Matter Wave Four-wave Mixing And Information Process Based On Spin Excitation In Many-body System

With the realization of ultracold atoms.especially the atomic Bose-Einstein condensate(BEC). atomic matter wave optics has developed into a new subject. Atom matter wave optics is based on the research of the matter wave property of ultralcold atoms. It plays an important role in quantum information quantum simulation and quantum precision measurements. Recently, the study of the matter wave optics has gradually extended to the field of quantum matter wave optics which focus on the non-classical property of the matter wave as well as its preparation. Analogy of its counterparts in optics, the non-classical states of matter wave have plenty of applications. Nowadays, the four-wave mixing of two collding BEC is an important method of producting quantum correlated atoms. The interaction between atoms in different spin levels will induce spin excitation. However, this effect has been ignored in recent studies. In this thesis, we study the four-wave mixing of two spinor BEC. We first introduce a method of producting entangled non-classical matter wave which is based on the spontaneous four-wave mixing of spinor BEC. We further study the parametric amplification due the atoms in other spin levels which act as the classic seeds and developed the theory of stimulated four-wave mixing. In addition, spin chain is an important model in quantum many-body physics which can be realized in solid as well as BEC trapped in optical lattices. In this thesis, we propose a theory model for integrated information transfer and storage in a high half-integer spin chain. We also give its implementation based on the current technology. The main conclusions of this article are as follows:(1) We consider the BEC trapped in magnetic well in m]:= 0 magnetics sublevel of F=1 hyperfine states. The BEC is then separated into two counterpropagating matter waves by Bragg diffusion. After that, the trap is turned off in order to let the matter wave expand freely. Due to the spin-exchanging collisons. a pair of atoms in m1=0 magnetic sublevel will excited into two atoms with magnetic sublevel mi=±1 respectively. This is the four-wave mixing of spinor atomic gas. We first study the spontaneous four-wave mixing using Bogoliubov method. We found a strong quantum correlation between the atoms scattered into the opposite direction with different magnetic sublevels. We further use this correlated atoms to test the Clauser-Horne-Shimony-Holt (CHSH) inequation which is a criteria for quantum non-locality. Strong violation of CHSH inequation is found which indicate the atoms scattered into the opposite direction with different magnetic sublevels are strongly entangled.However, it is difficult to make all the atoms of BEC in the same spin state. Thus we study the amplification effect due to the existence of atoms in other spin states. Two cases are considered:one is all the seed are in the same spin state and the other is the seed are uniformly distributed in the different spin states. Previous research on the stimulated process of the matter wave mainly focus on the total number of scattered atoms. The distribution of scattered atom is absent. We found the scattered atoms’ distribution in momentum space is nonuniform after calculating their density matrix. The density of scattered atoms will increase according to the seed’s density distribution. Due to the nonuniform distribution of scattered atoms, they can be stored in a well effectively. By studing the correlation property of scattered atoms, we found that although the correlation of atoms scattered in the opposite direction becomes weak as their density increases, the CHSH inequation is still violated and its value can be close to 2(?) again by increasing the ratio of nonlinear dispersion time to the collision time. This means we can get strongly entangled atoms from a selected direction.(2) We study the coherent transfer of a spin in high half-integer spin chain. We found this spin chain is a good candidate to act as a information processing device. We propose to use the half-integer spin chain to work both as a memory and data-bus. This proposal can avoid the complexity of high precision operating needed in the traditional hybrid system. We use the high-energy spin levels as a date-bus subspace and the low-energy spin levels as a memory subspace. With a large zero field energy splitting.the high-energy spin levels are directly coupled by exchange interacton. low-energy spin-levels are coupled only via higher-order processes. The different coupling strength make the high-energy subspace suitable for transmission tasks, while the low energy subspaces can act as a memory. Transitions between the two subspaces can be done at will by applying resonant external pulses. Decoherence and long-range interaction have little effect on the information tranfer and storage in our system. Molecular magnets is a good candidate for our theory proposal with current technology.