Discrete superpositions of coherent states and phase properties of the m-photon anharmonic oscillator

Abstract

The formation of discrete superpositions of coherent states via the unitary evolution of the m-photon anharmonic oscillator is studied. Exact analytical formulae for the superposition coefficients are obtained. It is shown that, in contrast to the two-photon anharmonic oscillator, for m>2 the superposition components enter the superposition with different amplitudes. The Pegg-Barnett phase formalism is used to calculate the phase distributions for the resulting states and to visualize their symmetry.