Cross-Kerr interaction
= Cross-Kerr interaction
{title2=$H_{\rm int}=\hbar\chi n_1n_2$}
An ideal two-mode intensity-intensity coupling makes the phase of each mode depend on the other's <photon number>. With this sign convention, evolution for time $t$ sends a mode-1 coherent amplitude to $\alpha e^{-i\chi t n_2}$ when mode 2 has definite occupation. This single-mode unitary model does not by itself establish a strong, noiseless interaction between real travelling single <photons>.