Theoretical Study Of Quantum Correlation Property In Atomic Bose-Einstein Condensation

ABSTRACT:Atom-number squeezing has attracted much attention due to its potential applications in quantum metrology and quantum information. So far, we can obtain indirectly the number squeezing through detecting the phase fluctuation, under the condition that the atom-number are constant. Because of the nontrivial relation between the variances of relative number and phase, it should be better to find away to detect the number fluctuation, which will be very necessary and meaningful.In this article, we mainly study the relationship between atom number squeezing and cross-correlation function in two-component Bose-Einstein condensation. We has find the relationship between the atomic number squeezing and the second-order cross-correlation function, which give us another way to detect the number squeezing indirectly. When we adopt frozen-spin approximation (FSA), under the large Josephson coupling be considered, we can find the analytical relationship between the atomic number squeezing and one-order cross-correlation function. Besides, we also find the analytical results of the entropy of entanglement. which provides us a more direct way to measure the number variance and entropy of entanglement through extracting phase coherence in atomic interference experiments. Besides, we also research the condition when the initial state departures spin coherent state(CSS). Considering some approximations ways to simple the progress of calculation, we find that the analytical results about the number squeezing and cross-correlation function.Because of high number squeezing requires very long spitting times, the necessary splitting time will exceed the condensates coherence and life time. Therefore, we consider a new way to obtain the strongest spin squeezing. In chapter 3, we pay our most attention to research the effect of de-coherence of the adiabatic generation. Dynamic generation of maximally spin squeezed state in a two-component Bose-Einstein condensation is proposed by quasi-adiabatic switching-off Josephson field. We show that the strongest spin squeezing with a fixed direction can be obtained by choosing a adiabatic passage route along the ground state of the spin system.In the actual process, due to the important impart of the decoherence in the quantum-classical transition which had been found for many years, we find that it is difficult to obtain the continuous and stable condensation of atomic gas under the extremely cold conditions of Bose-Einstein condensation. Therefore, in order to achieve the continuous condensate, we considerΩas a function of time, we will pay our most attention to optimize squeezing in trapped BECs in the context of atom chips. In this article, the squeezing that has been discussed by supposing an approximately exponential, although we known that the exponential splitting is not optimal, some meaningful results has been found. We find that the quantum fluctuations scales down to 1/N. Therefore, for large N case, the quantum fluctuations will be small enough, which can be depicted by classical field approximately. However, for long time limit, the initial small value of quantum fluctuations will grow rapidly when the classical dynamics is unstable, in fact, the initial small value of quantum fluctuation will grow logarithmically with N because of the instability of classical dynamically process. So the single-particle coherence is lost for interparticle entanglement. Considering the early state for large N case can be considered as the de-coherence of the reduced single-particle state which was caused by the coupling to a bath of quantum correlations. So we find that it has the crucial role of collision dephasing. At finite temperature, we find that local-site noise increases the loss of single-particle coherence in a two-mode BEC, so the noise induce the system be away from classical behavior.In this paper, we introduce two parameters to reflect the noise. We has research the effect of the noise effect to dynamics, we find some interesting results.In our paper, there are twenty-three pictures and seventy-four references.