A computational approach for investigating Coulomb interaction using Wigner–Poisson coupling

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.

A characteristic-spectral-mixed scheme for six-dimensional Wigner-Coulomb dynamics

“…The recently burgeoned developments in nano-science and semiconductors, such as the nano-wired FET at 3nm node, 1 as well as those in high energy density physics, 2 quantum tomography 3 and quantum optics, 4, 5 urgently demand efficient and highly accurate simulations of high-dimensional quantum models. Specifically, the Wigner equation 6 under the Coulomb interaction is of great importance in describing the non-equilibrium electron dynamics in quantum regime, including the electron-proton couplings in hot density matter, 2 the quantum entanglement in nano-wires, 7 the quantum tunneling effects in nanodevices, 8 strong-field atomic ionization processes 4,5 and visualization of quantum states, 9,10 owing to its huge advantage in calculating quantum statistics and experimental observability. 11 However, an investigation of realistic quantum systems in 3-D spatial space requires to solve the Wigner equation in 6-D phase space, so that the curse of dimensionality (CoD) poses a tremendous obstacle to its numerical resolution.…”

“…With these endeavors, we succeed in simulating 6-D Wigner-Coulomb dynamics of an electron wavepacket attracted by one or two protons. The solutions may help reveal the presence of electron-proton coupling, 2,7 uncertainty principle and quantum tunneling 33 in phase space.…”

Gate-Controlled Electron Quantum Interference Logic Devices

“…The fact that additional, specific current levels are available also in the remaining output channels provides a path towards parallelization as various logic operations can be realized in parallel. A particular attractive perspective is provided considering the recent advances towards two-electron sources: 4 The eQILD operation could be extended towards applications in entangletronics, 22,33,34 enabling the use of entanglement for non-local classical logic.…”

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

“…Benam et al introduced a computational approach for investigating Coulomb interaction using Wigner-Poisson coupling, thereby providing an option to investigate dynamic electron-electron entanglement [188]. The authors apply an approximation based on replacing the Wigner potential of the electron-electron interaction by a local electrostatic field, which is introduced through the spectral decomposition of the potential.…”