Fisica Generale 3

Bassano Vacchini

bassano.vacchini@mi.infn.it

Overview

Ø  Interference experiments

Ø  Neutron optics I: interference

Ø  Neutron optics I: amplitude versus probability

Interference and statistics

If your experiment needs statistics, you ought to have done a better experiment.

E. Rutherford

Diffraction

b θ

E=A cos(ωt-kx) ★ sin(β)/β I=|E|2 β=π sin(θ) (b/λ) λ = (2π)/k k = (2π)/λ First minimum of diffraction θ ≈ λ/b

Relevant path difference

λ ≈ b θ

Interference

b

b

d

E=A cos(ωt-kx) ★ sin(β)/β ★ cos(γ) I=|E|2 γ= π sin(θ) (d/λ) λ = (2π)/k k = (2π)/λ First minimum of interference θ ≈ ½ (λ/d)

Pattern

Young’s double slit

First double slit experiment with sunlight in 1801

Important but not final evidence against Newton’s corpuscular theory of light

Fizeau-Foucault experiment

Final disproof of Netwon’s particle theory in 1850 Light travels slower in water

Coherence

•  Radiation in which there are definite phase relationships between different points in a cross section of the beam

•  Relevant for collimation and interference properties •  Laser beams are spatially coherent •  Laser beams are temporally coherent

Statistics matters – brilliant source

Real time image without need to accumulate statistics

Statistics matters – single photon source

First counts just background noise

Statistics matters – single photon source

Interference pattern slowly appears Basic role of single events

Matter waves

“Die Quantentheorie ist so ein wunderbares Beispiel dafür, daß man einen Sachverhalt in völliger Klarheit verstanden haben kann und gleichzeitig doch weiß, daß man nur in Bildern und Gleichnissen von ihm reden kann.”

W. Heisenberg

Light versus matter, matter versus light

•  Optics –  optical elements made up of matter (slits, gratings, mirrors,

dispersive materials)

•  Matter optics –  optical elements realized through external fields, due to

interaction with both matter and electromagnetic waves

•  Kapitza-Dirac effect –  diffraction of matter by light gratings, stationary

electromagnetic wave obtaining through two counterpropagating laser beams

General ingredients

•  Brilliant source •  Collimation apparatus •  Diffraction apparatus •  Detection mechanism

Preparation apparatus

Registration apparatus

Interference experiments

System Mass (g)

Wavelength λdB (pm)

Velocity (m/s)

Early realizations

Light 1801

Electrons 10-27 4-6 108 1970-1990

Neutrons 10-24 200-2000 200-2000 1970-1990

Atoms 10-23 10-20 800-1000 1990-2000

Fullerenes 10-21 2-5 100-250 1990-2000

Phthalocyanine 10-24 5 150 2000-2010

Condensate 10-16 - - 1990-2000

Two-slits as basic experiment

Far-field electron diffraction as the “most beautiful experiment in physics”

poll by Physics World in 2002

masterpiece, as it were - rather than a process by which a hithertounknown truth becomes disclosed for the first time.

One Slashdot contributor touched on this after describing anexperiment in which he measured the acceleration of gravity using apin, a switch, a timer and a shuttlecock. "The most beautiful thingwasn't learning that gravity is 9.8 ms-2," he wrote, "but in showingus that from a fairly simple set-up we could quantitatively measuresomething important in physics."

The critical point

Beauty, Plato wrote, is not easy to define, but something that "slipsthrough and evades us". For this reason, many logic-orientedphilosophical approaches tend to divorce and even oppose truth andbeauty. "The question of truth", wrote logician Gottlob Frege in oneof his most influential works, "would cause us to abandon aestheticdelight for an attitude of scientific investigation."

I'm far more sympathetic to those philosophical traditions that viewtruth as involving, most fundamentally, the disclosure of somethingrather than accurate representation. These traditions allow us to seean intimate connection between scientific inquiry and beauty. At anygiven time, the scientific frontier is ambiguous and confusing, andrequires the skilful planning and performing of experimental actionsto sort out and bring clarity.

It is natural to call beautiful those that captivate and transform ourthinking, that make the result stand out clearly and economicallyand not abstractly as a lesson but in a materially embodied way, andthat reveal that we are actively engaging with something beyond us.To speak about beauty in science as belonging solely to the provinceof theory or equations is to misunderstand both beauty and science.

The quantum-mechanical world is likely to remain counterintuitive tohuman beings, no matter how well-versed or confident we are in thetheory. The double-slit electron-interference experiment brings itsreality before our eyes in a dramatic, economical and materiallyembodied way. It is therefore likely to remain in the pantheon ofbeautiful experiments for a long time to come.

The list below shows the top 10 most frequently mentionedexperiments by readers of Physics World.

Top 10 beautiful experiments

1 Young's double-slit experiment applied to the interference ofsingle electrons

2 Galileo's experiment on falling bodies (1600s)

3 Millikan's oil-drop experiment (1910s)

4 Newton's decomposition of sunlight with a prism(1665-1666)

5 Young's light-interference experiment (1801)

6 Cavendish's torsion-bar experiment (1798)

7 Eratosthenes' measurement of the Earth's circumference(3rd century BC)

8 Galileo's experiments with rolling balls down inclined planes(1600s)

9 Rutherford's discovery of the nucleus (1911)

10 Foucault's pendulum (1851)

Others experiments that were cited included:

Archimedes' experiment on hydrostatics

Roemer's observations of the speed of light

PhysicsWeb - The most beautiful experiment http://memo.cgu.edu.tw/yu-yen/PhysicsWeb - The most beauti...

4 of 5 10/22/13 12:35 PM

Electrons

Tonomura, Japan, 1989

Electrons

Coherent splitting via biprism Experiment duration approximately 30 minutes

Electrons made in Italy

Merli, Missiroli, Pozzi Italy, ‘70

http://www.bo.imm.cnr.it/users/lulli/downintel/electroninterfea.html�

Most beautiful experiment in physics

Controlled double-slit electron diffraction

Roger Bach1,3, Damian Pope2, Sy-Hwang Liou1

and Herman Batelaan1,3

1 Department of Physics and Astronomy, University of Nebraska-Lincoln,Theodore P Jorgensen Hall, Lincoln, NE 68588, USA2 Perimeter Institute for Theoretical Physics, 31 Caroline ST N, Waterloo,Ontario N2L2Y5, CanadaE-mail: roger.bach@huskers.unl.edu and hbatelaan2@unl.edu

New Journal of Physics 15 (2013) 033018 (7pp)Received 31 December 2012Published 13 March 2013Online at http://www.njp.org/doi:10.1088/1367-2630/15/3/033018

Abstract. Double-slit diffraction is a corner stone of quantum mechanics. Itillustrates key features of quantum mechanics: interference and the particle-waveduality of matter. In 1965, Richard Feynman presented a thought experimentto show these features. Here we demonstrate the full realization of his famousthought experiment. By placing a movable mask in front of a double-slit tocontrol the transmission through the individual slits, probability distributions forsingle- and double-slit arrangements were observed. Also, by recording singleelectron detection events diffracting through a double-slit, a diffraction patternwas built up from individual events.

S Online supplementary data available from stacks.iop.org/NJP/15/033018/mmedia

3 Authors to whom any correspondence should be addressed.

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal

citation and DOI.

New Journal of Physics 15 (2013) 0330181367-2630/13/033018+07$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

Most beautiful experiment in physics

Neutrons

Experiment duration approximately 300 hours

Single slit: glass plates coated with strong absorbers

Double slit: thin borum line

Neutrons

Rauch, Austria, ‘70

Atoms

Phase-shift induced by interaction with laser light

Fullerenes

Buckyballs: 60 or 70 Carbonium atoms in regular pattern

Fullerenes

Zeilinger, Austria, ‘90

Fullerenes

Phthalocyanines

Arndt, Austria, ‘10

Neutron optics I: interference

Neutron optics I: interference

Neutron optics I: interference

Neutron optics I: interference

Neutron optics I: interference

Neutron optics I: interference

Neutron optics II: amplitude versus probability

Neutron optics II: amplitude versus probability

Useful related links

•  http://www.quantumoptics.net/ •  http://www.quantumnano.at/ •  http://www.hitachi.com/rd/portal/research/em/

doubleslit.html •  http://vcq.quantum.at/research/research-groups/

zeilinger-group.html •  http://www.colorado.edu/physics/2000/bec/

Take home message

“One of the principal objects of theore t i ca l re s earch in any department of knowledge is to find the point of view from which the subject appears in the greatest simplicity.”

J. W. Gibbs