Coulomb Interaction-Driven Entanglement of Electrons on Helium

Niyaz R. Beysengulov, Øyvind S. Schøyen, Stian D. Bilek, Jonas B. Flaten, Oskar Leinonen, Morten Hjorth-Jensen, Johannes Pollanen, Håkon Emil Kristiansen, Zachary J. Stewart, Jared D. Weidman, Angela K. Wilson
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Abstract

The generation and evolution of entanglement in many-body systems is an active area of research that spans multiple fields, from quantum information science to the simulation of quantum many-body systems encountered in condensed matter, subatomic physics, and quantum chemistry. Motivated by recent experiments exploring quantum information processing systems with electrons trapped above the surface of cryogenic noble gas substrates, we theoretically investigate the generation of motional entanglement between two electrons via their unscreened Coulomb interaction. The model system consists of two electrons confined in separate electrostatic traps that establish microwave-frequency quantized states of their motion. We compute the motional energy spectra of the electrons, as well as their entanglement, by diagonalizing the model Hamiltonian with respect to a single-particle Hartree product basis. We also compare our results with the predictions of an effective Hamiltonian. The computational procedure outlined here can be employed for device design and guidance of experimental implementations. In particular, the theoretical tools developed here can be used for fine-tuning and optimization of control parameters in future experiments with electrons trapped above the surface of superfluid helium or solid neon.

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库仑相互作用驱动的氦上电子纠缠
多体系统中纠缠的产生和演化是一个活跃的研究领域,它横跨多个领域,从量子信息科学到凝聚态、亚原子物理和量子化学中遇到的量子多体系统的模拟。受最近探索电子被困在低温惰性气体基底表面上方的量子信息处理系统实验的启发,我们从理论上研究了两个电子之间通过非屏蔽库仑相互作用产生的运动纠缠。模型系统由两个电子组成,它们分别被限制在不同的静电陷阱中,并建立了微波频率的量子化运动状态。我们通过对模型哈密顿进行对角化,在单粒子哈特里乘积的基础上计算出电子的运动能谱以及它们之间的纠缠。我们还将结果与有效哈密顿的预测进行了比较。本文概述的计算过程可用于设备设计和指导实验实施。特别是,在未来的超流体氦或固体氖表面上方电子被困实验中,这里开发的理论工具可用于微调和优化控制参数。
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