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Chinese Journal of Chemical Physics

Fidelity and Mutual Entropy in Mixed States for Fermi-resonance Coupling Vibrations of CS2

Peng Dong-Ping, Xi-Wen Hou

Published Aug 1, 2010• 3 citations
Publisher

Abstract

The dynamics of four fidelities is studied for mixed coherent states and mixed squeezed states of Fermi-resonance coupling vibrations in molecule CS2. It is demonstrated that those fidelities are dominant-positively correlated with each other, one of which by Wang et al. (Phys. Lett. A 373, 58 (2008)) is the most striking in dominant anti-correlation with quantum mutual entropy. That is useful for molecular quantum computing and quantum information.

DOI
10.1088/1674-0068/23/04/393-396

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The entanglement dynamics of Fermi resonance coupling vibrations in a spectroscopic Hamiltonian for molecules CHD3\mathrm{C}\mathrm{H}{\mathrm{D}}_{3}CHD3​, CHCl3\mathrm{C}\mathrm{H}{\mathrm{Cl}}_{3}CHCl3​, and CHF3\mathrm{C}\mathrm{H}{\mathrm{F}}_{3}CHF3​ is studied in terms of the von Neumann entropy and negativity with three kinds of initial states that are direct products of coherent states, thermal states, and squeezed states of each mode. It is demonstrated that the increasing rate of entanglement in the early-time evolution is the largest for the squeezed states, while that is the smallest for the coherent states. For small parameters in the coherent and thermal states, entanglement displays a quasiperiodicity with the quasiperiod in CHF3\mathrm{C}\mathrm{H}{\mathrm{F}}_{3}CHF3​ being the longest. Furthermore, the dynamical correlation between the von Neumann entropy and negativity shows that positively correlated or anticorrelated behaviors of both measures strongly depend on initial states and molecules. For those states with small parameters, both measures exhibit dominantly positive correlation. These are useful for molecular quantum computing and information processing.
Several measures of entanglement have attracted considerable interest in the relationship of a measure of entanglement with other quantities. The dynamics of entropy, energy and negativity is studied for Fermi-resonance coupled vibrations in substituted methanes with three kinds of initial mixed states, which are the mixed density matrices of binomial states, thermal states and squeezed states on two vibrational modes, respectively. It is demonstrated that for mixed binomial states and mixed thermal states with small magnitudes the entropies of the stretch and the bend are anti-correlated in the same oscillatory frequency, so do the energies for each kind of state with small magnitudes, whereas the entropies exhibit positive correlations with the corresponding energies. Furthermore, for small magnitudes quantum mutual entropy is positively correlated with the interacting energy. Analytic forms of entropies and energies are provided with initial conditions in which they are stationary, and the agreement between analytic and numerical simulations is satisfactory. The dynamical entanglement measured by negativity is examined for those states and conditions. It is shown that negativity displays a sudden death for mixed binomial states and mixed thermal states with small magnitudes, and the time-averaged negativity has the minimal value under the conditions of stationary entropies and energies. Moreover, negativity is positively correlated with the mutual entropy and the interacting energy just for mixed squeezed states with small magnitudes. Those are useful for molecular quantum information processing and dynamical entanglement.
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.
The dynamical entanglement for Fermi coupled C-H stretch and bend vibrations in molecule CHD 3 is studied in terms of two negativities and the reduced von Neumann entropy, where initial states are taken to be direct products of photon-added coherent states on each mode. It is demonstrated that the negativity defined by the sum of negative eigenvalues of the partial transpose of density matrices is positively correlated with the von Neumann entropy. The entanglement difference between photon-added coherent states and usual coherent states is discussed as well.
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.