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Chinese Physics Letters

Quantum Entanglement and Normal-to-Local Transition in Molecule H 2 S

Liu Da-Ming, Peng Dong-Ping, Xi-Wen Hou

Published Apr 1, 2008• 3 citations
Publisher

Abstract

Quantum entanglement of two stretches in molecule H 2 S is investigated for various initial states in terms of the reduced-density von Neumann entropy and the mean entropy defined by average over time. It is shown that the maximal and the mean entropies of an initial state with local-mode character are smaller than those with normal-mode character, and the mean entropy displays a maximum near the position of the normal-to-local transition.

DOI
10.1088/0256-307x/25/4/027

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Quantum entanglement of two stretches in molecule H 2 S is investigated for various initial states in terms of the reduced-density von Neumann entropy and the mean entropy defined by average over time. It is shown that the maximal and the mean entropies of an initial state with local-mode character are smaller than those with normal-mode character, and the mean entropy displays a maximum near the position of the normal-to-local transition.
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.
In this Brief Report the properties of both dynamical and static entanglement in the integrable quantum dimer are studied in terms of the reduced-density linear entropy and von Neumann entropy with various coupling parameters, total boson numbers, and initial states. The mean entanglement, which is defined to be averaged over time, is used to describe the influence of the classical separatrix on the behavior of entanglement. It is shown that the mean entanglement exhibits a maximum near the position of the corresponding classical separatrix energy and that the static entanglement of the state with the largest eigenvalue of the quantum spectrum displays a maximum near the bifurcation point. For weak coupling and larger total boson number the maximum entanglement state is exactly at the position of the classical separatrix and bifurcation. In strong coupling all initial states have nearly the same mean entanglement.
The maximum von Neumann entropy principle subject to given constraints of mean values of some physical observables determines the density matrix. Similarly the stationary action principle in the case of time-dependent (dissipative) situations under similar constraints yields the density matrix. The free energy and measures of entanglement are expressed in terms of such a density matrix and thus define respective functionals of the mean values. In the light of several model calculations, it is found that the density matrix contains information about both quantum entanglement and phase transitions even though there may not be any direct relationship implied by one on the other.
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.