Localized solutions of Lugiato-Lefever equations with focused pump

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too -- in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.Comment: 26 pages, 9 figures, accepted for publication in Scientific Report

Localized modes in quasi-2D Bose-Einstein condensates with spin-orbit and Rabi couplings

We consider a two-component pancake-shaped, i.e., effectively two-dimensional (2D), Bose-Einstein condensate (BEC) 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 Schr\"odinger 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 Schr\"odinger 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.Comment: 8 pages, 9 figures - Physical Review A, in pres

Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation

We study effects of tight harmonic-oscillator confinement on the electromagnetic field in a laser cavity by solving the two-dimensional Lugiato-Lefever (2D LL) equation, taking into account self- focusing or defocusing nonlinearity, losses, pump, and the trapping potential. Tightly confined (quasi-zero-dimensional) optical modes (pixels), produced by this model, are analyzed by means of the variational approximation, which provides a qualitative picture of the ensuing phenomena. This is followed by systematic simulations of the time-dependent 2D LL equation, which reveal the shape, stability, and dynamical behavior of the resulting localized patterns. In this way, we produce stability diagrams for the expected pixels. Then, we consider the LL model with the vortical pump, showing that it can produce stable pixels with embedded vorticity (vortex solitons) in remarkably broad sta- bility areas. Alongside confined vortices with the simple single-ring structure, in the latter case the LL model gives rise to stable multi-ring states, with a spiral phase field. In addition to the numeri- cal results, a qualitatively correct description of the vortex solitons is provided by the Thomas-Fermi approximation.Comment: 11 pages, 15 figures, Eur. Phys. Journal D, in press (Topical Issue "Theory and Applications of the Lugiato-Lefever Equation"

Teleportation of entangled states without Bell-state measurement

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