As anticipated in the previous section, the project has achieved two major goals related to the subject of the funding:
first, we have devised a protocol to engineer multi-photon states in cavity QED systems involving spin one atoms. The protocol relies on the possibility to organise the energy levels of the system into an elegant staircase which can be climbed with the aid of an external pump field, and allow for the generation of the desired hybrid state of light coupled to matter. Even more interestingly, when subject to photon losses, and properly pumped, this system could exhibit the metastability and prethermal features at the centre of the funding scheme of the project.
second, we have studied the formation of time crystals in light-matter coupled systems. Time crystals are exotic behaviour of spin dynamics, where the atoms oscillate at a period which is the double of the period of the externally imposed field. This is a self-organising principle of quantum matter out-of-equilibrium and quite remarkably we have discovered that even this novel phenomenon could exhibit pre-thermal phenomena when interactions and dissipation were properly tuned in an experimentally viable window of parameters.
The work consisted in applying many body methods and concepts (Landau-Zener transitions, time dependent spin wave theory, cumulants for many body dynamics) to problems mutated from quantum optics.
These results were disseminated in several invited seminars and colloquia in the USA and in the UE, as well as in international workshops.
