Probing Ultracold Gases at Short Distances

The third lecture focusses on universal properties of ultracold gases probed at short distance which are a consequence of the fact that the effective range of interactions can be taken to zero. The resulting set of exact relations between thermodynamic properties and the short distance behavior of various correlation functions due to Tan provide an example for the operator product expansion originally developed in statistical and high-energy physics. In the context of ultracold gases, these methods allow to understand the negative line shift observed in Bragg scattering at large momentum which arises from processes where the momentum is transferred to two or more atoms simultaneously.