Controlling soliton interactions in Bose-Einstein condensates by synchronizing the Feshbach resonance and harmonic trap

TL;DR

This paper demonstrates how to precisely control soliton interactions in Bose-Einstein condensates by synchronizing Feshbach resonance tuning with harmonic trap modulation, enabling detailed manipulation of soliton dynamics.

Contribution

It introduces a method to control soliton interactions by synchronizing magnetic field modulation and trap frequency changes, providing exact solutions for the nonlinear Schrödinger equation.

Findings

Exact solutions for modulated soliton interactions are derived.

Control protocols for phenomena like fusion, fission, and oscillation are proposed.

Experimental conditions for observing these effects are outlined.

Abstract

We present how to control interactions between solitons, either bright or dark, in Bose-Einstein condensates by synchronizing Feshbach resonance and harmonic trap. Our results show that as long as the scattering length is to be modulated in time via a changing magnetic field near the Feshbach resonance, and the harmonic trapping frequencies are also modulated in time, exact solutions of the one-dimensional nonlinear Schr\"{o}dinger equation can be found in a general closed form, and interactions between two solitons are modulated in detail in currently experimental conditions. We also propose experimental protocols to observe the phenomena such as fusion, fission, warp, oscillation, elastic collision in future experiments.