Quantum non-Gaussian high Fock states of light pulses and their superpositions

The generation of high Fock states of light pulses and their superpositions with provable quantum non-Gaussian features is still very challenging, although the power of conditional methods to herald the approximate state from the available Gaussian states is growing. The atom-light interaction in the high-Q cavity has been considered a viable alternative to the heralded Fock states of the light pulses from nonlinear optics limited to three-photon Fock states for the last decade. Here, by optimizing the realistic protocol combining it with available optical delay elements we conclusively predict filtering of Fock states up to ten photons with a high success rate of $20\%$ using a hierarchy of quantum non-Gaussian criteria. Moreover, the filtering protocol enables the preparation of superposition of Fock states and we analyse this emerging case up to two photons with with provable quantum non-Gaussian coherence and high success rate $50\%$. To demonstrate their quality for applications, we evaluate the robustness of such features, the bunching capability in a linear network, and the sensing capability to estimate the magnitude of unknown force, noise and phase, These assessments outline the essential conditions and application criteria for realistic optical cavity QED interaction on light pulses to outperform photon detection methods.