There is a growing interest in the study of polaritonic systems, mixed states of photons and excitons, for both, the observation of quantum macroscopic phenomena, and the realisation of all-optical devices that could offer limitless advantages in terms of energy consumption, dissipation-less operation, and high clock frequencies .
Here we show several macroscopic quantum phenomena that can be observed in polariton condensates, both at low temperature, in inorganic semiconductor microcavities–for which the very long lifetime can show behaviour associated to the Berezinskii-Kosterlitz-Thouless (BKT) regime [2, 3]–and in organic based polaritons, where superfluidity can be observed at room temperature . We also show the possibility of observing interesting topological behaviours by exploiting the peculiar band structure that can show, under certain conditions, the appearance of a Berry curvature [5,6] as well as the emergence of artificial gauge fields acting on the propagation property of polariton fluids . Finally, we will show how such nonlinear systems could be used as hardware implementation of neuromorphic computing devices that demonstrate a high recognition rate compared to linear classifiers . Eventually we will also speculate on the possibility to reach the genuine quantum regime using single polaritons as quantum bits for the implementation of photonic nonlinear quantum devices .
 Sanvitto, D. & Kena-Cohen, S. The road towards polaritonic devices. Nat. Mater. 15, 1061–1073 (2016).
 D. Caputo, et al. Topological order and thermal equilibrium in polariton condensates. Nat. Mater. 17, 145–151 (2018).
 D. Caputo, et al. Josephson vortices induced by phase twisting a polariton superfluidNat. Phot. 13, 488 (2019)
 G. Lerario, et al. Room-temperature superfluidity in a polariton condensate. Nat Phys 13, 837 (2017).
 A. Gianfrate, et al., Measurement of the quantum geometric tensor and of the anomalous Hall drift. Nature 578, 381 (2020).
 L. Polimeno, et al. Tuning the Berry curvature in 2D Perovskite. arXiv:2007.14945.
 A. Fieramosca, et al. Chromodynamics of photons in an artificial non-Abelian magnetic Yang-Mills field. arXiv:1912.09684.
. D. Ballarini, et al. Polaritonic Neuromorphic Computing Outperforms Linear Classifiers. Nano Lett. 20, 3506 (2020).
 A. Cuevas, et al. First observation of the quantized exciton-polariton field and effect of interactions on a single polariton. Sci. Adv. 4, eaao6814 (2018).