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arXiv:2204.06977 · Physical Review A

Long-range entanglement in quantum dots with Fermi-Hubbard physics

Sanaa Abaach, Mustapha Faqir, M. El Baz

Published Aug 22, 2022• 5 citations
arXivHTMLPDF

Abstract

The range of entanglement in quantum dots, under the effect of the Coulomb interaction and the system's size, is investigated. As ququart systems, naturally described by the Fermi-Hubbard model, we show that quantum dots supply long-range entanglement up to the third neighbor. In conjunction with that and using the lower bound of concurrence, we show that the Coulomb interaction can be adjusted to create and increase entanglement between distant parties as well. A rigorous description of the pairs is given in terms of a local half-filled state associated with each pair with an electron number $N=2$ and a spin $S=0$. A thorough study of this state provides a proper explanation related to the pairwise entanglement, namely, its amount and its behavior under the effect of the Coulomb interaction together with the system's size. In addition, we show that the confinement state of quantum dots is genuinely four-partite entangled with a maximum amount for the smallest size $L=4$.

DOI
10.1103/physreva.106.022421

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The range of entanglement in quantum dots, under the effect of the Coulomb interaction and the system's size, is investigated. As ququart systems, naturally described by the Fermi-Hubbard model, we show that quantum dots supply long-range entanglement up to the third neighbor. In conjunction with that and using the lower bound of concurrence, we show that the Coulomb interaction can be adjusted to create and increase entanglement between distant parties as well. A rigorous description of the pairs is given in terms of a local half-filled state associated with each pair with an electron number N=2N=2N=2 and a spin S=0S=0S=0. A thorough study of this state provides a proper explanation related to the pairwise entanglement, namely, its amount and its behavior under the effect of the Coulomb interaction together with the system's size. In addition, we show that the confinement state of quantum dots is genuinely four-partite entangled with a maximum amount for the smallest size L=4L=4L=4.
We investigate the entanglement properties in semiconductor quantum dot systems modeled by the extended Hubbard model, focusing on the impacts of potential energy variations and electron interactions within a four-site quantum dot spin chain. Our study explores local and pairwise entanglement across configurations with electron counts N=4 and N=6, under different potential energy settings. By adjusting the potential energy in specific dots and examining the entanglement across various interaction regimes, we identify significant variations in the ground states of quantum dots. We extend this analysis to larger systems with L=6 and L=8, comparing electron counts N=L and N=L+2, revealing sharper entanglement transitions and reduced finite-size effects as the system size increases. Our results show that local potential shifts and the Coulomb interaction strength lead to notable redistributions of the electron configurations in the quantum dot spin chain, significantly affecting the entanglement properties. These changes are depicted in phase diagrams that highlight entanglements' dependencies on the interaction strengths and potential energy adjustments, illustrating complex entanglement dynamics shifts triggered by interdot interactions.
The long distance entanglement in finite size open Fermi-Hubbard chains, together with the end-to-end quantum teleportation are investigated. We show the peculiarity of the ground state of the Fermi-Hubbard model to support maximum long distance entanglement, which allows it to operate as a quantum resource for high fidelity long distance quantum teleportation. We determine the physical properties and conditions for creating scalable long distance entanglement and analyze its stability under the effect of the Coulomb interaction and the hopping amplitude. Furthermore, we show that the choice of the measurement basis in the protocol can drastically affect the fidelity of quantum teleportation and we argue that perfect information transfer can be attained by choosing an adequate basis reflecting the salient properties of the quantum channel, i.e. Hubbard projective measurements.
The long distance entanglement in finite size open Fermi-Hubbard chains, together with the end-to-end quantum teleportation are investigated. We show the peculiarity of the ground state of the Fermi-Hubbard model to support maximum long distance entanglement, which allows it to operate as a quantum resource for high fidelity long distance quantum teleportation. We determine the physical properties and conditions for creating scalable long distance entanglement and analyze its stability under the effect of the Coulomb interaction and the hopping amplitude. Furthermore, we show that the choice of the measurement basis in the protocol can drastically affect the fidelity of quantum teleportation and we argue that perfect information transfer can be attained by choosing an adequate basis reflecting the salient properties of the quantum channel, i.e. Hubbard projective measurements.
We investigate the Hubbard model, and the extended Hubbard model with and without correlated hopping, as an approximation to the average single-site (or local) entanglement of two-electron one-dimensional quantum dot chains with long range interactions. We focus on the effect of the chain length on the approximation accuracy. We also consider the particle-particle spatial entanglement of the three Hubbard models using the technique of Ref. [3] and compare the accuracy of this approximation to the numerically exact results of the nanostructure system.
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Strongly interacting electron systems can provide insight into quantum many-body phenomena, such as Mott insulating behavior and spin liquidity, facilitating semiconductor optimization. The Fermi-Hubbard model is the prototypical model used to study such systems. Recent research, however, has shown that the extended Fermi-Hubbard model, which accounts for long-range interactions, is more accurate, especially for systems far from half-filling. In this study, we use the extended Fermi-Hubbard model to mathematically analyze charge transport through a lattice of quantum dots. One-dimensional chains with spinless electrons and source-drain bias are observed, focusing on the transition between the ground state and the first excited state. Level repulsion decreases the expected energy levels of anticrossings as the hopping onto the chain tends to the hopping within the chain. The distribution of charge density along the chain is characterized in terms of the hopping, nuclear, and Coulomb parameters and novel plasmonic behavior is analyzed. Minor perturbations in electron transport are identified, corresponding to the one-dimensional nature of the observed systems. This research will lead to a better understanding of electron behavior in silicon-doped semiconductors, like the formation of correlation-induced band gaps, and open the door to using the extended Fermi-Hubbard model as a more accurate alternative to study quantum many-body systems.