Double-slit experiment

In the double -slit experiment is allowed waves, such as coherent light waves pass through a screen with two narrow, parallel columns. On an observation screen at a distance to the aperture, which is much greater than the distance a between the two column, shows a so-called interference pattern. This pattern is caused by diffraction of the wave propagation at a double slit. With monochromatic light (eg from a laser) is the pattern of light on the screen strips ( maxima ) and dark fringes ( minima ). Further requirement is that the wavelength λ is smaller than the distance a of the two gaps.

The experiment can be carried out not only with the "waves" of the light, but also with "particle" (electrons, neutrons, atoms, molecules, such as fullerenes, etc.). It is also in such cases, an interference pattern, such as in the implementation of light. This means that classical particles exhibit wave-like properties under certain conditions - this is called " matter waves " and the wave -particle duality. With the double-slit experiment can demonstrate it, and by so-called " Which way? " Experiments " hit the spot ". The aim is, if the particle has passed through the first or the second gap (if a particle is registered ), or the signal from a passing through both slits shaft originates. The subtle contradiction in terms is that in the first case, no interference appears possible, while in the latter case the question " Which way? " Can not be answered.

Therefore, this experiment is the most important experiment of quantum mechanics. Only in this theory, it can be treated adequately.

• 4.1 Double -slit experiment and helium scattering at the HD system
• 4.2 Registrant and predictive measurements

History

In 1802, Thomas Young, the experiment for the first time through, to prove the wave nature of light.

1927 Clinton Davisson and Lester Germer demonstrated the wave properties of electrons based on the diffraction of an electron beam on a nickel crystal. The crystal acts as a reflection grating. Instead of two column here are very many scattering centers in the game.

In 1961, the double-slit experiment was performed with electrons by Claus Jönsson and succeed now also with atoms and molecules.

In September 2002, it was chosen in a poll of British Physical Society in the journal " Physics World " for most physical experiment.

Experimental observation

• The two interfering waves must have a fixed phase relationship to each other, so that any interference can occur. Sufficient spatial coherence is achieved when the width of the source ( at a Young entrance slit ) from the perspective of the double gap can not be resolved (see Rayleigh criterion). The requirement for temporal coherence depends upon the number of strips will be seen next to the central strip. With ' incoherent ' daylight already the first diffraction order appears colorful. More information at coherence.
• Covers are one of the two diaphragm column that is observed now depending on the width b of the gap either a diffraction pattern at a single slit ( b → wavelength λ ) or a wide, bright strip behind each open gap with interference patterns behind the edges of the gap ( b> > λ ).
• Has tried to find out by any apparatus ( a so-called quantum eraser ) which way taken a particular particle ( through slit 1 or slit 2), the interference pattern disappears. This information can also be obtained by the fact that you cover one of the gaps. This disappearance is explained in the Copenhagen interpretation of quantum mechanics by the so-called collapse of the wave function. This means that the interference in the system in a superposition of the two possible ways, while a measurement of the actual path results in that only the "hits" will be. This is also true if the path of the particle is determined later.
• With respect to the interference pattern needs to be noted that the energy of the light is not reduced. Rather, it is merely a redistribution of energy (light ) - the energy is therefore retained.
• The interference pattern does not depend on the number of photons involved or simultaneity. On a slow sequence of individual particles, the interference pattern builds up slowly on the photo plate. After detecting more and more particles you can see the known distribution more accurately. This is really surprising, because each individual particle "knows" that sooner or later coming particles are not any " fly-through " of a particle through the double slit is independent of the others. Therefore, the distribution of the probability of arriving at the positions on the photographic plate at each individual through flight must occur. This can be interpreted as interference of the particles themselves.

Physical Description

Prerequisite for the following sections is the vertical incidence of a plane wave of wavelength on a double slit with slit width b and gap center distance a in the cleavage plane, the phases still in sync, phase differences that make the interference effect are, are only produced through the distances s of points in the stomata to the observation point (red lines). The distance d of the screen should be large, far-field approximation.

Locations of the minima and maxima

A minimum of intensity is found for those places where the path difference is from the gap midst of an odd multiple of half the wavelength, ie. Then the two partial waves are in antiphase and cancel each other out. This also applies to the case where the width of the slit openings is small compared to the wavelength. Although then varied considerably with the position s of the point within the slit width, but at any point where there is a gap at a distance from a point A in the other slit of the opposite phase of the arriving wave.

Maxima are located approximately midway between the minimum points where constructive interference is given by. For higher orders of diffraction n take from the peak intensities, because although the constructive interference is considered pairs of points in two columns, but not for the variation of the point position within the gap (see below).

The relationship between the phase difference and the position on the screen read off from the drawing:

Approximately so for small angles

This is the period of the stripe pattern.

The interference pattern

The intensity of the double slit can be represented as a product of the intensity of the single slit and the grating with n = 2:

By: and

Or

And

Here, the observation angle, the gap width, the gap distance, the wave number and the wave number component is perpendicular to the columns.

Influence of gap geometry and wavelength

Substituting the expressions for γ and δ in the equation of the interference pattern, the influence of the gap geometry and wavelength of the incident light on the appearance of the interference pattern will be apparent:

With k = 2π / λ.

• A change in the gap width b leads to a change in the position of the extrema of the single gap, the intensity distribution ( blue in the picture ) the envelope of the intensity distribution of the double slit forms ( red in the picture )

• A change in the gap distance A leads to a change in the position of the extremes of the double gap remains constant within the envelope

• A change in wavelength λ affects both the envelope, as well as on the intensity distribution of the double slit of

Calculation with Fourier optics

The interferogram of a gap constellation can be calculated with the help of Fourier optics. This takes advantage of that in the case of Fraunhofer diffraction, the diffraction pattern corresponds to the Fourier transform of the autocorrelation of the aperture function. The advantage of this approach is that also the diffraction pattern more complicated multi- column and grid can be calculated quickly. What is essential is the use of the convolution theorem.

The coordinate system is set so that the two single column at a distance a lie symmetrically to the intersection of the coordinate axes. The aperture function of two identical column with width b in the spatial domain is

Where the convolution operator and the rectangular function called.

The Fourier transform of the aperture function is given by the convolution product of the Fourier transform of the square function, and the Fourier transform of two delta distributions.

It follows for the intensity at the screen a cosine with a sinc function as the envelope. The function has the characteristic of a secondary maxima -fold gap (see also optical lattice ).

With a constant intensity.

For the following, the relationship already shown above for.

• Image and diffraction pattern from a double slit

Diffraction pattern of a double slit

Implications of the observations for the quantum mechanics

Considering the quantum mechanical description of the experiment, so has an important fact to: The measuring equipment must be included in the experiments because it decisively changed by the detection or measurement of the exact path of a given particle the result of the experiment ( surprisingly, this change can but even be reversed under certain conditions, such as a quantum eraser ). In classical physics, a measurement affects the outcome in any relevant extent.

In quantum physics, there are several approaches to describe this phenomenon. ( Called interpretations or interpretations ) All these approaches lead to the same result, but are conceptually different. Two interpretations have been particularly profiled:

Double-slit experiment and helium scattering at the HD system

Daniel Fischer and Robert Moshammer from the Max Planck Institute for Nuclear Physics in Heidelberg study in the November 2013 edition of the journal Physics Journal on pages 16 and 17 is an approximate realization of the quantum mechanical Doppelspaltexpertiments by exact calculation of the helium scattering on HD systems. It follows that it is necessary, all (!) Parts of the system, including the two " column" not to treat H ( proton ) or D ( deuteron ) classical or semi- classical, but strictly quantum mechanically - coherent. Then the above solves "apparent contradiction " to complete.

Registrant and predictive measurements

The apparent contradiction can - more philosophically or logically - even as follows be resolved: in the " Which way? " Experiments is registriende measurements on single particles in the interference experiments contrast to probabilistic averages of many measurements or to theories - such as quantum mechanics - makes probabilistic predictions. This contrast is similar, as in the discussion of Richard Feynman problem of the apparent contradiction between the possibility of simultaneous position and momentum measurements at registration to a single event and the impossibility of simultaneous prediction of position and momentum in quantum theory, ie a probabilistic theory.