Effective equations for repulsive quasi-1D BECs trapped with anharmonic transverse potentials

TL;DR

This paper derives effective 1D nonlinear Schrödinger equations for repulsive Bose-Einstein condensates in anharmonic traps, validated through numerical comparisons with full 3D models, enabling tailored 1D models via transverse confinement control.

Contribution

It introduces a method to derive accurate 1D equations for BECs in anharmonic traps, extending previous models and verified through numerical analysis.

Findings

Effective 1D equations match 3D results in various regimes.

Validation through numerical comparison of ground states and oscillations.

Control of transverse confinement influences 1D nonlinear model patterns.

Abstract

One-dimensional nonlinear Schr\"odinger equations are derived to describe the axial effective dynamics of cigar-shaped atomic repulsive Bose-Einstein condensates trapped with anharmonic transverse potentials. The accuracy of these equations in the perturbative, Thomas-Fermi, and crossover regimes were verified numerically by comparing the ground-state profiles, transverse chemical potentials and oscillation patterns with those results obtained for the full three-dimensional Gross-Pitaevskii equation. This procedure allows us to derive different patterns of 1D nonlinear models by the control of the transverse confinement.