# Decoherence effects

There are many reasons why we usually do not perceive the interference phenomena of matter in our everyday life.

This is partly due to the extremely tiny de Broglie wavelength of solid bodies. Another reason is that a quantum system can not be perfectly isolated and always interacts with an environment.

We can understand this from three different perspectives, that all are simultaneously valid in pure de Broglie interferometry (center of mass interferometry)::

1. The quantum phases, which are so important for constructive or destructive interference, are  randomly shifted by even minimal interactions with the environment. In our experiment this can be a small collision with a arbitrary molecule of the residual gas. Averaging over the randomly directed recoils on different molecules causes no (quantum) phase effects to be visible. This is very similar to Werner Heisenberg’s argument to explain the uncertainty principle.
2. This interaction can at the same time be considered as a position measurement. If the position of the particle is defined more precisely than two slits of the grating in the interferometer, the interference pattern vanishes. This corresponds to Niels Bohr’s argument on complementarity. It does not have to be a concious observer that does the measurement. It is sufficient if, for example, an atom whose position or momentum after scattering on the molecule could deduce the position of the molecule.
3. The coupling between the quantum system and its environment can be understood as quantum mechanical process, causing quantum entanglement between both. The quantum system and its environment are than inseparably correlated; but, at the same time  each one of them in an uncertain state. This is the approach of decoherence theory. If the environment consists of numerous particles – what usually is the case – the isolated system behaves as if it would have lost its coherence. Actually it is hidden in the much larger total system and therefore unusable for the experiment.
Extra: Heisenberg's and Bohr's argument

According to Abbé’s Theory of optics,  resolving a slit distance of $$d$$ needs light of a wave length smaller than $$\lambda_{photon} \simeq 2d$$.

If such a photon is scattered of a molecule flying through the slits, it transfers a momentum of $$\Delta p_{\mathrm{photon}}^\mathrm{recoil}=h/\lambda_{photon}=h/2d$$ on average on the massive particle.

To see if that is relevent, we look at the momentum transfer on the molecule when flying through the grating with period $$d$$. On its way to the first diffraction order it is deflected by the small angle $$\theta = \Delta p/p_0 \simeq \sin \theta = \lambda_{dB} / d$$, where $$\Delta p$$ is the momentum change by the grating and $$p_0$$ the original momentum in forward direction.

$$\Delta p_{\mathrm{molecule}}^\mathrm{diffraction}=p_0\cdot \theta = p_0\cdot\lambda_\mathrm{dB}/d = h/d$$

This shows that the recoil of a single photon is enough to push the molecule from a maximum to a minimum in the interference pattern. Averaging over many scattered photons causes the interference pattern to disappear.

Therefore, the molecules in our experiments need to be well isolated from their environment.

If, for example, the pressure in the vacuum chamber is too high, collisions of the molecules with the residual gas lead to decoherence effects. The phases are mixed and the interference contrast decreases.

In particular, if the quanta are composite complex objects like large molecules, they also have an internal temperature (unlike photons, neutrons and atoms!). With higher temperature, it is more likely that they emit thermal radiation while flying through the interferometer, i.e. they emit photons. They can hold information about the position of the molecules in the environment, causing the interference contrast to decrease.