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The Journal of Chemical Physics

Tripartite entanglement dynamics of vibrations in triatomic molecules

Liang-Jun Zhai, Yujun Zheng

Published Jun 17, 2016• 1 citation
Publisher

Abstract

In the present study, the dynamical behaviors of tripartite entanglement of vibrations in triatomic molecules are studied based on the Lie algebraic models of molecules. The dynamical behaviors of tripartite entanglement of the local mode molecule H2O and normal mode molecule NO2 are comparatively studied for different initial states by employing the general concurrence. Our results show that the dynamics of tripartite entanglement are relied on the dynamics of intramolecular energy distribution. The local mode molecule is more suitable to construct the tripartite entangled states. Also, the greater degree of tripartite entanglement can be obtained if the stretching vibration is first excited. These results shed new light on the understanding of quantum multipartite entanglement of vibrations in the polyatomic molecules.

DOI
10.1063/1.4953857

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The intramolecular energy transfer, dynamical entanglement of vibrations, and decoherence process in triatomic molecular systems are studied. The benchmark molecules of H2S{\mathrm{H}}_{2}\mathrm{S}H2​S, NO2{\mathrm{NO}}_{2}NO2​, and O3{\mathrm{O}}_{3}O3​ are sampled to investigate the intramolecular energy transfer and dynamical entanglement of stretching-stretching vibrational modes in triatomic molecular systems by restricting the bending vibration to its ground state. The comparative study is applied to explore the dynamical differences of initial local-mode and normal-mode characteristic states. Also, the decoherence process of the stretching-stretching qubits system caused by the bending vibration is discussed.
The dynamical entanglement of two stretching vibrations of triatomic molecules H2O{\mathrm{H}}_{2}\mathrm{O}H2​O and SO2\mathrm{S}{\mathrm{O}}_{2}SO2​ in an algebraic model is studied in terms of the reduced-density linear entropy with initial states that are, respectively, taken to be the product of Fock states and coherent states on each bond. It is shown that the entanglement of initial states with local-mode character is regular while that of states with normal-mode character is irregular. For initial coherent states with a small amplitude, the regularity of the entanglement with a long period appears in SO2\mathrm{S}{\mathrm{O}}_{2}SO2​ and ``classical'' beat phenomena of the entanglement happens in H2O{\mathrm{H}}_{2}\mathrm{O}H2​O, where the period of the beat is longer. Those long periods of the entanglement indicate that the entanglement sustains long enough so that quantum information process and quantum computation could be accomplished.
Quantum mutual information and concurrence are two important measures of quantum correlations, and their similar behavior for a bipartite pure state calls for inspecting whether such a behavior remains for a multipartite pure state. The dynamical correlation of quantum mutual information and tripartite entanglement is analytically and numerically studied for initial states, total boson numbers and coupling parameters in a symmetric trimer molecule, where the entanglement is measured in terms of concurrence. A correlation parameter is introduced to describe the correlation between mutual information and concurrence. It is shown that both quantities are positively or anti-correlated in irregular manner. However, they exhibit completely positive correlation for suitable states, with their explicit expressions being presented for arbitrary model parameters. The dynamical correlation between bipartite and tripartite entanglement is discussed as well. Those shed new light on the understanding of quantum correlations of vibrational states in polyatomic molecules.
In this Brief Report an improved u(2) algebraic model is proposed to study both stretching and bending vibrational spectra of a bent triatomic molecule. The model with fewer parameters is used to reproduce the observed spectra of hydrogen sulfide (H2{}_{2}2​S) with better precision than the u(4) algebraic model. Furthermore, the tripartite entanglement dynamics is investigated for vibrationally localized states in H2{}_{2}2​S. It is shown that the entanglement of a highly excited state in the bending mode displays better quasiperiodicity than that in the stretch. Those are useful for molecular vibrations and multipartite quantum entanglement.