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International Conference on Applications of Optics and Photonics

Pinching optical potentials for spatial nonlinearity management in Bose-Einstein condensates

Nuno A. Silva, João C. Costa, Miguel Gomes, Rúben Azinheira Alves, Ariel Guerreiro

Published Aug 22, 2017• 0 citations
Publisher

Abstract

Here we explore the possibility of controlling the inhomogeneities in quasi-1D Bose-Einstein condensates using a spatial variation of the transverse confinement potential and explore different optical strategies to realize these pinched traps. Furthermore, we also present some early stage results on the dynamics of matter-wave solitons in such systems using computational simulations of the full 3D Gross-Pitaevskii equation.

DOI
10.1117/12.2272062

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We study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose–Einstein condensate by including an imaginary three-body recombination loss term and an imaginary linear feeding one in the Gross–Pitaevskii equation, trapped in a shallow optical-lattice potential. Based on the direct approach of perturbation theory for the nonlinear Schrödinger equation, we demonstrate that the height (as well as width) of bright soliton may have little change through selecting experimental parameters.
This work presents a dimensional reduction of Bose-Einstein condensates confined by generalized transverse potentials, parametrized by an exponent n . Starting from the three-dimensional Gross-Pitaevskii equation, we employ a variational ansatz to derive an effective one-dimensional nonpolynomial Schrödinger equation, which self-consistently determines the transverse width dynamics. The model generalizes existing formalisms for harmonic and funnel-shaped transverse confinement potentials. We validate the approach through comprehensive numerical tests, demonstrating excellent agreement with full 3D simulations for ground-state properties across various interaction regimes. Finally, real-time simulations of matter-wave scattering at potential barriers verify the model’s dynamical robustness, successfully replicating the spatiotemporal evolution and energy-dependent transmission characteristics observed in full 3D calculations.
The mean-field dynamics of Bose-Einstein condensates loaded in an optical lattice, confined by a parabolic potential, and subjected to a change of scattering length by means of the Feshbach resonance is considered. The system is described by the Gross-Pitaevskii (GP) equation with varying nonlinearity, which in a number of cases is reduced to one-dimensional (1D) perturbed nonlinear Schr\"odinger (NLS) equations, the particular form of which depends on the relation among the parameters of the problem. We analytically describe the adiabatic dynamics of periodic solutions of the respective NLS equations, provide a numerical study of 1D models confined by a parabolic trap, and carry out numerical simulations of the matter-wave dynamics within the framework of the radially symmetric 3D GP equation. Special attention is paid to processes of generation of trains of bright and dark matter solitons from initially periodic waves. The results of the 1D approximation are compared with direct numerical simulation of the original 3D GP eqation, showing remarkable coincidence for definite regions of parameters.
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