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Europhysics Letters (EPL)

Vibrational effects on the formation of quantum W states

H. G. Mendonça, Fabricio Macedo de Souza

Published May 1, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/134/40001

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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 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.
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.
We examine the impact of time-dependent gate voltages on entanglement generation in two capacitively coupled charge qubits, with single-electron injection triggered on demand. The gate voltage modulates the tunnel coupling between the qubits and electronic reservoirs, initiating charge transport into the system. The formation of entangled states arises from the competition between interqubit Coulomb interactions and electron-hopping processes. Particular attention is paid to the temporal structure of the gate pulse, which plays a pivotal role in shaping the entanglement dynamics. By exploring a variety of pulse profiles, we uncover regimes of enhanced entanglement and identify optimal driving conditions. Additionally, we investigate how environmental dephasing deteriorates entanglement formation. Within the framework of the density-matrix formalism, we calculate fidelity, linear entropy, and negativity to identify robust operational windows. These results provide insights into controlling quantum correlations in mesoscopic systems and underscore the importance of error-mitigation strategies in realizing high-performance electronic quantum devices.
Abstract The formation of entanglement between the electronic and vibrational subsystems of two interacting molecules localized between tunneling contact leads was theoretically analyzed using the Keldysh diagram technique. The time evolution of concurrence after ‘switching on’ the coupling between the molecules was investigated. It was revealed that non-zero concurrence can be present in the system in the resonant case, even if the molecules are connected by the leads. It was also shown that the stationary value of concurrence can be directly expressed by the stationary tunneling current. It reveals non-monotonic behavior with increasing coupling between the molecule’s electronic states. In the regime of small tunneling rates between the molecules and the leads, ‘switching on and off’ the coupling between molecules multiple times, while detecting one of the molecules’ charge states after each ‘on’ and ‘off’ cycle, results in the appearance of non-classical phonon statistics and opens the possibility of creating a vibrational mode in a Fock state.
In the present work we theoretically analyze the emergence appearance of entanglement between electronic and vibrational states in a system of two coupled molecules after switching on the interaction between them. In the framework of the adiabatic approach this effect appears because the equilibrium position of one of the molecules is sensitive to its electron occupation. The time evolution of the system shows multiple changes between its entangled and unentangled states. If this evolution starts from a pure coherent vibrational mode state and a state of a single electron localized in one of the molecules, the Schr\"odinger-cat states can appear during the system's time evolution. The Schr\"odinger-cat states can arise as a quantum superposition of distinct coherent states of molecule vibrational mode. Such states are entangled with empty and singly occupied electronic states of the molecule. The presence of entanglement between electronic and vibrational molecule states can be revealed by measuring the electron occupation (charge) of a particular molecule.