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.

We consider a two-component pancake-shaped, i.e., effectively two-dimensional (2D), Bose-Einstein condensate coupled by the spin-orbit (SO) and Rabi terms. The SO coupling adopted here is of the mixed Rashba-Dresselhaus type. For this configuration, we derive a system of two 2D nonpolynomial Schrödinger equations (NPSEs), for both attractive and repulsive interatomic interactions. In the low- and high-density limits, the system amounts to previously known models, namely, the usual 2D Gross-Pitaevskii equation, or the Schrödinger equation with the nonlinearity of power 7/3. We present simple approximate localized solutions, obtained by treating the SO and Rabi terms as perturbations. Localized solutions of the full NPSE system are obtained in a numerical form. Remarkably, in the case of the attractive nonlinearity acting in free space (i.e., without any 2D trapping potential), we find parameter regions where the SO and Rabi couplings make 2D fundamental solitons dynamically stable

In a recent paper [Phys. Rev. A 70, 025803 (2004)] we presented a scheme to teleport an entanglement of zero- and one-photon states from a bimodal cavity to another one, with 100% success probability. Here, inspired on recent results in the literature, we have modified our previous proposal to teleport the same entangled state without using Bell-state measurements. For comparison, the time spent, the fidelity, and the success probability for this teleportation are considered.Comment: 4 pages, 1 figure, published in Phys. Rev. A 72, 045802 (2005

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We present new solutions to the nonautonomous nonlinear Schrödinger 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 breathers against random perturbation on the input profile of the solutions.

A recent work [1] proposed a type of cluster entangled coherent states and its generation. Here we present an alternative experimental arrangement for its generation 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.

Extending the recent work on models with spatially nonuniform nonlinearities, we study bright solitons generated by the nonpolynomial self-defocusing (SDF) nonlinearity in the framework of the one-dimensional (1D) Muñoz-Mateo -Delgado (MM-D) equation (the 1D reduction of the Gross-Pitaevskii equation with the SDF nonlinearity), with the local strength of the nonlinearity growing at |x| → ∞ faster than |x|. We produce numerical solutions and analytical ones, obtained by means of the Thomas-Fermi approximation (TFA), for nodeless ground states, and for excited modes with 1, 2, 3, and 4 nodes, in two versions of the model, with steep (exponential) and mild (algebraic) nonlinear-modulation profiles. In both cases, the ground states and the single-node ones are completely stable, while the stability of the higher-order modes depends on their norm (in the case of the algebraic modulation, they are fully unstable). Unstable states spontaneously evolve into their stable lower-order counterparts. [22], etc. This subject has been greatly upheld by the use of the Feshbachresonance (FR) technique, i.e., the control of the strength of the inter-atomic interactions by externally applied fields [23][24][25], which opens the possibility to implement sophisticated nonlinear patterns. In particular, the management of localized solutions of the Gross-Pitaevskii equation (GPE) [26] by means of the spatially inhomogeneous nonlinearity, which may be created by external nonuniform fields that induce the corresponding FR landscape, has attracted a great deal of interest in theoretical studies [27][28][29][30][31][32][33][34][35][36].In this vein, the existence of bright solitons in systems with purely repulsive, alias self-defocusing (SDF) nonlinearity, in the absence of external linear potentials, was recently predicted [37]. This result is intriguing because the existence of such solutions, supported by SDF-only nonlinearities, without the help of a linear potential, was commonly considered impossible. In the setting introduced in Ref.[37], the system is described by a nonlinear Schrödinger (NLS) equation with the SDF cubic term, whose strength increases in space rapidly enough towards the periphery. The discovery of bright solitons in this setting has ushered studies of solitary modes in other models with spatially growing repulsive nonlinearities, both local [38][39][40][41][42][43] and nonlocal [44]. More specifically, in Ref. [38] it was demonstrated that spatially inhomogeneous

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