Interference of C 60 molecules Why is it not macroscopic and how is it destroyed?

Transcription

1 Interference of C 60 molecules Why is it not macroscopic and how is it destroyed? Jan Schick Master seminar - Macroscopic quantum eects WS 2012/2013

2 1 Introduction A simple approach to the topic macroscopic quantum eects seams to be the idea to take a macroscopic object and to perform interferometry with it. A macroscopic object should behave classically and therefore we wouldn't expect to nd an interference pattern at the end. One of the most massive and complex objects with which we can perform such experiments is the C 60 molecule. The C 60 molecule is often called Buckyball, named after the architect Buckminster Fuller who is famous for his geodesic domes. Also footballs have the same shape. Abbildung 1: dimension and wavelength of the C 60 and C 70 molecule Since we want to study interference phenomena of a matterwave (a beam of molecules with an associated de Broglie wavelength), it is quite useful to review some basic principles of diraction theory. In order to determine the interference pattern behind a diracting object we would have to evaluate Kirchho's diraction formula. In practise a simplication is often applicable. Either the near eld (Fresnel) diraction or the far eld (Fraunhofer) diraction. The simplifying assumption in these cases is that the diracting object is small, and for 1

3 Abbildung 2: Fraunhofer diraction Fraunhofer diraction we assume additionally that the diraction pattern is viewed at a long distance from the diracting object. 2 Diraction of C 60 [1] Abbildung 3: setup C 60 fullerenes are sublimated in an oven at temperatures between 900K and 1000K (Abbildung 3). The molecular beam passes through two collimation slits, each about 10µm wide, separated by a distance of 1.04m. Then the beam passes a free standing SiNx grating (50nm wide slits, 100nm period, total width of 1µm). At a further distance of 1.25m 2

4 behind the diraction grating the interference pattern is scanned using a visible argonion laser. The laser is directed vertically so that we get dierent intensities depending on the position of the laser (e.g. at a minimum or a maximum). By focusing the laser with mirrors the resolution is about one micrometer. The C 60 fullerenes are being ionized by the laser, then accelerated towards a conversion electrode. The ejected electrons are counted by an electron multiplier. The whole set-up is in a vacuum chamber in order to keep the dark count rate at a minimum. An advantage of the ionization detection mechanism is that residual gases are not detected due to their higher ionization energy, which is also very favorable for low dark count rates. Abbildung 4: experimental data and t The t uses Fraunhofer diraction theory and assumes a gaussian variation of the slit width, which is very likely, because it's very challenging to fabricate 50nm wide slits accurately. The slit witdth given by the t is 38nm which is perceptibly smaller than the 55nm given by the manufactorer. Abbildung 5: close up of the silicon nitride grating The apparently narrower slit width obtained by the t can be interpreted as the inuence 3

5 of the van der Waals force acting on the molecules when they pass through one of the slits of the grating. This is in consistence with the results obtained in the diraction of noble gases and He clusters in other experiments. The eect is expected to be even more pronounced for C 60 due to their larger polarizability. The good quantitative agreement between experiment and theory supports the view that each C 60 molecule interferes with itself only. 3 Diraction of C 70 [2] Was C 60 not massive enough to destroy the interference? The next step would then be to move to a more massive molecule, C 70 for example. But moving to more massice particles means that we will have to deal with shorter de Broglie wavelengths. In the far eld the grating constant d scales linearly with the distance between grating and detection unit L, the wavelength λ and the distance of the maxima in our interference pattern x. Since L is limited by the size of our lab and x is limited by our resolution going to more massive particles (smaller wavelengths) means that we have to make our grating more and more accurate.the fabrication method of diraction gratings gives a limit to which this can be done. In the near eld, as we will see, we can achieve a scaling of the grating constant with the square root of both the distance L and the wavelenght λ. Therefore it is favourable to operate in the near eld when using C 70 molecules. 3.1 Talbot eect The Talbot eect is a near-eld diraction eect rst observed in 1836 by Henry Fox Talbot. When a periodic structure is illuminated by a coherent beam the (periodic) structure is repeated at discrete multiples of the Talbot length. Abbildung 6: sketch, illustrating the Talbot eect 4

6 3.2 Talbot-Lau interferometer The Talbot-Lau interferometer uses three (gold) gratings, separated by the Talbot length. The rst grating makes it possible to accept an incoherent source. The third grating scans across the (periodic) interference pattern. The laser beam ionizes the incoming molecules regardless of their transversal position. The ion detector is spatially extended. This leads to higher counting rates. Nevertheless we get dierent counting rates depending on the position of the third grating. Abbildung 7: setup, Talbot-Lau interferometer 3.3 Measurements and results Abbildung 8: periodic pattern in internsity 5

7 The visibility is dened as shown in gure 8. It's an important parameter because it characterizes the coherence of the beam throughout the apparatus. For a perfect alignment and a perfectly coherent beam the minima should go down to zero and the visibility is 100 percent. Whereas for a decoherent beam there wouldn't be minima and maxima at all and the visibility would be zero. But is the perodic signal necessarily a sign for quantum interference? No, it isn't. Because it could also be classical moiré fringes. Moiré fringes are classical shadow pattern resulting from straight rays passing through the gratings or being block by one of them. Abbildung 9: moiré fringe How can we distinguish the two cases? Well, moiré fringes do not depend on velocity. But the Talbot length scales with the de Broglie wavelenght and therefore with velocity (L T = d 2 /λ = d 2 mv/h). Thus the visibility varies for dierent velocities. Abbildung 10: visibility as a function of velocity 6

8 Figure 10 roots out a classical description (moiré fringes). Only the quantum mechanical description including van der Waals interaction is appropriate to describe the experimental data. So far we have seen that interferometry with C 70 gives us a periodic pattern. Further we determined that it results from quantum interference. Now we can ask ourselves. Does it make a dierence if we treat the C 70 molecule as a black body? Does it make a dierence if we heat up the molecules before they enter the interferometer? 4 Decoherence by thermal black body radiaton [3] Abbildung 11: setup The setup for this experiment is basically the same as we have seen already in gure 7. The only dierence is that the molecules encounter a heating stage before they enter the interferometer. Note that this will not accelerate the particles e.g. the de Broglie wavelength remains unchanged, but energy is pumped into internal degrees of freedom of the molecules. On the way through the apparatus the C 70 molecules will emit thermal photons eventually. The wavelength of this thermal black body radiation depends on the temperature (Wien's Law). If the wavelength is smaller than the grating constant d, we shouldn't see an interference pattern any more. This is indicated by gure 12. 7

9 Abbildung 12: sketch, to illustrate the eect of thermal black body radiation Abbildung 13: interference pattern for dierent heating powers As shown in gure 13 the visibility decreases with increasing laser heating power. At a laser power of 10W the visibility is zero. Thus decohernce occurs. 8

10 5 Summary C 60 diraction far eld diraction have to include van der Waals interaction linear scaling dependence gives a limit to the wavelenght that can be resolved C 70 diraction in the near eld better scaling by taking advantage of the Talbot eect Talbot-Lau interferometer periodic interference pattern (moiré nges?) velocity dependent measurement of the visibility Decoherence by thermal black body radiation emission of thermal photons destroys interference pattern visibility as a function of heating power Literatur [1] Markus Arndt, Olaf Nairz, Julian Vos-Andreae, Claudia Keller, Gerbrand van der Zouw, and Anton Zeilinger. wave-particle duality of C60 molecules. letters to nature, 401, [2] Bjoern Brezger, Lucia Hackermueller, Stefan Uttenthaler, Julia Petschinka, Markus Arndt, and Anton Zeilinger. Matter-wave interferometer for large molecules. Physical Review Letters, 88, [3] Lucia Hackermueller, Klaus Hornberger, Bjoern Brezger, Anton Zeilinger, and Markus Arndt. Decoherence of matter waves by thermal emission of radiation. letters to nature, 427,