FAFA Föreläsning 4, läsvecka 2 6 november 2017

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1 FAFA Föreläsning 4, läsvecka 2 6 november 2017

2 Salbyten Grupp F1.06: tisdagar > K262 Grupp F1.11: salbyten under lv Uppdatera Time Edit Learning log uppgift

3 Bragg reflektion: kristaller som multispalt

4 Dubbelspalt-experiment med enstaka elektroner Tonomura

5 Elektronmikroskop: att titta med elektronvågor Scanning electron microscope (SEM) Elektronvåglängden bestämmer hur små saker man kan se. Liten våglängd tillåter hög upplösning ( några nm)

6 SEM bilder Ögat hos en fluga Nanotråd med elektriska kontakter

7 Counts in 1 s in a futu C60 molekyl ferometer 200 ( Bucky ball ) b be a parti 200 up to 1 m much larg 150 case, the through should th 100 controlle internal 50 environm the inter 0 gases. The Montreal Biosphère by Buckminster An im Fuller, Photo: Ryan Mallard. Position (µm) example, which we Figure 2 Interference pattern produced by C60 molecules. a, Experimental recording whole spe (open circles) and fit using Kirchhoff diffraction theory (continuous line). The expected study the zeroth and first-order maxima can be clearly seen. Details of the theory are discussed in 1 nm and wav the text. b, The molecular beam profile without the grating in the path of the molecules. NATURE VOL OCTOBER Macmillan Magaz

8 energies. Our good quantitative agreement between experiment and blackb absorbed light then ionized the C 60 fullerenes via heating and shown in Fig. 2a, but does not fit the wings of th theory indicates that the latter do not influence the observed sured subsequent thermal emission of electrons Interferensexperiment 12. The detection region coherence. All Agreement these observations with support the experimental the view that each data, C med C60 molekyler 60 includin a typic 200 ferometer molecule interferes with itself only. time b be a parti corres 200 l 1 up to 1influe m 100 nm diffraction Scanning photoionization stage Figure 1,2001 Diagram a of the experimental set-up (not to scale). molec Hot, n grating leave the oven through a nozzle of 0:33 mm 1:3 much mm 0: larg m 1,000 be neg 150 (width height depth), pass through two collimating slits of As 0: s Oven case, (width800 height) separated by 1.04 m, traverse a SiN x the grating photo (perio the second slit, and are detected via thermal ionization through by ainduc laser 600 intern grating. The ions are then accelerated and directed towards a conv 100 shouldinterfe th Ion ejected 400 electrons are subsequently counted by a Channeltron elec A va 10 µ m 10 µ m detection laser focus can be reproducibly scanned transversely controlle to the beam in a fu unit 200 ferom Collimation slits b be a p 200 internal 50 up to Laser environm much 150 case, the inter throug Figure 1 Diagram of the experimental set-up (not to scale). Hot, neutral C 60 molecules 1999 Macmillan Magazines Ltd NATURE VOL OCTOBER should 1 leave the oven through a nozzle of 0:33 0 mm 1:3 mm 0:25 mm gases. contro (width height depth), pass through 100 two collimating slits 50 of 0:01 mm 5 mm 0 50 intern (width height) separated by 1.04 m, traverse a SiN x An grating (period 100 nm) 0.1 m after enviro im Position (µm) the second slit, and are detected via thermal ionization by a laser 1.25 m behind the the in 0 example, gases. grating. The ions are then accelerated and directed towards a conversion electrode. The An ejected Figure electrons 2 Interference are subsequently counted pattern by a Channeltron produced electronby multiplier. C 60 The molecules. a, Experimental Position recording (µm) whichexamp we laser focus can be reproducibly scanned transversely to the beam with 1- m resolution. Figure 2 Interference pattern produced by C 60 molecules. a, Experimental recording which (open circles) and fit using Kirchhoff diffraction theory (open (continuous circles) and fit using Kirchhoff line). diffraction The expected whole theory (continuous line). The expected whole spe zeroth and first-order maxima can be clearly seen. Details of the theory are discussed in study zeroth and first-order maxima can be clearly seen. Details of the theory are discussed in study the text. b, The molecular beam profile without the grating in the path of the molecules. and thew Counts in 1 s the text. b, The molecular beam profile without the grating in the path of the molecules. Counts in 1 s Counts in 50 s NATURE VOL OCTOBER in a futu and wav 1999 Macmillan Ma NATURE VOL OCTOBER Macmillan Magaz

9 ... Wave particle duality of C 60 molecules Markus Arndt, Olaf Nairz, Julian Vos-Andreae, Claudia Keller, Gerbrand van der Zouw & Anton Zeilinger Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria Quantum superposition lies at the heart of quantum mechanics and gives rise to many of its paradoxes. Superposition of de Broglie matter waves 1 has been observed for massive particles such as electrons 2, atoms and dimers 3, small van der Waals clusters 4, and neutrons 5. But matter wave interferometry with larger objects has remained experimentally challenging, despite the development of powerful atom interferometric techniques for experiments in fundamental quantum mechanics, metrology and lithography 6. Here we report the observation of de Broglie wave interference of C 60 molecules by diffraction at a material absorption grating. This molecule is the most massive and complex object in which wave behaviour has been observed. Of particular interest is the fact that C 60 is almost a classical body, because of its many excited internal degrees of freedom and their possible couplings to the environment. Such couplings are essential for the appearance of decoherence 7,8, suggesting that interference experiments with large molecules should facilitate detailed studies of this process. NATURE VOL OCTOBER

10 I ett experiment skickas fotoner (elektroner), en foton (elektron) i taget, mot en dubbelspalt. En detektor på andra sidan visar att fördelningen motsvarar ett interferensmönster. Experimentet upprepas, men nu blockeras spalt 1 under första halvan av experimentet, och spalt 2 under andra halvan. Fördelningen som detekteras i det andra experimentet blir A) densamma som i det första experimentet: många interferens-toppar B) en annan: två intensitetstoppar C) varken eller.

11 I ett experiment skickas fotoner (elektroner), en foton (elektron) i taget, mot en dubbelspalt. En detektor på andra sidan visar att fördelningen motsvarar ett interferensmönster. Experimentet upprepas, men nu blockeras spalt 1 under första halvan av experimentet, och spalt 2 under andra halvan. Fördelningen som detekteras i det andra experimentet blir A) densamma som i det första experimentet: många interferens-toppar B) en annan: två intensitetstoppar C) varken eller. Eftersom var och en av fotonerna (elektronerna) ser bara en spalt, kan ingen interferens uppträda. Man ser i stället summan av enkelspalts-intensiteter. Interferens observeras när varje foton (elektron) kan välja mellan två spalter.

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14 En partikel har en en-dimensionell (1D) sannolikhetstäthet ρ(x,t). Vilken enhet har ρ? 1) [ ρ ] = 1 2) [ ρ ] = m 3) [ ρ ] = 1/m 4) [ ρ ] = 1/s 5) [ ρ ] = 1/m s 6) Något annat

15 En partikel har en en-dimensionell (1D) sannolikhetstäthet ρ(x,t). Vilken enhet har ρ? 1) [ ρ ] = 1 2) [ ρ ] = m 3) [ ρ ] = 1/m 4) [ ρ ] = 1/s 5) [ ρ ] = 1/m s 6) Något annat Integralen P =!! ρ!,!!"!! behöver ha enhet 1 (sannolikhet). dx leder till multiplikation med m ( [dx] = m ).

16 En partikel har en normerad, en-dimensionell sannolikhetsfördelning som är symmetrisk kring noll. Sannolikheten att hitta partikeln mellan x = 0 och x = 5 nm beräknas vara 0,3. Vad är sannolikheten att hitta partikeln i intervallet (5 nm < x < )? 1) 0 2) 0,7 3) 0,3 4) 0,2 5) Man behöver mer information för att kunna svara.

17 En partikel har en normerad, en-dimensionell sannolikhetsfördelning som är symmetrisk kring noll. Sannolikheten att hitta partikeln mellan x = 0 och x = 5 nm beräknas vara 0,3. Vad är sannolikheten att hitta partikeln i intervallet (5 nm < x < )? 1) 0 2) 0,7 3) 0,3 4) 0,2 Den totala sannolikheten att hitta partikeln mellan - och + måste vara lika med 1. På grund av symmetrin måste sannolikheten att hitta partikeln i intervallet 0 < x < + vara 0,5. Därmed ligger sannolikheten 0,5-0,3 = 0,2 i intervallet 5 nm < x < + 5) Man behöver mer information för att kunna svara.

18 e ikx 2 = A) e 2ikx B) e -2ikx C) 0 D) -1 E) 1

19 e ikx 2 = A) e 2ikx B) e -2ikx C) 0 D) -1 E) 1 z 2 = z z* e ikx 2 = e ikx e -ikx = 1