parametric Downconversion: Type I

UV

Pump

Signal B

Idler A

Degenerate (Entangled) Case: s=iDegenerate (Entangled) Case: s=i

s, s, ks A i, i, ks B i, i, ki A s, s, ks B

Type I

Photon Pairs

Parametric Downconversion: Type I

QuickTime™ and aSorenson Video decompressorare needed to see this picture.

A

B

Parametric Downconversion: Type II

HAV

B VAH

B

Degenerate (Entangled) Case: s=iDegenerate (Entangled) Case: s=i

QuickTime™ and aAnimation decompressor

are needed to see this picture.

Putting Entangled Light to Work

Tests of Bell’s Inequalities at Innsbruck

Anton ZeilingerAlice

Bob

Type II Downcoversion

Quantum Teleportation

Teleportation Experiment at Innsbruck

Bell State Analysis

EPR Source

Experiment

NIST Heralded Photon Absolute Light Source

Output characteristics : photon # knownphoton timing knownwavelength knowndirection knownpolarization known Alan Migdall

0

ω2

ω1

PARAMETRIC CRYSTAL

COUNTER

COINC COUNTER

AbsoluteQuantumEfficiency

COUNTER

N

Detector to be Calibrated

Trigger or “Herald” DetectorN1=η1N N2=η2N NC=η1η2N

η1=NC/ N2

Detector Quantum Efficiency Scheme

No External Standards Needed!No External Standards Needed!

Black BoxGenerates arbitrary Entangled States

QWP

QWP

HWP

HWP

PBS

PBS

Detector

Detector

This setup allows measurement of an arbitrary polarization

state in each arm.

Any two-photon tomography requires 16 of these measurements.

ExamplesArm 1 Arm 2 H V H R D D

Characterizing Two-Photon Entanglement

Paul KwiatU. Illinois

#1

H-polarized(from #1)Type-I phase-matching

#2V-polarized(from #2)

#1

H-polarized(from #1)Type-I phase-matching

Kwiat Super-Bright Source

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Maximally-Entangled Mixed States

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Linear entropy, SLPure

states

Product States

Bell StatesImpossible States

Mixed states

Characterization of Entangled States

Werner States

Bob and “Charly” Share Random Crypto Key

Quantum Cryptography at University of Geneva

System Under Lake Geneva

Nicolas Gisin

New York Times

The Hong-Ou-Mandel Effect

Leonard Mandel

EASY (BUT USELESS?) FOR N=2ABA′B′CBSMMPS - Two Photon Absorption

1

A1

B

0A

2B

+ e2 i ϕ

2A

0B

2

Parametric Downcoversion

Classical One-Photon Absorption —Classical Two-Photon Absorption —Quantum Two-Photon Absorption —

- p 0 pj

0.5

1

1.5

2D

Quantum PeakIs Narrower andSpacing is HALVED!

Quantum PeakIs Narrower andSpacing is HALVED!

Quantum Optical Lithography

squeezed vacuum : OPA

+ 0.920.08

coherent beam

wave plate

R=0.92

33cm

lens f=3cm

3.3cm

Image of the wave plate plane with

waist=300m

Displacement Measurements and Gravity Waves

Hans BachorAustralian National University

Δxclassical=λ, Δxshotnoise=λN

, ΔxHeisenberg=λN

Quantum Clock Synchronization

Entangled Photons Can Synchronize Past the Turbulent Atmosphere!Entangled Photons Can Synchronize Past the Turbulent Atmosphere!

SethLloydMIT

A B

Quantum Computing

Quantum Controlled-NOT Gate using and Entangled-Light Source, Beam Splitters, and Detectors.

Entangled Photons are a Resource for Scalable Quantum Computation!Entangled Photons are a Resource for Scalable Quantum Computation!

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

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

GerardMilburnUniversityOfQueensland

Computing

CommunicationsClock SynchronizationImaging

SensorsMetrology

The Yellow-Brick Roadmap