Quantum Entanglement of Two Harmonically Trapped Dipolar Particles

Przemysław Kościk

doi:10.1007/s00601-015-0947-2

Abstract

We study systems of two identical dipolar particles confined in quasi one-dimensional harmonic traps. Numerical results for the dependencies of the entanglement on the control parameters of the systems are provided and discussed in detail. In the limit of a strong interaction between the particles, the occupancies and the von Neumann entropies of the bosonic and fermionic ground states are derived in closed analytic forms by applying the harmonic approximation. The strong correlation regimes of the system with the dipolar bosons and the system with the charged ones are compared with each other in regard to aspects of their entanglement.

Highlights

In recent years, systems of quasi one-dimensional (1D) systems of cold atoms with a short-range interaction have attracted considerable research attention
In the limit as → ∞ the system of bosons gets fermionized for any g = 0 [2,7], which is due to the singular behavior of the interaction potential |x2 − x1|−3 at x1 = x2
The above function is nothing else but a TG wavefunction, which means that the 1D dipolar bosons form a TG gas in the weak interaction regime

Summary

Introduction

Systems of quasi one-dimensional (1D) systems of cold atoms with a short-range interaction have attracted considerable research attention. We address this issue and gain some insight into the quantum entanglement properties of systems composed of two particles confined in a harmonic trap. The theoretical description of such quasi-1D systems can be simplified, since one can assume that the particles stay in the lowest transverse confinement mode and the single-mode approximation (SMA) can be applied Within this approximation, the system of four dipolar bosons in a trap of anisotropy of = 50 has recently been considered in [7], wherein the effects of the interaction strength on various characteristics (such as the density, the momentum distribution, and the occupation number distribution) have been determined. We discuss the effect of both the anisotropy parameter and the interaction strength g on the entanglement in the bosonic and fermionic ground states.

The Measure of Entanglement

The Weak-Interaction Limit

The Strong-Interaction Limit

Numerical Analysis

Summary