Entanglement, coherence and correlation in atomic and molecular systems (2020)
ABSTRACT: In the present work, we have computed the entanglement between the electronic and nuclear motions in two molecular model systems: the one-dimensional hydrogen molecular ion (H2+) and the Shin-Metiu model, considering the molecules as a bipartite systems: electron and nuclear motion. For that purpose, we have computed the Born-Oppenheimer and non-Born-Oppenheimer (Born-Huang) wave function in terms of the Fourier Grid Hamiltonian basis that expands both the electronic and nuclear wave functions. Also, according to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, there is a much shorter but equivalent expansion in terms of the Schmidt bases for the electronic and nuclear sub-spaces. In these models of distinguishable coupled particles we have shown that the entanglements contents do not increase monotonically with the excitation energy. In the hydrogen molecular ion and in the ShinMetiu model, the entanglements contents for each Born-Oppenheimer electro-nuclear state is quantified through the von-Neumann and linear entropies and we have shown that entanglement serves as a witness of distinguishability of nuclear states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes.