Wave mixing in an optical medium is one of the fundamental nonlinear parametric processes. However, it has not yet been thoroughly studied on single atoms. This effect requires a strong coupling of atoms to propagating waves and is hard to demonstrate with natural atoms. Nevertheless, it is possible to investigate the properties of artificial superconducting atoms coupled with coplanar waveguides. We have prepared an experimental setup and developed a topology of a superconducting chip. This setup is to be used to investigate the mixing of superpositions of the vacuum and single-photon states with coherent pulses on single atoms. An on-chip single-photon source is proposed to generate such states.