Study On Dynamical Entanglement Of Vibrations In Small Molecules

In the field of quantum information science, quantum entanglement plays an extremely important role. Entanglement, as unique physical characteristics of quantum system, can not only verify the basic problem of quantum mechanics, but also act as an important resource of quantum computing and quantum information processing. By far, people have made extensive researches on quantum entanglement, including the measurement and manipulation of entangled states, as well as the generation of the entanglement in various physical systems and their applications, etc. In recent years, the studies of quantum entanglement have been generalized to the case of continuous-variable entangled states. In general, continuous-variable-type entanglement is related to coherent state or squeezed state, and it has been extensively applied to quantum dense coding, quantum teleportation and quantum cryptography, etc. Recently, the studies of quantum computing with molecular vibrational states have attracted much attention. For molecular systems, nonlinear interaction is generic among the vibrational, or rovibrational states, these states can be used to encode quantum information and achieve quantum information process.In this thesis, we investigate the properties of dynamical entanglement of vibrations in the systems of integrable dimer and small molecules with the initial state of each system being in a two-mode squeezed vacuum state. As a measure of the amount of entanglement, the linear entropy of the two systems is calculated. It is found that for the integrable dimer system, the behavior of the linear entropy appears to be periodic for weak coupling strength (c=0.2,1) and small squeezing parameter (r=0.2), and there exists classical beat phenomenon for strong coupling strength and large squeezing parameter. Moreover, for the symmetric small molecule system, the linear entropy is quasi-periodic for small squeezing parameter (r=0.2), and the classical beat phenomenon occurs with the increase of the squeezing parameter for molecules C2D2 and SO2, which indicates that there exist strong coupling strength between the two modes for the two molecules and they are normal mode molecules.We also investigate the properties of dynamical entanglement and correlation of vibrations in small molecules with the initial states of the system being in two-mode squeezed vacuum state and two-mode SU(1,1) coherent state. It is found that for the case of small squeezing parameter, the maximum value and the changing rate of linear entropy for the two-mode SU(1,1) coherent state are larger than those for the two-mode squeezed vacuum state, while for the case of large squeezing parameter in the opposite situation. Moreover, for both of the two initial states, with the increasing of squeezing parameter r, the maximal linear entropy increases and the fluctuation of the entropies is changed from a good quasi-periodicity to some irregularity. It is also found that the positively correlated or anti-correlated phenomena between linear entropy and negativity depend on both the initial states and the types of molecules, as well as the positive correlation is predominant for small r. The positive correlation between both measures can at least provide a possibility to set up a standard measure of entanglement among so many quantities of entanglement for quantum information processing.Our results might be useful in quantum computing and quantum information based on molecular vibrational states.