Investigations On Landau Damping Of Collective Excitations In Bose-Einstein Condensates

Bose-Einstein Condensation (BEC) is a phenomenon of macroscopic occupation in one or several quantum states by a large number of identical bosons when the temperature of system is below to a critical temperature. BEC is one of the most basic conclusions in quantum statistic mechanics and the physical origin of many kinds of macroscopic quantum phenomena. BEC theory is also the foundation of superconductivity and superfluidity. The research of BEC is the cross point of many disciplines, including atom and molecular physics, nonlinear and quantum optics, statistical physics and condensed matter physics, and hence has significant importance from the theoretical viewpoint. On the other hand, the study of BEC has also promising future prospects in practical applications, including designing atom laser and increasing largely the measurement precision for fundamental physical quantities.The research of elementary excitations is one of the basic topics in statistical physics and condensed matter physics. Collective excitations are the most basic excitation modes in BEC at low temperature. The study of collective excitations is very important for understanding the properties of ground state, superfluidity and thermodynamics of BECs. The inter-particle interaction results in not only the generation ofcollective excitations, but also the decay of their amplitudes (called as damping) and the shift of their oscillating frequencies. For the bosons trapped in a potential, a collective-mode amplitude decays with respect to time via mainly the mechanics of Landau damping, i. e. a quasiparticle absorbs the collective mode and then transferred into a new quasiparticle. Landau damping is the most basic phenomenon in trapped BEC and its precision calculation may be used to explain many experimental phenomena, and test and develop the quantum manybody theory for condensed matter. The precision measurement of Landau damping can also be inversely used to deduce the interparticle interaction and superfluid property of the system. Although there exist a lot of studies on the Landau damping of collective excitations in trapped BECs made by many famous laboratories and theoretical groups in the world, however, there is still no satisfactory theoretical explanation on the experimental results up to now.In this thesis, we have developed a new, systematic analytical method for making a thorough study on the Landau damping of collective excitations in BECs. The main research results are listed below:1. We have studied the Landau damping of the lowest breathing mode in the BEC of a ⁸⁷Rb atomic gas trapped in a spherical symmetric (anisotropy parameter λ=1) harmonic potential. By using a improved Thomas-Fermi approximation we have obtained the ground state wavefunction of the condensate. Based on this we have solved Bogoliubov-de Gennes equations satisfied by collective excitations and quasiparticles and obtained the analytical solutions of divergence-free Bogoliubov amplitudes andcoupling matrix elements describing the interaction among collective excitations and quasiparticles. Utilizing these analytical results we have calculated the Landau damping of the breathing mode based on the time-dependent Hatree-Fock-Bogoliubov mean-field theory. The result has been compared with numerical simulation and found a good agreement.2. Based on the time-dependent Hatree-Fock-Bogoliubov mean-field theory we have constructed and developed a general theoretical method for studying the Landau damping of collective modes in anisotropic BECs. Bymeans of this method we have investigated the Landau damping of ω_- modein the BEC of a ⁸⁷Rb atomic gas trapped in an anisotropic (λ =8^1/2) potential.We have calculated coupling matrix elements of three-mode interaction, damping strength and damping coefficient, and discussed the relations among the damping coefficient, temperature, particle number, and trapping frequencies. The calculating result agrees well with the experimental one.3. We have investigated the Landau damping of ω₊ and ω_- modes intrapped BEC of ⁸⁷Rb atomic gases for various anisotropic parameters A. We have calculated the three-mode coupling matrix elements and damping strength, discussed the relations among the Landau damping coefficient, temperature, particle number and trapping frequencies. Our theoretical results are in agreement well with the experimental ones reported up to now.