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The problem of generating discrete superpositions of coherent states in theprocess of light propagation through a nonlinear Kerr medium, which is modelledby the anharmonic oscillator, is discussed. It is shown that under anappropriate choice of the length (time) of the medium the superpositions withboth even and odd numbers of coherent states can appear. Analytical formulaefor such superpositions with a few components are given explicitly. Generalrules governing the process of generating discrete superpositions of coherentstates are also given. The maximum number of well distinguished states that canbe obtained for a given number of initial photons is estimated. Thequasiprobability distribution $Q(\alpha,\alpha^*,t)$ representing thesuperposition states is illustrated graphically, showing regular structureswhen the component states are well separated.

Generation of discrete superpositions of coherent states in the anharmonic oscillator model