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Physical Review A

Local management of the nonlinearity of Bose-Einstein condensates with pinched potentials

Ariel Guerreiro, Nuno A. Silva

Published Dec 5, 2016• 3 citations
Publisher

Abstract

We present a proposal for the local control of the nonlinearity in quasi-one-dimensional Bose-Einstein condensates induced by a local pinching of the transverse confining potential. We investigate the scattering of bright matter-wave solitons through a pinched potential using numerical simulations of the full three-dimensional Gross-Pitaevskii equation and the corresponding effective one-dimensional model with spatially varying nonlinearity.

DOI
10.1103/physreva.94.063602

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We present a proposal for the local control of the nonlinearity in quasi-one-dimensional Bose-Einstein condensates induced by a local pinching of the transverse confining potential. We investigate the scattering of bright matter-wave solitons through a pinched potential using numerical simulations of the full three-dimensional Gross-Pitaevskii equation and the corresponding effective one-dimensional model with spatially varying nonlinearity.
We present a controlling potential method for solving the three-dimensional Gross-Pitaevskii equation (GPE), which governs the nonlinear dynamics of the Bose-Einstein condensates (BECs) in an inhomogeneous potential trap. Our method allows one to construct ground and excited matter wave states whose longitudinal profiles can have bright solitons. This method provides the confining potential that filters and controls localized BECs. Moreover, it is predicted that, while the BEC longitudinal soliton profile is controlled and kept unchanged, the transverse profile may exhibit oscillatory breathers (the unmatched case) or move as a rigid body in the form of either coherent states (performing the Lissajous figures) or a Schrödinger cat state (matched case).
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.
An analytical study on the dynamics of bright solitons of Bose–Einstein condensates (BEC) with a time-varying atomic scattering length in a time-varying expulsive parabolic potential is presented. Exact solutions of the one-dimensional Gross–Pitaevskii equation are obtained. The results show that the bright soliton (including the higher-order bright soliton) can be compressed into a desired width and amplitude in a controllable manner by changing the scattering length and external potential. Furthermore, it is shown numerically that the present method is also efficient for the two-dimensional BEC's compression.
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.
We theoretically investigate the dynamics of a matter-wave soliton created in a harmonic potential, which is attractive in the transverse direction but expulsive in the longitudinal direction. This Bose-Einstein-condensate (BEC) bright soliton made of 7Li^{7}\mathrm{Li}7Li atoms has been observed in a recent experiment [Khaykovich et al., Science 296, 1290 (2002)]. We show that the nonpolynomial Schr\"odinger equation, an effective one-dimensional equation we derived from the three-dimensional Gross-Pitaevskii equation, is able to reproduce the main experimental features of this BEC soliton in an expulsive potential.