Study Of Quantum Entanglement And Dynamics Property Of Coupled Harmonic Oscillators Chain System

The article studied the entanglement dynamics of a system with a large number of coupled harmonic oscillators chain, in which the oscillators coupled with its neighbors by springs or in rotating wave approximation. The whole research was based on the result of Gaussian quantum channels. The covariance matrix is used to describe the quantum state, and the logarithmic negativity is used to measure the quantum entanglement.Chapter 1 is an introduction about the history of quantum information, the importance of quantum entanglement and the description of the relevant concept with entanglement.Chapter 2 is about the Hamiltonian, potential matrix and kinetic matrix of both interaction model.Chapter 3 is about the analytical results of the equation of motion for both models.In chapter 4, the evolution of entanglement is studied for both models under special initial conditions. The logarithmic negativity, measurement of entanglement, is obtainedIn chapter 5, the entanglement dynamics is studied. The numerical results of the dynamics of entanglement are shown with figures. For the harmonic oscillators chain coupled by springs, we first switch off all the interaction in the chain, cool it to near the ground state and then switch on the interaction suddenly at the time t=0, the results show that the entanglement will be generated over large distances and it will propagate along the chain. However, for RWA model, we can not see this scenario because we dropped the items which are not energy conservation. In another case, if there exists entanglement at the beginning, the propagation of entanglement along both models behave similarly, they all have a saturation value. The differences lie in their velocity of propagation and the transmission efficiency: the RWA model is faster than the spring model; the transmission efficiency of the spring model increases first then decreases, while the RWA model's decreases monotonically, high transmission efficiency can be obtained by squeezing the transmitted unit. If the chain is very long, the velocity of entanglement propagation is a constant dependent on c.Chapter 6 is about the summary, discussion and the potential work in the future.