A computational approach for investigating Coulomb interaction using Wigner\u2013Poisson coupling

Majid Benam,Josef Weinbub,Mauro Ballicchia,Mihail Nedjalkov,Siegfried Selberherr

doi:10.1007/s10825-020-01643-x

Majid Benam, Josef Weinbub + Show 3 more

Open Access

https://doi.org/10.1007/s10825-020-01643-x

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Abstract

Entangled quantum particles, in which operating on one particle instantaneously influences the state of the entangled particle, are attractive options for carrying quantum information at the nanoscale. However, fully-describing entanglement in traditional time-dependent quantum transport simulation approaches requires significant computational effort, bordering on being prohibitive. Considering electrons, one approach to analyzing their entanglement is through modeling the Coulomb interaction via the Wigner formalism. In this work, we reduce the computational complexity of the time evolution of two interacting electrons by resorting to reasonable approximations. In particular, we replace the Wigner potential of the electron–electron interaction by a local electrostatic field, which is introduced through the spectral decomposition of the potential. It is demonstrated that for some particular configurations of an electron–electron system, the introduced approximations are feasible. Purity, identified as the maximal coherence for a quantum state, is also analyzed and its corresponding analysis demonstrates that the entanglement due to the Coulomb interaction is well accounted for by the introduced local approximation.

Highlights

Collective phenomena such as Coulomb interaction play a dominant role in determining the behaviour of classical microelectronic devices [1]
We have investigated the effect of Coulomb interaction in the evolution of two electrons in a 2D quantum wire through the use of the computationally affordable Wigner formalism
The spectral decomposition of the input potential into a slowly varying classical component and a rapidly varying quantum mechanical component is analyzed in order to minimize the computational burden

Summary

Introduction

Collective phenomena such as Coulomb interaction play a dominant role in determining the behaviour of classical microelectronic devices [1]. In the considered case of a Coulomb entangler [10], the Wigner potential, which in this two-electron case depends on 2 × 6 ( , , ) arguments for 2D structures, must be updated during the evolution in timesteps of the order of one femtosecond This gives rise to an enormous computational effort and motivates the development of approximative methods. We present a computationally efficient approach for a Wigner–Poisson coupled scheme in order to investigate the evolution of interacting electrons For this purpose, it is important to inspect conditions which allow adjusting the non-locally acting Wigner potential (the electron–electron Coulomb interaction) to a local action of the electric force.

Computational problem

Wigner potential decomposition

Coulomb entangler

Conclusions