The particle-wave duality is one of the most exciting ideas of Quantum Mechanics. In recent years Bose-Einstein-Condensates (BECs) have given us for the first time access to coherent matter-waves with a large number of atoms. The conjugate of the coherent state is the Fock state, where the atom number is precisely known. Imaging a BEC with single atom resolution would project the coherent state onto a spatially resolved Fock state, thus allowing us to study its correlation functions in great detail.
Recently, we have developed dark-ground imaging as a novel ultra-sensitive imaging technique. Based on the existing infrastructure of this project, you will test and implement a custom-made Zeiss objective, which will push the resolution limit down to little more than one micro meter. The associated increase in the photon-collection efficiency will allow us for the first time to image free single neutral atoms in situ.
We plan to use this new technique to observe finite size effects in BECs of just a few atoms.
Figure: Images taken of a few atoms in a magento-optical trap. The fact that the atoms are trapped allow us to observe them for a longer time and thus resolve the atom number relatively easily with standard optics.