Modulated trapping of interacting bosons in one dimension

TL;DR

This paper studies how harmonically confined interacting bosons respond to trap modulations, revealing resonance structures and the effects of interactions on dynamics, using exact solutions for extreme cases and approximations for finite interactions.

Contribution

It provides a comprehensive analysis of resonant dynamics in trapped Lieb-Liniger gases, including exact solutions for extreme interaction regimes and a variational approach for finite interactions.

Findings

Resonance structures depend on driving frequency and interaction strength.

Strong interactions lead to exponential growth in size and energy oscillations.

Interactions modify resonance behavior in weakly driven systems.

Abstract

We investigate the response of harmonically confined bosons with contact interactions (trapped Lieb-Liniger gas) to modulations of the trapping strength. We explain the structure of resonances at a series of driving frequencies, where size oscillations and energy grow exponentially. For strong interactions (Tonks-Girardeau gas), we show the effect of resonant driving on the bosonic momentum distribution. The treatment is `exact' for zero and infinite interactions, where the dynamics is captured by a single-variable ordinary differential equation. For finite interactions the system is no longer exactly solvable. For weak interactions, we show how interactions modify the resonant behavior for weak and strong driving, using a variational approximation which adds interactions to the single-variable description in a controlled way.