Probing strongly correlated states of ultracold atoms in optical lattices

This thesis describes experiments which investigate ultracold atom ensembles in an optical lattice. Such quantum gases are powerful models for solid state physics. Several novel methods are demonstrated that probe the special properties of strongly correlated states in lattice potentials. Of these, quantum noise spectroscopy reveals spatial correlations in such states, which are hidden when using the usual methods of probing atomic gases. Another spectroscopic technique makes it possible to demonstrate the existence of a shell structure of regions with constant densities. Such coexisting phases separated by sharp boundaries had been theoretically predicted for the Mott insulating state. The tunneling processes in the optical lattice in the strongly correlated regime are probed by preparing the ensemble in an optical superlattice potential. This allows the time-resolved observation of the tunneling dynamics, and makes it possible to directly identify correlated tunneling processes.

A scanning electron microscope for ultracold quantum gases

This thesis presents a new imaging technique for ultracold quantum gases. Since the first observation of Bose-Einstein condensation, ultracold atoms have proven to be an interesting system to study fundamental quantum effects in many-body systems. Most of the experiments use optical imaging rnmethods to extract the information from the system and are therefore restricted to the fundamental limitation of this technique: the best achievable spatial resolution that can be achieved is comparable to the wavelength of the employed light field. Since the average atomic distance and the length scale of characteristic spatial structures in Bose-Einstein condensates such as vortices and solitons is between 100 nm and 500 nm, an imaging technique with an adequate spatial resolution is needed. This is achieved in this work by extending the method of scanning electron microscopy to ultracold quantum gases. A focused electron beam is scanned over the atom cloud and locally produces ions which are subsequently detected. The new imaging technique allows for the precise measurement of the density distribution of a trapped Bose-Einstein condensate. Furthermore, the spatial resolution is determined by imaging the atomic distribution in one-dimensional and two-dimensional optical lattices. Finally, the variety of the imaging method is demonstrated by the selective removal of single lattice site. rn