Related papers: Nonlinear Tight-Binding Approximation for Bose-Ein…
Employing a general variational method and perturbation theory, we derived explicit solutions for the description of one-dimensional two species Bose-Einstein condensates confined by a harmonic trap potential in an optical lattice. We…
We investigate the nonlinear dynamics of a combined system which is composed of a cigar-shaped Bose-Einstein condensate and an optical cavity. The two sides couple dispersively. This system is characterized by its nonlinearity: after…
We demonstrate that nonlinearity plays a constructive role in supporting the robustness of dynamical localization in a model which is discrete, in one dimension and continuous in the orthogonal one. In the linear regime, time-periodic…
We experimentally investigate the atom-optical delta-kicked harmonic oscillator for the case of nonlinearity due to collisional interactions present in a Bose-Einstein condensate. A Bose condensate of rubidium atoms tightly confined in a…
Using a set of general methods developed by Krotov [A. I. Konnov and V. A. Krotov, Automation and Remote Control, {\bf 60}, 1427 (1999)], we extend the capabilities of Optimal Control Theory to the Nonlinear Schr\"odinger Equation (NLSE).…
The Gross-Pitaevskii equation, or more generally the nonlinear Schr\"odinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the…
We present a comprehensive study of modulational instability (MI) in a binary Bose-Einstein condensate with spin-orbit coupling, confined to a deep optical lattice. The system is modeled by a set of discrete Gross-Pitaevskii equations.…
We study the response of a trapped Bose-Einstein condensate to a sudden turn-on of a rotating drive by solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and…
The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial…
We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schr{\"o}dinger type. While our computations relate to…
The paper studies the dynamics of a Bose-Einstein condensate loaded into a 1D parabolic optical lattice, and excited by a sudden shift of the lattice center. Depending on the magnitude of the initial shift, the condensate undergoes either…
This paper employs a Bose-Einstein condensates to simulate the dynamical response of bound electrons in a strongly oscillating pulsed laser field. We investigate the excitation dynamics of Bose-Einstein condensates with repulsive…
We introduce a two-dimensional (2D) discrete nonlinear Schr\"{o}dinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong…
A model of a Bose-Einstein condensate in a ring optical lattice with atomic dissipations applied at a stationary or at a moving location on the ring is presented. The localized dissipation is shown to generate and stabilize both stationary…
In this paper, we study the bound state analysis of a one dimensional nonlinear version of the Schr\"{o}dinger equation for the harmonic oscillator potential perturbed by a $\delta$ potential, where the nonlinear term is taken to be…
We study dynamical and energetic instabilities in the transport properties of Bloch waves for atomic multi-component Bose-Einstein condensates in optical lattices in the tight-binding limit. We obtain stability criteria analytically, as a…
We study the dynamics of nonlinear localized excitations (solitons) in two-dimensional (2D) Bose-Einstein condensates (BECs) with repulsive interactions, loaded into an optical lattice (OL), which is combined with an external parabolic…
We study normal modes propagating on top of the stable uniform background in arrays of dipolar Bose-Einstein condensate (BEC) droplets trapped in a deep optical lattice. Both the on-site mean-field dynamics of the droplets and their…
We study theoretically Bose-Einstein condensates with polarized dipolar interactions in anisotropic traps. We map the parameter space by varying the trap frequencies and dipolar interaction strengths and find an irregular-shaped region of…
Bloch oscillations of Bose-Einstein condensates realize sensitive matter-wave interferometers. We investigate the dynamics and stability of bright-soliton wave packets in one-dimensional tilted optical lattices with a modulated mean-field…