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International Journal of Modern Physics C

ENTROPY EXCHANGE AND CORRELATION IN u(2) ALGEBRAIC MODEL

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

Published Oct 1, 2008• 1 citation
Publisher

Abstract

The dynamics of entropy exchange and correlation in u(2) algebraic model for two stretches of H2O and SO2is studied in terms of the linear entropy with diagonal approximation, where various initial states are respectively taken to be the product of thermal states and squeezed states on each mode. It is shown that with a suitable parameter in initial states, the entropies in each stretch are positively correlated or anticorrelated, which depend on initial states and a molecule. The entropy correlation is also studied in terms of a correlation index. It is demonstrated that the correlation index and the sum of linear entropies in each stretch are identical in oscillation. The differences in the linear entropy in each stretch and the correlation index of the thermal states and the squeezed states between H2O and SO2are noticed. These may be useful for quantum computing and quantum information processing based on two stretching modes in both molecules.

DOI
10.1142/s0129183108013047

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The dynamics of entropy exchange and correlation in u(2) algebraic model for two stretches of H2O and SO2is studied in terms of the linear entropy with diagonal approximation, where various initial states are respectively taken to be the product of thermal states and squeezed states on each mode. It is shown that with a suitable parameter in initial states, the entropies in each stretch are positively correlated or anticorrelated, which depend on initial states and a molecule. The entropy correlation is also studied in terms of a correlation index. It is demonstrated that the correlation index and the sum of linear entropies in each stretch are identical in oscillation. The differences in the linear entropy in each stretch and the correlation index of the thermal states and the squeezed states between H2O and SO2are noticed. These may be useful for quantum computing and quantum information processing based on two stretching modes in both molecules.
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.
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.
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.
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 .
We investigate the quantum dynamics for a molecular-state-model system interacting with a resonant two-mode squeezed coherent field, in which each mode is initially correlated. As an example, we consider a three-state molecular model, which mimics the electronic excited states of trans-octatetraene obtained by a full-configuration-interaction calculation using the Pariser-Parr-Pople Hamiltonian, interacting with a two-mode squeezed coherent field. For comparison, we also perform parallel studies, in which the initial fields are prepared in uncorrelated two-mode states, i.e., a two-mode coherent state and a two-mode thermal state. It is well known that the case of two-mode coherent field leads to the usual collapse-revival phenomena of the Rabi oscillations, while the case of a two-mode thermal state leads to an irregular evolution of them. Although the two-mode squeezed coherent field exhibits similar collapse-revival behavior to that for the two-mode coherent field, some differences are detected in the amplitudes and periods of collapse-revival oscillations. Further, the dynamics of off-diagonal molecular density matrices between the ground and second excited states for these two fields are found to be distinctively different from each other. Such attractive behavior is found to be closely associated with the two-mode photon-phase dynamics obtained by the Pegg-Barnett phase operator and the initial quasiprobability (Q function) distribution of photons. These differences in phase properties are also shown to significantly affect the dynamics of the information entropy for a molecule, i.e., molecular entropy, which represents the degree of entanglement between the molecule and photons.