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arXiv:quant-ph/0610238 · Theoretical and Mathematical Physics

Entanglement of electrons in interacting molecules

Tina A. C. Maiolo, Fabio Della Sala, L. Martina, Giulio Soliani

Published Aug 1, 2007• 8 citations
arXivHTMLPDF
DOI
10.1007/s11232-007-0098-9

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In this thesis, we will analyze quantum entanglement phenomena in systems composed of quantum molecules, considering two different models. In the first, N molecules, each with a single excess electron, interact via Coulomb coupling. This interaction is restricted to the first neighbors. In the second system, electrons from distinct molecules interact with each other through the electron-phonon coupling. Considering the N-molecule system, we broadened our studies started in the master’s degree to verify the characteristics of the energy spectrum and eigenstates for the molecule system. We focus on the scalability of the system and its effect on entanglement, showing that some specific eigenstates are systematically associated with the maximally entangled GHZ states, regardless of the number of molecules. In the second part of the work, we explore the entanglement of both the electronic subsystem and the phonon subsystem, defining a new base composed of Bell’s electronic states associated with the excitation states in vibrational modes, which allows rewriting the Hamiltonian to the composite system. From this point of view, it is possible to determine a set of 4 ⊗ 4 matrix subspaces that elucidated the study of the entanglement behavior in both subsystems, allowing the determination of distinct sets of parameters effective in generating highly entangled states in the electronic subsystem and now in the phononic subsystem.
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.