A. T. Avelar

Solitons with cubic and quintic nonlinearities modulated in space and time.

This work deals with soliton solutions of the nonlinear Schrödinger equation with cubic and quintic nonlinearities. We extend the procedure put forward in a recent paper [J. Belmonte-Beitia, Phys. Rev. Lett. 100, 164102 (2008)], and we solve the equation in the presence of a linear background and cubic and quintic interactions which are modulated in space and time. As a result, we show how a simple parameter can be used to generate brightlike or darklike localized nonlinear waves which oscillate in several distinct ways, driven by the space and time dependence of the parameters that control the trapping potential and the cubic and quintic nonlinearities.

Modulation of breathers in cigar-shaped Bose–Einstein condensates

Abstract We present new solutions to the nonautonomous nonlinear Schrodinger equation that may be realized through convenient manipulation of Bose–Einstein condensates. The procedure is based on the modulation of breathers through an analytical study of the one-dimensional Gross–Pitaevskii equation, which is known to offer a good theoretical model to describe quasi-one-dimensional cigar-shaped condensates. Using a specific ansatz , we transform the nonautonomous nonlinear equation into an autonomous one, which engenders composed states corresponding to solutions localized in space, with an oscillating behavior in time. Numerical simulations confirm stability of the modulated breathers against random perturbation on the input profile of the solutions.

Solitons of two-component Bose–Einstein condensates modulated in space and time

In this Letter we present soliton solutions of two coupled nonlinear Schrodinger equations modulated in space and time. The approach allows us to obtain solitons for a large variety of solutions depending on the nonlinearity and potential profiles. As examples we show three cases with soliton solutions: a solution for the case of a potential changing from repulsive to attractive behavior, and the other two solutions corresponding to localized and delocalized nonlinearity terms, respectively.

Controlled teleportation via photonic Faraday rotations in low-Q cavities

This paper presents feasible experimental schemes to realize controlled teleportation protocols via photonic Faraday rotations in low-Q cavities. The schemes deal with controlled teleportation of superposition states and two-particle entanglement of atomic states. The information is encoded in lambda configured three-level atoms trapped inside coupled cavities by optical fibers. Also, we estimate the success probability and the current feasibility of the schemes.

Generation of a 4-qubit cluster of entangled coherent states in bimodal QED cavities

We propose a scheme to generate a 4-qubit cluster of entangled coherent states in bimodal QED cavities. The scheme employs a single two-level atom that interacts dispersively with cavity modes initially prepared in coherent states. The fidelity and success probability of the state preparation are obtained considering the influence of atomic velocity spread and atomic efficiency detection. The scheme is also generalized for higher order cluster states.

Modulation of breathers in the three-dimensional nonlinear Gross-Pitaevskii equation

In this paper we present analytical breather solutions of the three-dimensional nonlinear generalized Gross-Pitaevskii equation. We use an Ansatz to reduce the three-dimensional equation with space- and time-dependent coefficients into a one-dimensional equation with constant coefficients. The key point is to show that both the space- and time-dependent coefficients of the nonlinear equation can contribute to modulate the breather excitations. We briefly discuss the experimental feasibility of the results in Bose-Einstein condensates.

A note on entanglement swapping of atomic states through the photonic Faraday rotation

We propose two schemes of entanglement swapping of atomic states confined in cavities QED useful for quantum computation and quantum communication via a photonic Faraday rotation. They employ a source of linearly-polarized photon, a single photodetector, a quarter-wave plate, and three or four cavities, respectively.

Controlling statistical properties of a Cooper pair box interacting with a nanomechanical resonator

We investigate the quantum entropy, its power spectrum, and the excitation inversion of a Cooper pair box interacting with a nanomechanical resonator, the first initially prepared in its excited state, the second prepared in a “Schrodinger-cat” state. The method employs the Jaynes–Cummings model with damping, with different decay rates of the Cooper pair box and different ranges of detuning, going from resonant to off-resonant cases, including time dependent detunings. Concerning the entropy, it is found that the time dependent detuning turns the entanglement more stable in comparison with previous results in the literature. With respect to the Cooper pair box excitation inversion, while the presence of detuning destroys the collapses and revivals, it is shown that convenient time dependent detunings recover such effects in a nice way.

Bright and dark solitons in a periodically attractive and expulsive potential with nonlinearities modulated in space and time

Abstract This work deals with soliton solutions of the nonlinear Schrodinger equation with a diversity of nonlinearities. We solve the equation in a potential which oscillates in time between attractive and expulsive behavior, in the presence of nonlinearities which are modulated in space and time. Despite the presence of the periodically expulsive behavior of the potential, the results show that the nonlinear equation can support a diversity of localized excitations of the bright and dark types.

Modulation of localized solutions for the Schrödinger equation with logarithm nonlinearity

Abstract We investigate the presence of localized analytical solutions of the Schrodinger equation with logarithm nonlinearity. After including inhomogeneities in the linear and nonlinear coefficients, we use similarity transformation to convert the nonautonomous nonlinear equation into an autonomous one, which we solve analytically. In particular, we study stability of the analytical solutions numerically.