The strong non-linearity plays a significant role in physics, particularly, in designing novel quantum sources of light and matter as well as in quantum chemistry or quantum biology. In simple systems, the photon-photon interaction can be determined analytically. However, it becomes challenging to obtain it for more compex systems. Therefore, we show here how to measure strong non-linearities via allowing the sample to interact with a weakly pumped quantized leaking optical mode. We found that the detected mean-photon number versus pump-field frequency shows several peaks. Interestingly, the interval between neighbour peaks equals the photon-photon interaction potential. Furthermore, the system exhibits sub-Poissonian photon statistics, entanglement and photon switching with less than one photon. Finally, we connect our study with existing related experiments.

4 pages, 3 figures