Fisica Generale 3. Bassano Vacchini.
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1 Fisica Generale 3 Bassano Vacchini bassano.vacchini@mi.infn.it
2 Overview Ø Interference experiments Ø Diffraction and interference with light Ø Interference with light in the limit of low intensity Ø The relevance of statistics Ø Matter optics with electrons, neutrons, atoms, fullerenes, Ø Neutron optics I: interference Ø Neutron optics I: amplitude versus probability
3 Interference and statistics If your experiment needs statistics, you ought to have done a better experiment. E. Rutherford
4 Diffraction E=A cos(ωt-kx) sin(β)/β d θ L Δz I= E 2 β=π sin(θ) (d/λ) λ = (2π)/k k = (2π)/λ Relevant path difference First minimum of diffraction λ d θ θ λ/d Δz/L λ/d
5 Interference a d d E=A cos(ωt-kx) sin(β)/β cos(γ) I= E 2 β=π sin(θ) (d/λ) γ= π sin(θ) (a/λ) λ = (2π)/k k = (2π)/λ First maximum of interference θ λ/a
6 Pattern -λ/d λ/a λ/d
7 Pattern
8 Young s double slit First double slit experiment with sunlight in 1801 Important but not final evidence against Newton s corpuscular theory of light
9 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
10 Statistics matters single photon source
11 Statistics matters brilliant source Real time image without need to accumulate statistics
12 Statistics matters single photon source First counts just background noise
13 Statistics matters single photon source Interference pattern slowly appears Basic role of single events
14 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
15 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
16 General ingredients Brilliant source Collimation apparatus Diffraction apparatus Detection mechanism Preparation apparatus Registration apparatus
17 Interference experiments System Mass (g) Wavelength λdb (pm) Velocity (m/s) Light 1801 Early realizations Electrons Neutrons Atoms Fullerenes Phthalocyanine Condensate
18 Two-slits as basic experiment Far-field electron diffraction as the most beautiful experiment in physics poll by Physics World in 2002 Top 10 beautiful experiments 1 Young's double-slit experiment applied to the interference of single 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 ( ) 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)
19 Electrons Tonomura, Japan, 1989
20 Electrons Coherent splitting via biprism Experiment duration approximately 30 minutes
21 Electrons made in Italy Merli, Missiroli, Pozzi Italy, 70
22 Most beautiful experiment in physics Controlled double-slit electron diffraction Roger Bach 1,3, Damian Pope 2, Sy-Hwang Liou 1 and Herman Batelaan 1,3 1 Department of Physics and Astronomy, University of Nebraska-Lincoln, Theodore P Jorgensen Hall, Lincoln, NE 68588, USA 2 Perimeter Institute for Theoretical Physics, 31 Caroline ST N, Waterloo, Ontario N2L2Y5, Canada roger.bach@huskers.unl.edu and hbatelaan2@unl.edu New Journal of Physics 15 (2013) (7pp) Received 31 December 2012 Published 13 March 2013 Online at doi: / /15/3/ Abstract. Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. In 1965, Richard Feynman presented a thought experiment to show these features. Here we demonstrate the full realization of his famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individual slits, probability distributions for single- and double-slit arrangements were observed. Also, by recording single electron detection events diffracting through a double-slit, a diffraction pattern was built up from individual events.
23 Most beautiful experiment in physics
24 Neutrons Single slit: glass plates coated with strong absorbers Double slit: thin borum line Experiment duration approximately 300 hours
25 Neutrons Rauch, Austria, 70
26 Atoms Phase-shift induced by interaction with laser light
27 Fullerenes Buckyballs: 60 or 70 Carbonium atoms in regular pattern
28 Fullerenes Zeilinger, Austria, 90
29 Fullerenes
30 Phthalocyanines Arndt, Austria, 10
31 Neutron optics I: interference
32 Neutron optics I: interference
33 Neutron optics I: interference
34 Neutron optics I: interference
35 Neutron optics I: interference
36 Neutron optics I: interference
37 Neutron optics II: amplitude versus probability
38 Neutron optics II: amplitude versus probability
39 Useful related links eslit.html
40 Take home message One of the principal objects of theoretical research in any department of knowledge is to find the point of view from which the subject appears in the greatest simplicity. J. W. Gibbs
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1 (a) (i) Explain what is meant by a progressive wave.... [2] (ii) State two differences between a progressive and a stationary wave. 1... 2... [2] (b) Fig. 4.1 shows, at time t = 0, the shape of a section
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