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We study the strong coupling limit of a quadratic-nonlinear Landau-Zener problem for coherent photo- and magneto-association of cold atoms taking into account the atom-atom, atom-molecule, and molecule-molecule elastic scattering. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct a highly accurate and simple analytic approximation describing the time dynamics of the coupled atom-molecule system. We show that the approximation describing time evolution of the molecular state probability can be written as a sum of two distinct terms; the first one, being a solution to a limit first-order nonlinear equation, effectively describes the process of the molecule formation while the second one, being a scaled solution to the linear Landau-Zener problem (but now with negative effective Landau-Zener parameter as long as the strong coupling regime is considered), corresponds to the remaining oscillations which come up when the process of molecule formation is over. [ABSTRACT FROM AUTHOR]

We present a theoretical analysis, analytical and numerical, of the oscillation regimes for the semi-linear photorefractive oscillator beyond the instability threshold. This analysis includes the limiting cases of dominating transmission and reflection gratings as well as the cases of spontaneous violation of the frequency degeneracy between the oscillation and pump waves. [ABSTRACT FROM AUTHOR]

A general analysis of the threshold behavior for the photorefractive semi-linear oscillator is performed within the linear approximation on the basis of the classical wave-coupling model. This analysis shows that the well known particular results on the frequency degenerate oscillation are valid only within a restricted range of the external parameters. The theory specifies the conditions for onset and properties of the frequency non-degenerate oscillations, including the necessary values of the coupling strength, pump intensity ratio, the increments of the instability, and the frequency splits. Important generalizations of the basic model are considered. [ABSTRACT FROM AUTHOR]

We propose a scheme for the construction of a CNOT gate by adiabatic passage in an optical cavity. In opposition to a previously proposed method, the technique is not based on fractional adiabatic passage, which requires the control of the ratio of two pulse amplitudes. Moreover, the technique constitutes a decoherence-free method in the sense that spontaneous emission and cavity damping are avoided since the dynamics follows dark states. [ABSTRACT FROM AUTHOR]

We analyze the implementation of the time-reversal (TR) transformation in the algebraic approach to tetrahedral local molecules through the chain of groups . We determine the general form of the TR operation using a purely algebraic realization, based exclusively on the requirement that the irreducible representations must not be changed under the time inversion symmetry. As a result we can determine the TR behavior of purely algebraic operators. [ABSTRACT FROM AUTHOR]