K. Tara

We introduce states defined by \ensuremath{\Vert}\ensuremath{\alpha},m〉=${\mathit{a}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathit{m}}$\ensuremath{\Vert}\ensuremath{\alpha}〉 up to a normalization constant, where \ensuremath{\Vert}\ensuremath{\alpha}〉 is a coherent state and m an integer. We study the mathematical and physical properties of such states. We demonstrate phase squeezing and the sub-Poissonian character of the fields in such states. We study in detail the quasiprobability distributions and the distribution of the field quadrature. We also show how such states can be produced in nonlinear processes in cavities.

A criterion is evolved for testing the nonclassical character of the field even if it does not exhibit squeezing and sub-Poissonian statistics. An explicit example of a state of the field is given to demonstrate the utility of this criterion. The production of such a state by state-reduction methods is also shown. This criterion also enables us to study the nonclassical character of the Schr\"odinger cat state in regions where it does not exhibit sub-Poissonian statistics.

We show how a special class of Schr\"odinger macroscopic quantum-superposition states can be produced by a coherent field propagating through a Kerr medium. We show that these states are eigenstates of the mth power of the photon-annihilation operator leading also to the possibility of producing these using multiphoton Jaynes-Cummings systems. We further show how superpositions of squeezed coherent states can be produced.

Quantum-mechanical phase distributions are investigated for some nonlinear optical phenomena which, at a classical level, involve only changes in the phase of the electric field. The phenomena investigated include reflection from a phase-conjugate mirror and propagation through an optical fiber. It is found that, while the peaks of the respective phase distributions exhibit the expected classical behavior, the widths of the phase distributions also undergo substantial changes. The relation between the input and the output phase distributions in the two cases mentioned above is investigated analytically as well as numerically. The results are compared with a phase distribution defined via the Wigner function.

We show how the Einstein-Podolsky-Rosen paradox for continuous variables can be tested using the quadrature amplitudes of a radiation field in the pair-coherent state. Correlated pairs of photons are produced by two competing nonlinear processes---four-wave mixing and two-photon absorption.