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Chinese Physics Letters

Entanglement Dynamics in Typical Local- and Normal-Mode Molecules

Xi-Wen Hou, Ming-Fang Wan, Zhong-Qi Ma

Published Jun 1, 2007• 1 citation
Publisher

Abstract

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 .

DOI
10.1088/0256-307x/24/6/032

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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 .
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.
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.
Quantum entanglement of anharmonic stretches in molecules H 2 O and SO 2 is studied in terms of the reduced-density linear entropy with initial squeezed vacuum states and thermal states. It is shown that the entropy of both kinds of initial states with a small amplitude [Formula: see text] is quasi-periodic with the period of thermal states being larger than that of squeezed vacuum states for each molecule. The entropy evolution of both kinds of initial states with a larger amplitude [Formula: see text] is irregular. For each kind of initial state, the frequency of oscillation of the entropy for SO 2 is larger than that for H 2 O . That can be useful in quantum computing based on vibrational states in H 2 O and SO 2.
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.