Double slit experiment

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Double slit experiment

When double-slit experiment is allowed coherent waves, such as light - or matter waves , by two narrow, parallel column occur. An interference pattern appears on an observation screen at a distance from the diaphragm which is much greater than the distance a between the two slits . This pattern is created by the diffraction of the wave propagation at the double slit. With monochromatic light (e.g. from a laser ) this pattern on the screen consists of light stripes (maxima) and dark stripes (minima). The interference pattern only arises when the wavelength λ is smaller than the distance a between the two columns.

The experiment is one of the key experiments in physics. It was first carried out in 1802 by Thomas Young with light and led to the rejection of the then still prevailing corpuscle theory of light in favor of the wave theory . It was only Albert Einstein's work on the photoelectric effect in 1905 that revealed the particle character of light. In quantum physics , the double slit experiment is often used to demonstrate the wave-particle dualism . It can be carried out not only with light, but also with particles ( electrons , neutrons , atoms , molecules such as fullerenes ). The interference patterns observed here show that objects that are classically only viewed as particles have wave properties. In these matter waves , the De Broglie wavelength takes the place of the wavelength of light.

history

Thomas Young

1802 led Thomas Young , the experiment first time to prove the wave nature of light. In 1927, Clinton Davisson and Lester Germer showed the wave properties of electrons using the diffraction of an electron beam on a nickel crystal. The crystal acts as a reflection grating . Instead of two gaps, a lot of scatter centers are involved here.

The double slit experiment with electrons was carried out in 1961 by Claus Jönsson . With whole atoms, Jürgen Mlynek and Olivier Carnal succeeded in 1990 , with large molecules such as B. C 60 ( buckyballs ) in 2003 Nairz et al.

Experimental observation

Interference pattern of a double slit experiment with different numbers of electrons:    b : 200,   c : 6,000,   d : 40,000,   e : 140,000 
  • The two interfering waves must have a fixed phase relationship to one another so that interference fringes can be observed. Sufficient spatial coherence is given if the width of the source (an entry slit for Young) cannot be resolved from the perspective of the double slit (see Rayleigh criterion ). The requirement for temporal coherence depends on how many stripes are to be recognized next to the central stripe.
  • An addition to the apparatus that determines through which of the two slits a particle has reached the detector ( "which path" information ) inevitably causes the interference fringes to disappear. This also applies if no macroscopic measuring device shows which gap was taken. The physical possibility is sufficient. Conversely, structures in which it is impossible to find out which gap was taken always show an interference pattern. (In the case of photons, the path information can simply be implemented by polarization filters . If the two columns are combined with filters with mutually orthogonal polarization planes, the polarization of the photon decides which path the photon takes. In this case, there is no interference on the screen.)
  • The two previous statements apply even if the decision as to whether the information is determined via the path is only made after a particle has passed the gap. The decision not to find the path leads to interference patterns being observed in the detector. This can be interpreted as meaning that the information about the route taken is subsequently deleted. Hence, such a structure is called a quantum eraser .
  • The interference pattern does not depend on the number or simultaneity of the photons involved. At a lower intensity, the interference pattern only builds up more slowly at the detector, but remains the same in shape. This happens even if there is at most one particle between the source and the detector at any given time. Therefore, the distribution of the probability of arrival at the positions on the detector must also arise for each individual flight. This phenomenon can be interpreted as interference of the particles with themselves.

Calculation of the interference pattern

Schematic representation of the double slit experiment

The following section assumes a perpendicular incidence of a plane wave of wavelength on a double slit with slit width b and slit center distance a . In the slit plane the phases are still in the same mode, phase differences, which make up the interference effect, arise only from the distances s from points in the slit openings to the observation point (red lines). The distance d of the screen should be large , far-field approximation .

Locations of the minima and maxima by interference of the two columns

A minimum of intensity is found for those places where the path difference is from the gap middle of an odd multiple of half the wavelength, ie . Then the two partial waves are out of phase and cancel each other out. This also applies in the event that the width of the stomata is not small compared to the wavelength. Then s varies noticeably with the position of the point within the gap width, but for every point in one gap there is a point in the other gap at distance a , from which the wave arrives in antiphase.

Maxima are located approximately in the middle between the minimum points where there is constructive interference with . For higher diffraction orders n the maximum intensities decrease, because the constructive interference applies in pairs for points in both columns, but not for the variation of the point position within the gap (see below).

The relationship between the path difference and the position on the screen can be read from the drawing:

so for small angles approximately

This is the period of the stripe pattern when the screen spacing is large compared to the gap spacing.

The interference pattern

Intensity distribution behind a double slit (red). The envelope (gray) is the diffraction pattern of one of the two individual slits.

However, each of the two individual slits already has a diffraction pattern, since for certain angles the upper and lower halves of the individual slit of width cancel each other out. The intensity of the double slit is therefore the product of two intensities: the diffraction at the single slit of the width and that of two point sources at a distance :

where the phase difference of the waves from the upper and lower edge of a gap is, and the phase difference between the two partial waves from both gaps.

Here is the observation angle, the slit width, the slit distance, the wave number .

Influence of gap geometry and wavelength

If the expressions for and in the equation of the interference pattern are used, the influences of the slit geometry and wavelength of the incident light on the appearance of the interference pattern become clear:

with .

  • A change in the slit width b leads to a change in the position of the extremes of the single slit, the intensity distribution of which (blue in the picture) forms the envelope curve of the intensity distribution of the double slit (red in the picture)
→ The wider the gap , the narrower the envelope becomes
  • A change in the gap distance a leads to a change in the position of the extremes of the double gap within the envelope curve, which remains constant
→ The larger the gap , the closer the extremes of the double gap are
  • A change in the wavelength λ affects both the envelope and the intensity distribution of the double slit
→ The longer the wavelength , the wider the envelope and the interference distances of the double slit

Calculation with Fourier optics

The interferogram of a gap constellation can also be calculated with the help of Fourier optics . This makes use of the fact that in the case of Fraunhofer diffraction, the diffraction pattern of the Fourier transform corresponds to the autocorrelation of the diaphragm function. The advantage of this approach is that the diffraction pattern of more complicated multiple slits and gratings can also be calculated quickly. It is essential to use the convolution theorem .

The coordinate system is placed in such a way that the two individual columns with a distance a are symmetrical to the intersection of the coordinate axes. The diaphragm function of the two identical gaps with width b in the spatial space is

where denotes the convolution operator and the rectangular function.

According to the convolution theorem, the Fourier transform of the given aperture function is the product of the Fourier transform of the rectangular function and the Fourier transform of the two delta distributions .

This results in a cosine with a sinc function as the envelope for the intensity on the screen . The function has the characteristic secondary maxima of a -fold slit (see also optical grating ).

With as an intensity constant.

For follows the relationship shown above for .

literature

  • John Gribbin: Looking for Schrödinger's cat. Quantum Physics and Reality . 5th edition. Piper, 2004, ISBN 3-492-24030-5 .
  • Claus Jönsson: Interference of electrons at the double slit . In: Zeitschrift für Physik , No. 161, 1961, pp. 454–474.
  • David Halliday, Robert Resnick, Jearl Walker: Physics . 2nd Edition. Wiley-VCH, 2003, ISBN 3-527-40366-3 .
  • Wolfgang Demtröder : Experimental Physics. Vol. 2: Electricity and optics . 3. Edition. Springer, Berlin, 2004, ISBN 3-540-20210-2 .

Web links

Wiktionary: double column experiment  - explanations of meanings, word origins, synonyms, translations
Commons : double slit experiment  - collection of images, videos and audio files
Wikibooks: Optics # Diffraction at a double slit  - learning and teaching materials

Individual evidence

  1. Anil Ananthaswamy: Through two doors at once - the elegant experiment did captures the enigma of our quantum reality . Dutton, New York 2018, ISBN 978-1-101-98609-7 . A legible history of the double slit experiment from Young to the quantum eraser.
  2. ^ C. Davisson, LH Germer: Diffraction of Electrons by a Crystal of Nickel . In: Physical Review . tape 30 , no. 6 , 1927, pp. 705-740 , doi : 10.1103 / PhysRev.30.705 .
  3. Claus Jönsson: Electron interference on several artificially produced fine slits . In: Journal of Physics A Hadrons and Nuclei . tape 161 , no. 4 , 1961, pp. 454-474 , doi : 10.1007 / BF01342460 .
  4. ^ Claus Jönsson: Electron Diffraction at Multiple Slits . In: American Journal of Physics . tape 42 , 1974, pp. 4-11 .
  5. Olivier Carnal, Jürgen Mlynek: Young's double-slit experiment with atoms: A simple atom interferometer . In: Physical review letters . tape 66 , 1991, pp. 2689-2692 , doi : 10.1103 / PhysRevLett.66.2689 .
  6. Olaf Nairz, Markus Arndt, Anton Zeilinger : Quantum interference experiments with large molecules . In: American Journal of Physics . tape 71 , no. 4 , 2003, p. 319–325 ( online [PDF; accessed February 11, 2019]).
  7. Description, picture a and source see here
  8. What is light ?: from classical optics to quantum optics , Thomas Walther and Herbert Walther, CH Beck, 2004, p. 91 ff.