Time-optimal variational control of bright matter-wave soliton

TL;DR

This paper develops a time-optimal control method for manipulating bright matter-wave solitons in a harmonic trap by adjusting atomic interactions, aiming to minimize transition time while avoiding heating and atom loss.

Contribution

It introduces a combined variational and optimal control approach to design smooth, time-efficient control protocols for matter-wave solitons in experimental settings.

Findings

Derived motion equations for soliton shape dynamics.

Designed smooth, time-optimal control protocols.

Reduced heating and atom loss in practical implementations.

Abstract

Motivated by recent experiments, we present the time-optimal variational control of bright matter-wave soliton trapped in a quasi-one-dimensional harmonic trap by manipulating the atomic attraction through Feshbach resonances. More specially, we first apply a time-dependent variational method to derive the motion equation for capturing the soliton's shape, and secondly combine inverse engineering with optimal control theory to design the atomic interaction for implementing time-optimal decompression. Since the time-optimal solution is of bang-bang type, the smooth regularization is further adopted to smooth the on-off controller out, thus avoiding the heating and atom loss, induced from magnetic field ramp across a Feshbach resonance in practice.