# Quench Dynamics of Two One-Dimensional Harmonically Trapped Bosons Bridging Attraction and Repulsion

## TL;DR

This paper investigates the nonequilibrium quantum dynamics of two one-dimensional bosons under harmonic confinement during interaction quenches between repulsive and attractive regimes, providing analytical solutions and identifying key eigenstates.

## Contribution

It derives a closed-form expression for the expansion coefficients of the time-evolved wavefunction and analyzes the dynamics using various reduced density matrices and spectral methods.

## Key findings

- Identification of dominant eigenstates governing the dynamics
- Signatures of higher-lying states triggered by the quench
- Analytical form of the expansion coefficients for the wavefunction

## Abstract

We unravel the nonequilibrium quantum dynamics of two harmonically confined bosons in one spatial dimension when performing an interaction quench from finite repulsive to attractive interaction strengths and vice versa. A closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction is derived, while its dynamics is determined in terms of an expansion over the postquench eigenstates. For both quench scenarios the temporal evolution is analyzed by inspecting the one- and two-body reduced density matrices and densities, the momentum distribution and the fidelity. Resorting to the fidelity spectrum and the eigenspectrum we identify the dominant eigenstates of the system that govern the dynamics. Monitoring the dynamics of the above-mentioned observables we provide signatures of the energetically higher-lying states triggered by the quench.