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Teleportation of a weak coherent cavity field state
(2016) Cardoso, Wesley Bueno; Wen-Chao, Qiang; Avelar, Ardiley Torres
In this paper we propose a scheme to teleport a weak coherent cavity field state. The scheme relies on the resonant atom-field interaction inside a high-Q cavity. The mean photon-number of the cavity field is assumed much smaller than one, hence the field decay inside the cavity can be effectively suppressed.
Modulation of localized solutions in an inhomogeneous saturable nonlinear Schrödinger equation
(2017) Alves, Luciano Calaça; Cardoso, Wesley Bueno
In this paper we study the modulation of localized solutions by an inhomogeneous saturable nonlinear medium. Throughout an appropriate ansatz we convert the inhomogeneous saturable nonlinear Schrödinger equation in a homogeneous one. Then, via a variational approach we construct localized solutions of the autonomous equation and we present some modulation patterns of this localized structures. We have checked the stability of such solutions through numerically simulations.
Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation
(2017) Cardoso, Wesley Bueno; Salasnich, Luca; Malomed, Boris A.
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 stability 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 numerical results, a qualitatively correct description of the vortex solitons is provided by the Thomas-Fermi approximation.
Quasi-one-dimensional approximation for Bose–Einstein condensates transversely trapped by a funnel potential
(2019) Santos, Mateus Calixto Pereira dos; Malomed, Boris A.; Cardoso, Wesley Bueno
Starting from the standard three-dimensional (3D) Gross–Pitaevskii equation (GPE) and using a variational approximation, we derive an effective one-dimensional nonpolynomial Schrödinger equation (1D-NPSE) governing the axial dynamics of atomic Bose–Einstein condensates (BECs) under the action of a singular but physically relevant funnel-shaped transverse trap, i.e. an attractive 2D potential ∼−1/r (where r is the radial coordinate in the transverse plane), in combination with the repulsive self-interaction. Wave functions of the trapped BEC are regular, in spite of the potential's singularity. The model applies to a condensate of particles (small molecules) carrying a permanent electric dipole moment in the field of a uniformly charged axial thread, as well as to a quantum gas of magnetic atoms pulled by an axial electric current. By means of numerical simulations, we verify that the effective 1D-NPSE provides accurate static and dynamical results, in comparison to the full 3D GPE, for both repulsive and attractive signs of the intrinsic nonlinearity.
Anderson localization induced by interaction in linearly coupled binary Bose-Einstein condensates
(2021) Santos, Mateus Calixto Pereira dos; Cardoso, Wesley Bueno
In this paper we investigate the existence of Anderson localization induced by one specific component of a binary Bose-Einstein condensate (BEC). We use a mean-field approach, in which each type of particle of the BEC is considered as a specific field, and we consider that only one kind of particle is subject to a quasiperiodic potential, which induces a localization in the partner field. We assume the system is under a Rabi coupling, i.e., a linear coupling mixing the two-field component, and we investigate the conditions associated with the parameter values of the system for observing the localization. Numerical simulations are performed, confirming the existence of Anderson localization in the partner field.