No abstract

The effect of cubic-quintic nonlinearity and associated intercomponent couplings on the modulational instability ͑MI͒ of plane-wave solutions of the two-component discrete nonlinear Schrödinger ͑DNLS͒ equation is considered. Conditions for the onset of MI are revealed and the growth rate of small perturbations is analytically derived. For the same set of initial parameters as equal amplitudes of plane waves and intercomponent coupling coefficients, the effect of quintic nonlinearity on MI is found to be essentially stronger than the effect of cubic nonlinearity. Analytical predictions are supported by numerical simulations of the underlying coupled cubic-quintic DNLS equation. Relevance of obtained results to dense Bose-Einstein condensates ͑BECs͒ in deep optical lattices, when three-body processes are essential, is discussed. In particular, the phase separation under the effect of MI in a two-component repulsive BEC loaded in a deep optical lattice is predicted and found in numerical simulations. Bimodal light propagation in waveguide arrays fabricated from optical materials with non-Kerr nonlinearity is discussed as another possible physical realization for the considered model.

Static and dynamic properties of matter-wave solitons in dense Bose-Einstein condensates, where three-body interactions play a significant role, have been studied by a variational approximation (VA) and numerical simulations. For experimentally relevant parameters, matter-wave solitons may acquire a flat-top shape, which suggests employing a super-Gaussian trial function for VA. Comparison of the soliton profiles, predicted by VA and those found from numerical solution of the governing Gross-Pitaevskii equation shows good agreement, thereby validating the proposed approach.

Modulation instability (MI) in continuous media described by a system of two cubic-quintic nonlinear Schrödinger equations (NLSE) has been investigated with a focus on revealing the contribution of the quintic nonlinearity to the development of MI in its linear and nonlinear stages. For the linear stage we derive analytic expression for the MI gain spectrum and compare its predictions with numerical simulations of the governing coupled NLSE. It is found that the quintic nonlinearity significantly enhances the growth rate of MI and alters the features of this well known phenomenon by suppressing its time-periodic character. For the nonlinear stage by employing a localized perturbation to the constant background we find that the quintic nonlinearity notably changes the behavior of MI in the central oscillatory region of the integration domain. In numerical experiments we observe emergence of multiple moving coupled solitons if the parameters are in the domain of MI. Possible applications of the obtained results to mixtures of Bose-Einstein condensates and bimodal light propagation in waveguide arrays are discussed.

We investigate the security of a model based on continuous variable QKD with Einstein–Podolsky–Rosen correlations against Gaussian clone–anticlone attacks. We find that the eavesdropper distils more information using the individual Gaussian anticlone attack than the optimal Gaussian cloner. However, a secure key can still be generated for the transmission coefficient of the quantum channel bigger than 0.5. Thus, the model is secure for clone–anticlone attacks.