Quantum dynamics of two trapped bosons following infinite interaction quenches

TL;DR

This paper analyzes the quantum dynamics of two bosons in a one-dimensional trap after sudden changes in interaction strength, providing analytical solutions and exploring the crossover between bosonic and fermionic behaviors.

Contribution

It offers the first analytical solutions for the wave function and Loschmidt Echo after interaction quenches in a two-boson system, revealing crossover phenomena.

Findings

Wave function and Loschmidt Echo are analytically derived.

Crossover between bosonic and fermionic properties observed.

Dynamics of momentum distribution and density matrix analyzed.

Abstract

We investigate the quantum dynamics of two identical bosons in a one-dimensional harmonic trap following an interaction quench from zero to infinite interaction strength and vice versa. For both quench scenarios, closed analytical expressions for the temporal evolution of the wave function as well as the Loschmidt Echo are found and the dynamics of the momentum distribution as well as the reduced single-particle density matrix are analyzed. We observe a crossover of these quantities between bosonic, "symmetrized" fermionic and fermionic properties. Furthermore, several combined quenches are analyzed as well.