The molecular source

or how to make a particle forget where it is

The source region is one of the key components of the experiment. Here we have to treat molecules in such a way that they behave like a wave later in the experiment rather than like a point-particle with a well-defined position. This is the prerequisite for diffraction of matter-waves at extended gratings like the one we use in this experiment.

First of all, the molecules have to fly from the source to the detector, a distance of more than 2 m. This is achieved by illuminating them with a tightly focused laser through a glass window. The molecules are prepared as a thin film on the window surface. As soon as the molecules are hit by the laser, they absorb the light, get hot, and evaporate. In order to make sure that the molecules can fly the whole distance of the apparatus unperturbed, it is constantly evacuated to a pressure below 10^-8 mbar, 10 billion times smaller than in the lab.

The laser beam (blue) is focused on the thin layer of molecules (violet) on the glass slide. Moving the window results in a constant supply of new material.

In order to start the journey of the molecules always from the same position, the laser is kept in place and the window is moved to constantly deliver new sample.

However, this does not lead to delocalization. For this to happen, we make use of Heisenberg’s uncertainty relation:

$\Delta x \cdot m\Delta v_x \geq \hbar/2$

This equation states that you cannot measure the position of a particle x and its velocity along this axis v_x better than $\hbar$ /2 at the same time. The value of $\hbar$ is 1·10^-34 Joules × second, which is 34 zeros before the 1. This value is so small that it is of no concern to us in our daily life. As an example, we make a small thought experiment.

Thought experiment: Heisenberg’s slit

In this experiment, we consider helium atoms, let them fly through a slit, and detect the size of the resulting stripe 1 m behind the slit at a detector. The width of the slit measures the position of the atoms in the x-direction, as the atoms have to pass it to reach the detector. According to Heisenberg, this measurement induces a change in the velocity along the axis we measure, x. To simplify things, we start with atoms that move only along the z-direction with 500 m/s, but not at all along x. As soon as the measurement has an effect on the molecules, they will also start to move in the x-direction and the signal at the detector will be wider than the slit.

Taking a slit width of 1 m broadens the signal at the detector by the diameter of an atom – clearly too small a change to detect.

At a slit width of 1 mm, the signal at the detector is 1.00000003 mm in size, still a negligibly small change.

When we reduce the slit width by another factor of 1000, we get to 1 µm, 1/80 of the thickness of a piece of paper. Sending the helium atoms through such a tiny slit leads to a signal which is 32 times larger than the slit itself! Intuitively, we would expect the signal at the detector to be the same as the slit – 1 µm. However, on these scales, Heisenberg’s uncertainty relation starts to have an effect and the increase in width at the detector is clearly visible.

This effect does not only occur in theory but can also be observed in real experiments. Nairz et al., for instance, have shown this for the molecules C₆₀ [1].

The peculiar point is that it is fundamentally impossible to know by how much the velocity component v_x of a single atom is changed in advance. Hence, we cannot ascribe a determined position to the atom anymore as soon as it leaves the slit – it got delocalized.

In the experiment, we use the same principle that we just discussed to prepare delocalized molecules. This is why we focus the laser down to a spot size of ≈1.5 µm and let the molecules fly for 1.5 m before they reach the grating. There, the delocalized molecules will diffract.

[1] O. Nairz, M. Arndt, and A. Zeilinger, Experimental verification of the Heisenberg uncertainty principle for fullerene molecules, Phys. Rev. A 65, 032109 (2002)