| Bose-Einstein condensation is a macroscopic quantum phenomena. In1924, Einstein generalized Bose’s statistical theory of electromagnetic radiation to massive atoms, and predicted that if the temperature of a Boson gas was lowered to a critical value, the lowest energy state should be macroscopically occupied, which gave the name of BEC. This was the first example in history that a phase transition occurs purely due to quantum effect, without the help of interaction.Due to the technical limitations, BEC has not been observed for a long time. In1995, three groups in JILA, Rice University and MIT cooled a cloud of rubidium atoms to20billions of a kelvin through laser cooling and evaporative cooling, and for the first time realized BEC in experiment. Till now, BEC has been realized experimentally in dilute gases of hydrogen, lithium, sodium, potassium, rubidium etc. The rich internal structures of various atoms provide with people powerful tools for quantum simulation.In early experiments the atoms were confined by magnetic traps, and usually only atoms occupying a certain internal state can be confined. Since the introduction of optical trap,the internal degrees of freedom are released and the trapped atoms can occupy different internal states simultaneously, which could be called multicomponent BEC. Since the internal states are conventionally denoted as spin components, it can also be called spinor BEC. The purpose of this thesis is to study the property of a mixture of two species of spinor BEC, including two parts:one is the mixture of two species of pseudospin-1/2atoms, another is the mixture of two species of spin-1atoms.The paper is organized as follows:In Chapter1, we first give a brief introduction of the early history of BEC study-ing and the experimental technique of laser cooling and magnetic-optical trap, then we use Gross-Pitaevskii equation and effective field theory to solve the elementary excitations, finally we discuss the relation between BEC and superfluidity.Chapter2describes spinor BEC, mainly the ground state and elementary exci-tations of two component BEC and spin-1BEC. Then we present the way of con-structing interaction Hamiltonian for atoms with arbitrary spins.Chapter3study the property of mixed pseudospin-1/2Boson gases. We first find the mean field ground state of the system,then by path integral we develop a low energy effective theory to describe the phase fluctuations of the order parameters and give the elementary excitations. When considering the homogeneous fluctuations, the effective theory is coincident with the single mode approximation. In3+1D the phase diagram of this system can be obtained from mean field theory. In1+1D the effective theory describes a Sine-Gordon field coupled with a free scalar field. By renormalization analysis we find that the phase diagram belongs to the Kosterlitz-Thouless universality class.In Chapter4, we investigate the influence of quantum fluctuations to the ground state of mixed spin-1Boson gases. At the mean field level, the ground state pos-sesses accidental degeneracy. We use nonlinear a model and Bogliubov theory to study the low energy spin dynamics and give the spectrum of spin waves. The two results coincide in the long wane length limit. The effective potential produced by the quantum fluctuations lift the ground state degeneracy, leading to the ’spin lock’ effect between the two species of atoms. We also discussed the oscillation of the two species’s collective spins induced by the effective potential.which may be observed in experiment. |
