Recently, we have for the first time observed the pseudogap phase in a two-dimensional Fermi gas, in which a superconducting pairing gap opens up without the appearance of a symmetry-broken phase [M. Feld et al., Nature 480, 75 (2011)]. This work paves the way for emulating and understanding high-temperature superconductors. However, our research has also demonstrated that usual cooling methods have reached their limits in efficiently and economically achieving ultralow temperatures, and that radically new concepts are required. This project aims at demonstrating a novel cooling technique, which does not rely on thermodynamic engines but on a dynamical division of the systems into sub systems of high and low entropy. It is a fundamentally new approach to cooling and, if successful, would immediately transform the field of quantum materials because new states of matter will come within reach and open questions, for example regarding the origin of high-temperature superconductivity, will be answered.