Quantum Interference and Duality
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1 Quantum Interference and Duality Kiyohide NOMURA Department of Physics December 21, / 49
2 Quantum Physics(Mechanics) Basic notion of Quantum Physics: Wave-Particle Duality Light (electromagnetic wave) Light as wave Interference, Diffraction, Polarization Light as a particle: Photon Photoelectric effect, Compton effect 2 / 49
3 Quantum Physics(Mechanics) Basic notion of Quantum Physics: Wave-Particle Duality Light (electromagnetic wave) Light as wave Interference, Diffraction, Polarization Light as a particle: Photon Photoelectric effect, Compton effect Electron Electron as a particle Mass-to-charge ratio Elementary electric charge (Millikan s oil drop experiment) Electron as wave Davisson-Germer experiment ( ) 2 / 49
4 Light as wave (Interference) Interference: a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude MOVIE: Interference of waves from two point sources. 3 / 49
5 Light as wave (Interference) Interference: a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude MOVIE: Interference of waves from two point sources. Figure: Left: constructive interference; Right: destructive interference 3 / 49
6 Light as wave (Interference of thin film) Figure: Interference pattern on a soap bubble 4 / 49
7 Light as wave (Newton s ring) Another (and quantitative) example of interference: Newton s ring (1717) 5 / 49
8 Light as wave (Newton s ring) Another (and quantitative) example of interference: Newton s ring (1717) an interference pattern created by placing a very slightly convex curved glass (lens) on an optical flat glass. 5 / 49
9 Light as wave (Newton s ring) When viewed with monochromatic light, Newton s rings appear as a series of concentric, alternating bright and dark rings centered at the point of contact between the two surfaces. 6 / 49
10 Light as wave (Newton s ring) 7 / 49
11 Light as wave (Newton s ring) R: the radius of curvature of the glass lens d: the vertical distance between the glass lens and the flat glass R 2 = (R d) 2 + r 2 = R 2 2Rd + d 2 + r 2 (1) ( r 2 = 2Rd 1 d ) 2Rd ( d R) (2) 2R 8 / 49
12 Light as wave (Newton s ring) Reflection at the glass-air boundary causes no phase shift Reflection at the air-glass boundary causes a half-cycle phase (π) shift Thus, when the distance 2d is mλ(λ: the wavelength), the two waves interfere destructively. The radius r of the Nth dark ring is given by r = mλr, (m = 0, 1, 2, ) (3) 9 / 49
13 Light as wave: Double Slit 10 / 49
14 Light as wave: Double Slit Figure: Up Single slit Down: Double Slit distance between slits 0.7mm 11 / 49
15 Light as wave: Diffraction Diffraction: various phenomena which occur when a wave encounters an obstacle or a slit Figure: diffraction pattern from a slit of width four wavelengths with an incident plane wave 12 / 49
16 Light as wave: Diffraction MOVIE: diffraction pattern from a slit of width equal to five times the wa 13 / 49
17 Light as wave: Diffraction Figure: 14 / 49
18 Light as wave: Diffraction 15 / 49
19 Light as wave: Bragg s law (X ray diffraction) 16 / 49
20 Light as wave: Bragg s law (X ray diffraction) 17 / 49
21 Light as wave: Bragg s law (X ray diffraction) 2d sin θ = nλ (n = 1, 2, ) (4) λ: the wavelength of incident wave. d: separation between planes of lattice points θ: the scattering angle 18 / 49
22 Light as wave: Bragg s law (X ray diffraction) Figure: Laue pattern 19 / 49
23 Light as wave: Bragg s law (X ray diffraction) 20 / 49
24 Light as a particle: Photoelectric effect Figure: the production of electrons or other free carriers when light is shone onto a material 21 / 49
25 Light as a particle: Photoelectric effect E kin = hν W (5) h: Planck s constant ( m 2 kg/s) ν: the frequency of the incident photon 22 / 49
26 Light as a particle: Photoelectric effect The work function W (which gives the minimum energy required to remove a delocalised electron from the surface of the metal) is different between materials. 23 / 49
27 Light as a particle: Photoelectric effect Internal photoemission Solar cell CCD photosynthesis in plants 24 / 49
28 Light as a particle: Photoelectric effect Theory of the solar cell 25 / 49
29 Light as a particle: Photoelectric effect CCD 26 / 49
30 Light as a particle: Compton scattering scattering between a photon (X-ray or gamma ray) and a charged particle (electron) ` λ λ = h (1 cos θ) (6) m e c λ: the initial wavelength, λ : the wavelength after scattering,λ > λ θ: the scattering angle h: the Planck constant ( (29) m 2 kg/s) m e : the electron rest mass ( (40) kg) c: the speed of light ( m/s) 27 / 49
31 Light as a particle: Compton effect Energy quanta relation(quantum) E = hν (7) The relation of the wavelength λ,frequency ν, and light speed c c = λν (8) The relation between the energy E and the momentum p of the electromagnetic wave E = c p (9) We obtain the relation between the momentum and the wavelength p = h λ (10) 28 / 49
32 Electron as a particle (Mass-to-charge ratio) F = q(e + v B) (11) (Lorentz force law) F = ma = m dv dt (Newton s second law of motion) Combining the two previous equations yields: (12) ( ) m a = E + v B (13) q 29 / 49
33 Electron as a particle (Mass-to-charge ratio) Figure: The cathode ray tube by Thomson Cathode rays were emitted from the cathod C, passed through slits A (the anode) and B (grounded), then through the electric field generated between plates D and E, finally impacting the surface at the far end. 30 / 49
34 Electron as a particle (Mass-to-charge ratio) Figure: Crookes tube 31 / 49
35 Electron as a particle (Mass-to-charge ratio) Figure: Crookes tube with the electric field The cathode ray was deflected by the electric field 32 / 49
36 Electron as a particle (Mass-to-charge ratio) Figure: Crookes tube with the electric field 33 / 49
37 Electron as a particle (Mass-to-charge ratio) Figure: Crookes tube under the magnetic field 34 / 49
38 Electron as a particle (Charge) Millikan s oil drop experiment(1909) cover several thousand volts oil spray d microscope uniform electric eld Figure: Millikan s oil drop experiment 35 / 49
39 Electron as a particle (Charge) Figure: Millikan s oil drop experiment 36 / 49
40 Electron as a particle (Charge) Figure: Millikan s oil drop experiment electric charge (35) C 36 / 49
41 Electron as a wave Figure: electron diffraction by Ta 2 O 5 37 / 49
42 Electron as a wave Figure: left: diffraction by X-ray right: diffraction by electron (Al film) The similarity of the two diffraction patterns means that the electron has a wave character as X-ray. 38 / 49
43 Electron as a wave (de Broglie wave) L. de Broglie proposed (1924) that the electron (in general matter) with momentum p behaves as a wave with wavelength λ = h p (14) from the analogy with the photon. 39 / 49
44 Electron as a wave Double slit experimenta. Tonomura, 1982 Electrons pass through a device called the electron biprism, which consists of two parallel plates and a fine filament at the center The filament is thinner than 1 micron. 40 / 49
45 Electron as a wave 1. At the beginning of the experiment, we can see that bright spots (electrons) begin to appear here and there at random positions (Fig. 2 (a) and (b)) 41 / 49
46 Electron as a wave 1. At the beginning of the experiment, we can see that bright spots (electrons) begin to appear here and there at random positions (Fig. 2 (a) and (b)) 2. Electrons are detected one by one as particles 41 / 49
47 Electron as a wave 1. At the beginning of the experiment, we can see that bright spots (electrons) begin to appear here and there at random positions (Fig. 2 (a) and (b)) 2. Electrons are detected one by one as particles 3. Clear interference fringes can be seen in the last scene of the experiment after 20 minutes (Fig. 2(d)). 41 / 49
48 Electron as a wave MOVIE: the electron double slit experiment 42 / 49
49 Electron as a wave Supplement for double slit experiment 1. Electron source: Field-emission gun more coherent and with up to three orders of magnitude greater current density or brightness than can be achieved with conventional thermionic emitters 2. These electrons were accelerated to 50,000 V (50keV), the speed is about 40 % of the speed of the light, i. e., it is 120,000 km/second. 3. There is no more than one electron in the microscope at one time, since only 10 electrons are emitted per second. 4. No interaction between electrons. 43 / 49
50 Electron as a wave Supplement for double slit experiment 1. Electron source: Field-emission gun more coherent and with up to three orders of magnitude greater current density or brightness than can be achieved with conventional thermionic emitters 2. These electrons were accelerated to 50,000 V (50keV), the speed is about 40 % of the speed of the light, i. e., it is 120,000 km/second. 3. There is no more than one electron in the microscope at one time, since only 10 electrons are emitted per second. 4. No interaction between electrons. Single electron is enough to create a quantum interference! 43 / 49
51 Neutron as a wave Figure: A double-slit interference pattern made with neutrons. 44 / 49
52 Neutron as a wave Figure: neutron interferrometer 45 / 49
53 Molecule as a wave: Phthalocyanine 46 / 49
54 Molecule as a wave: Phthalocyanine Figure: 47 / 49
55 Molecule as a wave: Phthalocyanine Figure: 48 / 49
56 Molecule as a wave: Phthalocyanine 49 / 49
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