Theory of Cross Phase Modulation for the Vibrational Modes of Trapped   Ions
  We analyze nonlinear coupling between individual vibrational quanta for trapped ions. The nonlinear Coulomb interaction causes a Kerr-type Hamiltonian, for which we derive an analytical expression for the coupling constant. In contrast to a previously published formula [1], our result is in close agreement with experimental data. 
X. Rebecca Nie, Christian F. Roos, Daniel F. V. James