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The Journal of Atomic and Molecular Sciences

Dynamics of Bipartite Vibrational Entanglement under the Inherent Decoherence Process in $H_2O$

Yuanyuan Cheng, Liang-Jun Zhai

Published Jul 1, 2016• 2 citations
Publisher

Abstract

In present study, the dynamics of stretching-stretching and stretching-bending entanglement in $H_2O$ are studied with considering the inherent decoherence process. It is shown that the excitation in the bending vibration can lead to the decrease of the generation rate of stretching-stretching entanglement for the non-superposed state and the degeneration of entanglement for the initial entangled states. For specific initial entangled states, the stretching-stretching entanglement can live for a long time, and the correspondence between energy transfer and entanglement is still maintained for the initial local mode states. For the stretching-bending vibrations, the stretching-bending entanglement is much lower than the stretching-stretching vibration, and the degeneration rate of stretching-bending entanglement is higher than that of the stretching-stretching entanglement. The excitation in the remaining stretching vibration can induce a higher degree of stretching-bending entanglement.

DOI
10.4208/jams.061616.081016a

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Dynamics of Bipartite Vibrational Entanglement under the Inherent Decoherence Process in H2OH_2OH2​O
In present study, the dynamics of stretching-stretching and stretching-bending entanglement in H2OH_2OH2​O are studied with considering the inherent decoherence process. It is shown that the excitation in the bending vibration can lead to the decrease of the generation rate of stretching-stretching entanglement for the non-superposed state and the degeneration of entanglement for the initial entangled states. For specific initial entangled states, the stretching-stretching entanglement can live for a long time, and the correspondence between energy transfer and entanglement is still maintained for the initial local mode states. For the stretching-bending vibrations, the stretching-bending entanglement is much lower than the stretching-stretching vibration, and the degeneration rate of stretching-bending entanglement is higher than that of the stretching-stretching entanglement. The excitation in the remaining stretching vibration can induce a higher degree of stretching-bending entanglement.
The dynamics of stretching–stretching (SS) and stretching–bending (SB) entanglement in the normal mode molecule SO2 are studied by the Lie algebraic method. The influence of the decoherence from the remaining vibrational mode is considered. We have found that SS vibrations can achieve a higher degree of entanglement than the SB vibrations, and the degeneration rate of SB entanglement is higher than the SS entanglement. By the comparative study, the SS vibrations are found to be more suitable to construct a biqubit system rather than the stretching–bending vibrations. © 2014 Wiley Periodicals, Inc.
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 dynamics of quantum entropy, energy, and entanglement is studied for various initial states in an important spectroscopic Hamiltonian of bent triatomic molecules H2O, D2O, and H2S. The total quantum correlation is quantified in terms of the mutual information and the entanglement by the concurrence borrowed from the theory of quantum information. The Pauli entropy and the intramolecular energy usually used in the theory of molecules are calculated to establish a possible relationship between both theories. Sections of two quantities among these four quantities are introduced to visualize such relationship. Analytic and numerical simulations demonstrate that if an initial state is taken to be the stretch- or the bend-vibrationally localized state, the mutual information, the Pauli entropy, and the concurrence are dominant-positively correlated while they are dominantly anti-correlated with the interacting energy among three anharmonic vibrational modes. In particular, such correlation is more distinct for the localized state with high excitations in the bending mode. The nice quasi-periodicity of those quantities in D2O molecule reveals that this molecule prepared in the localized state in the stretching or the bending mode can be more appreciated for molecular quantum computation. However, the dynamical correlations of those quantities behave irregularly for the dislocalized states. Moreover, the hierarchy of the mutual information and the Pauli entropy is explicitly proved. Quantum entropy and energy in every vibrational mode are investigated. Thereby, the relation between bipartite and tripartite entanglements is discussed as well. Those are useful for the understanding of quantum correlations in high-dimensional states in polyatomic molecules from quantum information and intramolecular dynamics.
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.
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.
The dynamics of quantum entanglement described by the von Neumann entropy is studied for the localized states of Fermi-resonance coupling vibrations in molecule CS2, where the interacting energy between the stretching and the bending modes is considered to establish a connection between entanglement and energy. It is shown that entanglement reveals dominant anti-correlation with the interacting energy for the stretch-localized state, while that exhibits dominantly positive correlation for the bend-localized state. The entanglement and the energy for the dislocalized states are discussed as well. Those are useful for molecular quantum computing and quantum information in high dimensional states.