Creating and imaging atomic wave functions beyond the diffraction limit

In cold atom experiments, the application of optical fields is the cornerstone for the manipulation and imaging of atoms. The wavelength of the light field sets a limit on the size of features that can be resolved. To beat this diffraction limit, we exploit the non-linear optical response of a three-level atom coupled by two light fields and create ultra-narrow potential barriers with widths less than lambda/50, physically realizing a Kronig-Penney potential. We also demonstrate a new imaging technique for probing the wavefunction of atoms trapped in an optical lattice with a spatial resolution of lambda/50 and a sub-microsecond temporal resolution, thereby introducing super-resolution microscopy to the field of cold atom systems. With this technique, we study the static and dynamic properties of the wavefunctions of atoms in the unit cell of an optical lattice.