QUASI-PROBABILITY DISTRIBUTION Q(ALPHA,ALPHA-STAR) VERSUS PHASE DISTRIBUTION P(THETA) IN A DESCRIPTION OF SUPERPOSITIONS OF COHERENT STATES

The generation of discrete superpositions of coherent states in the anharmonic oscillator model is discussed from the point of view of their quasi-probability distribution Q(alpha,alpha*) and phase probability distribution P-(theta). It is shown that for the superposition with well-distinguishable states both distributions show the same rotational symmetry. The maximum number of well-distinguishable states is estimated. The two functions are illustrated graphically to show explicitly their symmetry and the influence of the interference terms. The similarity between the Q function integrated over the amplitude and the phase distribution P(theta) is shown to exist for the anharmonic oscillator states.