Quantum non-Gaussian light and motion

The talk will report our recent theoretical and experimental achievements opening the door to highly non-Gaussian quantum physics with light and mechanical oscillators needed for quantum computation with continuous variables. This territory is challenging for investigation, both theoretically and experimentally. After briefly introducing the quantum non-Gaussian effects for light (Phys. Rev. Lett. 123, 043601 (2019), Phys. Rev. Lett. 126, 213604 (2021)), we will present recent theoretical and experimental activities, including the faithful hierarchy of quantum non-Gaussianity for multiphonon generation, its unpublished experimental verification and sensing capabilities Phys. Rev. Lett. 129, 013602 (2022)). Further, we will continue recent experimental results on generating quantum nonGaussianity of light from hot atomic ensembles (arXiv:2201.05366, accepted to npj Quant. Inf.). The talk will conclude with new unpublished results on non-Gaussian quantum coherence, the following challenges in theory and experiments with light and mechanical oscillators to stimulate discussion and further development of this field.