Coherent control of nonlinear mode transitions in Bose-Einstein condensates

TL;DR

This paper demonstrates how to coherently control the formation of excited nonlinear modes in Bose-Einstein condensates by manipulating potential and scattering length modulations, revealing new possibilities beyond traditional Schrödinger dynamics.

Contribution

It introduces a method to control nonlinear mode transitions in BECs through phase manipulation of modulations, combining analytical and numerical approaches.

Findings

Coherent control of nonlinear modes is achievable via phase manipulation.

Using combined modulations can alter transition speeds.

The approach offers new control possibilities not present in linear quantum systems.

Abstract

We investigate the formation of non-ground-state Bose-Einstein condensates within the mean-field description represented by the Gross-Pitaevskii equation (GPE). The objective is to form excited states of a condensate known as nonlinear topological modes, which are stationary solutions of the GPE. Nonlinear modes can be generated by modulating either the trapping potential or the atomic scattering length. We show that it is possible to coherently control the transitions to excited nonlinear modes by manipulating the relative phase of the modulations. In addition, we show that the use of both modulations can modify the speed of the transitions. In our analysis, we employ approximate analytical techniques, including a perturbative treatment, and numerical calculations for the GPE. Our study evidences that the coherent control of the GPE presents novel possibilities which are not accessible for the Schr\"odinger equation.