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

TL;DR

This paper explores how to generate discrete superpositions of coherent states in a nonlinear Kerr medium modeled by an anharmonic oscillator, providing analytical formulas and rules for their creation.

Contribution

It introduces explicit analytical formulas and general rules for generating discrete superpositions of coherent states in an anharmonic oscillator model.

Findings

Superpositions with even and odd numbers of states can be generated.

Maximum distinguishable states depend on initial photon number.

Graphical illustrations show regular structures of superpositions.

Abstract

The problem of generating discrete superpositions of coherent states in the process of light propagation through a nonlinear Kerr medium, which is modelled by the anharmonic oscillator, is discussed. It is shown that under an appropriate choice of the length (time) of the medium the superpositions with both even and odd numbers of coherent states can appear. Analytical formulae for such superpositions with a few components are given explicitly. General rules governing the process of generating discrete superpositions of coherent states are also given. The maximum number of well distinguished states that can be obtained for a given number of initial photons is estimated. The quasiprobability distribution $Q(\alpha,\alpha^*,t)$ representing the superposition states is illustrated graphically, showing regular structures when the component states are well separated.