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Physical Review A

Dynamical entanglement of vibrations in small molecules through an analytically algebraic approach

Yan Liu, Yujun Zheng, Weiyi Ren, Shiliang Ding

Published Sep 30, 2008• 30 citations
Publisher

Abstract

We study the dynamical entanglement of vibrations in small molecules by employing algebraic models. We analytically obtain the linear entropy, von Neumann entropy, and the Lyapunov function for the integrable dimer and realistic small molecules for both initial Fock states and coherent states. The contributions of states to the dynamical entropy are also investigated.

DOI
10.1103/physreva.78.032523

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We study the dynamical entanglement of vibrations in small molecules by employing algebraic models. We analytically obtain the linear entropy, von Neumann entropy, and the Lyapunov function for the integrable dimer and realistic small molecules for both initial Fock states and coherent states. The contributions of states to the dynamical entropy are also investigated.
By means of the reduced-density linear entropy, we investigate the properties of dynamical entanglement of vibrations in integrable dimer and realistic small molecules which are initially in the two-mode squeezed vacuum state. It is found that the entropy of the integrable dimer is periodic for weak coupling strength c 1 and small squeezing parameter r, and there exists a beat phenomenon for strong c 1 and large r. Moreover, the entropy of the small molecules is quasi-periodic for small r, and the beat phenomenon occurs in the entropy evolution of the two molecules C 2 D 2 and SO 2 for large r. Our results might be used for molecular quantum computing based on vibrational states.
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.
The entanglement dynamics of two stretching vibrations in theoretically typical local- and normal-mode molecules and realistic molecules H 2 O and SO 2 in an algebraic model is studied in terms of the reduced-density linear entropy with initial entangled states taken to be two-mode squeezed vacuum states. It is shown that the behaviour of the entropy in theoretically typical molecules appears to be more regular than that in realistic ones, and that the entropy becomes irregular as the amplitude of two-mode squeezed vacuum states increases. For initial states with a small amplitude, it is demonstrated that the periodicity and the ``classical'' beat phenomenon of the entropy occur with the beat in theoretically typical molecules being more regular than that in realistic molecules H 2 O and SO 2 .