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Talbot-Lau effect:
Interference with incoherent sources

To this day, we do not know of any coherent sources for large molecules. Hence, we need to prepare the spatial and spectral coherence of our molecular beam in order to conduct quantum interference experiments.

We have already prepared the spectral coherence of our beam using velocity selection.

Spatial coherence can be generated by minimising the size of the source aperture. However, this reduces the number of useful molecules.  This problem can be solved by the Talbot-Lau effect. With an additional grating we realize many such small apertures side by side at the same time. By means of this technique we can increase the signal by more than 10’000 times compared to the far-field diffraction image of a single grating.

The openings are as small as \(90 \, \mathrm{nm}\). When the molecules fly through the openings their location is so well defined that they experience a large uncertainty in their transversal momentum according to Heisenberg’s uncertainty principle. In contrast to the momentum distribution behind the oven apperture, this is a continuous quantum mechanical superposition of momentum states. While travelling, this leads to a spatial delocalisation (position uncertainty) over a region which grows linearly with the distance from the grating. By the time a molecule reaches the second grating, in our experiment, it is delocalized over more than 10 grating openings. In practice, this depends on the velocity of the molecules; a delocalization over two grating openings is still sufficient for the Talbot-Lau effect.

At the position of the second grating no interference pattern forms, as there is no constant phase relation between molecules travelling through different slits. Instead, we expect a homogeneous distribution of molecules.

The delocalization and coherence of the molecules appear when the second grating diffracts the matter waves anew and, thereby, reunites them.

A spatially resolving detector, at the same distance \(L\) to \(G2\) as \(G2\) to \(G1\), could measure the constructive interference of partial waves as density distributions. The distance \(L\) has to be of the same order of magnitude as the Talbot length \(L_T\).

In our experiment, the spatial resolution of the interference pattern is realized with a third grating. More on that later.