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The phase properties of the cavity field of one- as well as two-photon JCM in a Kerr medium are studied by means of a Pegg - Barnett Hermitian phase operator formalism. The time evolution of the phase probability distribution, the phase fluctuations and the number - phase correlation are obtained. The effect of nonlinear interaction of a Kerr-like medium on the phase properties is analysed by comparing our results with those of usual JCMs.

Phase properties of binomial and negative binomial states are studied within the Pegg-Barnett hermitian phase formalism.

We analyze the phase properties of a strong cavity field interacting with an ensemble of initially excited N two-level atoms. Using the Pegg-Barnett phase formalism [Phys. Rev. A 39, 1665 (1989)], we calculate the phase probability distribution as well as the phase variance. The phase probability density exhibits a (N+1)-peak structure at the initial stages of the evolution. The phase variance is used to illustrate the progressive randomization of the phase on the long-time evolution. The difference in the phase dynamics for the N even and the N odd case is pointed out.

The phase distribution obtained within the Pegg–Barnett Hermitian phase formalism is compared to the phase distributions obtained from the s-parametrized quasiprobability distributions integrated over the "radial" variable for some real states of the field. Exact analytical formulas for the s-parametrized phase distributions of coherent states, squeezed states, and displaced number states are obtained. A general formula relating the s-parametrized phase distributions to the Pegg–Barnett distribution is derived. Numerical examples illustrating the similarities and differences are presented in a graphical form.

The phase properties of the fractional coherent states are discussed from the point of view of the Pegg-Barnett Hermitian phase formalism. Exact analytical formulas for the phase variance are obtained and illustrated graphically. The results can serve as a test for the range of validity of the scaling law for the phase variance.

The phase properties of the self-squeezed states generated during the evolution of the anharmonic oscillator are discussed from the point of view of the new phase formalism of Pegg and Barnett. The phase distribution, the expectation values and the variances of the Hermitian phase operator are obtained and their evolution illustrated graphically. The mean values for the phase cosine and sine functions as well as their variances are also calculated. The results are compared to the Susskind-Glogower formalism results and the results based on the measured phase concept. The relation between squeezing and the phase properties of the field is discussed briefly.

The joint probability distribution P (θ a , θ b ) for the phases θ a and θ b of the fundamental and second-harmonic modes is calculated, according to the Pegg-Barnett hermitian phase formalism, for different initial states of the fundamental mode undergoing second harmonic generation. The evolution of P (θ a , θ b ) is shown for four different initial states of the field (coherent, squeezed vacuum, Fock, and chaotic). Phase properties of the resulting fields are shortly discussed.

Quantum phase fluctuations in the second-harmonic generation are examined from the point of view of the Hermitian phase formalism introduced by Pegg and Barnett. The joint probability distribution as well as the variances for the phases of the fundamental and second-harmonic modes are calculated numerically. Their evolution is illustrated graphically, and the phase properties of the generated light are discussed.

Phase properties of pair coherent states are re-examined from the point of view of the Pegg-Barnett hermitian phase formalism. The joint probability distribution for the phases of the two modes is calculated and illustrated graphically. Strong correlation between the two phases is shown to exist, and the correlation coefficient calculated. The variance of the cosine of the phase-sum- operator is calculated. The results are compared to the earlier results of Agarwal.

The problem of the formation of discrete superpositions of coherent states when elliptically polarized light is propagating through a nonlinear Kerr medium is considered, It is shown that superpositions with any number of components can be obtained if the evolution time is taken as a fraction MIN of the period, where M and N are mutually prime integers. Exact analytical formulae for finding the superposition coeffi- cients are given. It is shown that the coupling between the two circularly polarized components of the ellpitically polarized light caused by the asymmetry of the nonlinear properties of the medium can suppress the number of components in the superposition from N' to N, if the asymmetry parameter takes appropriate values. The phase distri- bution function P(.9,, e.) for the two-mode field is obtained according to the new Pegg-Barnett phase formalism. This function exhibits a well resolved, multi-peak struc- ture, clearly indicating the formation of the discrete superpositions of coherent states. Examples of the phase distribution function for several superposition states are illustrated graphiczlly. showing in a very spectacular way the formation of such superpositions.

The phase properties of the two-mode squeezed vacuum states are re-examined from the point of view of the Hermitian phase formalism introduced by Pegg and Barnett. The joint probability distribution for the phases of the two models is obtained, and the phase properties associated with this distribution are discussed thoroughly.