Entanglement in interacting quenched two-body coupled oscillator system

TL;DR

This paper analytically and numerically investigates how a quantum quench affects entanglement in a two-body coupled oscillator with quartic interaction, revealing behavior across different time regimes and coupling strengths.

Contribution

It provides analytical expressions for entanglement measures in a non-Gaussian, interacting system using the invariant operator method under perturbation.

Findings

Entanglement entropy varies significantly across different time regimes.

Analytical formulas for von Neumann and Renyi entropies are derived.

Entanglement measures depend on coupling strength and quench parameters.

Abstract

In this work, we explore the effects of a quantum quench on the entanglement measures of a two-body coupled oscillator system having quartic interaction. We use the invariant operator method, under a perturbative framework, for computing the ground state of this system. We give the analytical expressions for the total and reduced density matrix of the system having non-Gaussian, quartic interaction terms. Using this reduced density matrix, we show the analytical calculation of two entanglement measures viz., Von Neumann entanglement entropy using replica trick and Renyi entanglement entropy. Further, we give a numerical estimate of these entanglement measures with respect to the dimensionless parameter $(t/\delta t$) and show its behaviour in the three regimes, i.e; late time behaviour, around the quench point and the early time behaviour. We comment on the variation of these entanglement measures for different orders of coupling strength. The variation of Renyi entropy of different orders has also been discussed.