Phase-coherence and amplitude-coherence

Weight function P(alpha) in the diagonal representation of density operator , rho = integrald(2)alphaP(alpha)\alpha][alpha\, is reduced to define separ ately the weight functions for phase, arg(alpha), and amplitude, \alpha\, w hich leads to concepts of phase-coherence and amplitude-coherence. For a si ngle mode phase-coherent field, it is shown that (i) we can have Hermitian operator of form, ape(i psi), where a is annihilation operator and psi is a constant, and (ii) the normally ordered characteristic function, chi (N)(x i), is a function of only the imaginary part of xie(i psi). For a single mo de amplitude-coherent field, it is shown that a rhoa dagger = ka dagger, wh ere a dagger is creation operator and k is a positive real constant. When t he weight function for the field is non-classical, each of the reduced weig ht function may or may not be non-classical irrespective of the nature of t he other. Examples of generation of phase-coherent and amplitude-coherent f ields are given.