Entanglement in Bound States of Two Particles with a Localized Center-of-Mass Wave-Function

Abstract

We explore some entanglement-related features of systems consisting of two particles coupled through a central potential. We consider two types of systems, constituted by particles in one spatial dimension interacting through an attractive Dirac Delta potential, or through a harmonic quadratic potential. The degree of freedom corresponding to the system’s center of mass is either regarded as confined within a one dimensional box, or described by a localized Gaussian wave-packet. As a quantitative indicator of the degree of entanglement between the particles, we use the linear entropy of the one-particle marginal density matrix. In general, this quantity cannot be calculated analytically (except in some special cases related to the Harmonic interaction). Consequently, the linear entropy has to be evaluated numerically. Since the concomitant numerical problem consist in evaluating a multi-dimensional integral in four dimensions, the Monte Carlo integration method is an appropriate one for this task. We explore numerically how the system’s entanglement depends on the different interaction potentials, on the different types of confinement for the system’s center of mass, and on the associated parameters describing the size and geometry of the system.