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Progress of Theoretical Physics

Lie Algebraic Approach to Dynamical Entanglement of Vibrations in Triatomic Molecules

Hao Feng, Ping Li, Yujun Zheng, Shiqian Ding

Published Feb 1, 2010• 9 citations
Publisher

Abstract

The relation between dynamics of quantum entanglement and dynamics of molecular vibrations is explored by the Lie-algebraic approach. The analytical expression of reduced-density matrices is obtained by using the algebraic model. The linear entropy, von Neumann entropy and the Lyapunov function are employed to measure the quantum entanglement for various initial states, respectively. The mean values of entropy and the Lyapunov function are also discussed.

DOI
10.1143/ptp.123.215

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Journal of Physics A Mathematical and Theoretical•Jan 21, 2009•7 citations
The relation between dynamics of quantum entanglement and dynamics of molecular vibrations is explored by the Lie-algebraic approach. The analytical expression of reduced-density matrices is obtained by using the algebraic model. The linear entropy, von Neumann entropy and the Lyapunov function are employed to measure the quantum entanglement for various initial states, respectively. The mean values of entropy and the Lyapunov function are also 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.
As an alternative with potential connections to actual experiments, other than the systems more usually used in the field of entanglement, the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well-established algebraic model, with parameters extracted from fitting to highly excited spectral experimental results for molecules H 2 O and SO 2 , is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode. For a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti-correlation. And the linear entropy of each mode is positively correlated with the negativities just for the mixed-squeezed states with small parameters in H 2 O while they do not display any correlation in other cases. For the mixed-squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy. The differences in the linear entropy and the negativities between H 2 O and SO 2 are discussed as well. Those are useful for molecular quantum computing and quantum information processing.