Light-matter interaction has been of paramount importance to unravel the mysteries of the quantum world. In general, atoms in free space weakly couple to radiation. In order to enhance this coupling, atoms are placed inside a cavity QED, which also give rise to a quasiparticle namely “Polariton”. The polariton is a bipartite state between the atom and a Fock state of the electromagnetic field that exhibits a very interesting dynamics such as quantum phase transition from Mott Insulator to Superfluid.

Open quantum systems are usually modeled following a Markovian dynamics. However, it has been pointed out through different examples that a Non-Markovian behavior is the rule rather than the exception. For instance, in Non-Markovian environments there is a backflow of quantum information that leads to new insights on the dynamic of the coherence.

In our group we are interested in studying quantum phase transitions in a cavity QED array where each cavity interacts with a single atom inside. Moreover, we expect to find Non-Markovian signature by engineering the environment between the cavities.