Entanglement dynamics of delocalized interacting particles

TL;DR

This paper investigates how engineered exchange symmetry affects entanglement dynamics in two distinguishable particles, revealing regimes where purity and coherence are significantly influenced by interaction strength and initial conditions.

Contribution

It introduces a scheme to continuously tune particle statistics from bosonic to fermionic using a phase parameter, uncovering how this impacts entanglement evolution.

Findings

Strong interactions suppress coherence in bound states.

Coherence grows linearly for particles on neighboring sites.

Tuning phase parameter reveals high-purity regions at intermediate interactions.

Abstract

Quantum entanglement in systems of identical particles is often obscured by the interplay between exchange-induced correlations and the operational framework used to define entanglement. To study the role of exchange statistics, we propose a scheme using two \textit{distinguishable} particles where an exchange symmetry is artificially engineered via a relative phase $\theta$ in the initial state. This approach allows continuous tuning from bosonic ($\theta = 0$) to fermionic ($\theta = \pi$) statistics. By monitoring the interplay between purity and coherence, we uncover distinct dynamical regimes dictated by the interaction strength $U$ and the phase $\theta$. For particles initially loaded in a bound state, strong $U$ suppresses coherence development by avoiding the scattering band, reducing the purity toward its minimum. For particles initially on neighboring sites, coherence grows linearly in time. While non-symmetric inputs feature a sharp purity reduction at intermediate $U$, due to the competition between bound and unbound states, symmetric initial conditions produce transient coherence bursts that significantly enhance the purity. More generally, tuning the phase $\theta$ reveals a high-purity region over a range of $\theta$ at intermediate interactions, with the purity collapsing to $1/2$ as $\theta$ approaches the fermionic limit. Our results show that the imposed statistics, or lack thereof, reshapes the entanglement dynamics and its response to the interaction $U$.