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arXiv:1804.01123 · Physical Review A

Quantum entanglement driven by electron-vibrational mode coupling

Fabricio Macedo de Souza, P. A. Oliveira, L. Sanz

Published Oct 14, 2019• 19 citations
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Abstract

In this work, we show how electron-vibrational mode coupling can be used to drive maximally entangled states. The physical system consists of two pairs of quantum dots, each pair with a single electron able to tunnel between the dots, thus encoding a qubit. The electron-vibrational mode coupling, described by the strength parameter $g$, yields to an effective electron-electron interaction, responsible for the formation of a maximally entangled quantum state. Both the formation time and the relative phase of the aforementioned state are strongly dependent on $g$. The quantum dynamics exhibits a nonmonotonic behavior as $g$ increases, an effect explained through an effective Hamiltonian that takes into account high-order transition processes.

DOI
10.1103/physreva.100.042309

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In this work, we show how electron-vibrational mode coupling can be used to drive maximally entangled states. The physical system consists of two pairs of quantum dots, each pair with a single electron able to tunnel between the dots, thus encoding a qubit. The electron-vibrational mode coupling, described by the strength parameter ggg, yields to an effective electron-electron interaction, responsible for the formation of a maximally entangled quantum state. Both the formation time and the relative phase of the aforementioned state are strongly dependent on ggg. The quantum dynamics exhibits a nonmonotonic behavior as ggg increases, an effect explained through an effective Hamiltonian that takes into account high-order transition processes.
We theoretically investigate the formation of W states in a tripartite system composed of three charge qubits coupled to vibrational modes. The electromechanical coupling is responsible for second-order virtual processes that result in an effective electron-electron interaction between neighbor qubits, which leads to the formation of W states. Based on the Lang-Firsov transformation and perturbation theory, we analytically solve the quantum dynamics, providing a mathematical expression for the maximally entangled W state. Dephasing is also taken into account, paying particular attention to the robustness of bipartite entanglement against local dephasing processes.
We theoretically investigate the formation of WWW states in a tripartite system composed of three charge qubits coupled to vibrational modes. The electromechanical coupling is responsable for second order virtual processes that result in an effective electron-electron interaction between neighbor qubits, which yields to the formation of WWW states. Based on the Lang-Firsov transformation and perturbation theory, we analytically solve the quantum dynamics, providing a mathematical expression for the maximally entangled WWW state. Dephasing is also taken into accout, paying particular attention on the robustness of bipartite entanglement against local dephasing processes.
In this paper, we present a proof of principle of the formation of pure maximally entangled states from the Greenberger-Horne-Zeilinger (GHZ) class, in the experimental context of charged quantum dots. Each qubit must be identified as a pair of quantum dots, sharing an excess electron, coupled by tunneling. The electron-electron interaction is accounted for and is responsible for the coupling between the qubits. The interplay between coherent tunneling events and many-body interaction gives rise to the formation of highly entangled states. We begin by treating the problem of encoding three qubits in a system with three pairs of quantum dots, and the numerical analysis of the exact quantum dynamics to find the conditions for the generation of the GHZ states. An effective two-level model sheds light on the role of a high-order tunneling process behind the dynamics. The action of the main decoherence process, the charge dephasing, is quantified in the process. We then evaluate the physical requirements for the dynamical generation of GHZ states in an NNN-qubit scenario, and its challenges.
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