# Analytical treatment of the interaction quench dynamics of two bosons in a two-dimensional harmonic trap

## TL;DR

This paper provides an exact analytical study of the quantum dynamics of two bosons in a 2D harmonic trap after interaction quenches, revealing detailed behaviors of correlations and system responses.

## Contribution

It introduces a closed-form analytical solution for the postquench wavefunction expansion coefficients in a 2D bosonic system, enabling detailed dynamical analysis.

## Key findings

- Bound state initialization leads to the most efficient perturbation.
- Response is enhanced when quenching towards the non-interacting limit.
- Short-range two-body correlations are unveiled through Tan contact analysis.

## Abstract

We investigate the quantum dynamics of two bosons, trapped in a two-dimensional harmonic trap, upon quenching arbitrarily their interaction strength thereby covering the entire energy spectrum. Utilizing the exact analytical solution of the stationary system we derive a closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction, whose dynamics is determined by an expansion over the postquench eigenstates. The emergent dynamical response of the system is analyzed in detail by inspecting several observables such as the fidelity, the reduced one-body densities, the radial probability density of the relative wavefunction in both real and momentum space as well as the Tan contact unveiling the existence of short range two-body correlations. It is found that when the system is initialized in its bound state it is perturbed in the most efficient manner compared to any other initial configuration. Moreover, starting from an interacting ground state the two-boson response is enhanced for quenches towards the non-interacting limit.