arXiv:1905.10320 · Physical Review A

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

G. Bougas, S. I. Mistakidis, Peter Schmelcher

Published Nov 4, 2019• 19 citations

Abstract

We investigate the quantum dynamics of two bosons, trapped in a two-dimensional harmonic trap, upon quenching arbitrarily their interaction strength and 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 wave function, 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 wave function in both real and momentum space, and the Tan contact, which unveils the existence of short range two-body correlations. When the system is initialized in its bound state, it is perturbed in the most efficient manner as compared to any other initial configuration. Moreover, starting from an interacting ground state, the two-boson response is enhanced for quenches toward the noninteracting limit.

DOI: 10.1103/physreva.100.053602

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