  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.
