“…Our theory constitutes an ideal framework for the exploration of a wide range of many-body phenomena on the level of the reduced atomic non-Markovian dynamics in the strong-coupling regime, such as phase transitions [91], measurement-induced phase transitions [92,93], neural network like behaviors such as associative memories [28,94], cavity-enhanced transport [95][96][97][98][99] and superconductivity [100], continuous measurement of transport [101], or cavity cooling with higher capture range [102] and its monitoring [103]. New schemes for quantum information processing and production of entanglement [32] could also be investigated, exploiting the higher coherence achievable in the strong-coupling regime, the use of different cavity modes to realize quantum gates (or conversely the use of the atoms to realize quantum gates between photonic qubits [104,105]), or the potential of using the feedback formalism to implement error correction protocols. Finally, it is important to stress again that while we use the language of optical cavity QED, the underlying model is universal and can equally be applied to plasmonic cavities [40], cold atoms reservoirs [37][38][39], electron-phonon systems [36], or circuit QED [33,35].…”