The Coupling Of The Λ-type Cold Atoms With Cavity

The coupling system of two-level cold atomic gas with optical cavity has drawn lots of attentions both theoretically and experimentally. It is found that there exhibit much more interesting features in the quantum phase diagram. In this thesis, we briefly introduce the theoretical model of atom-field interaction and the stimulated Raman adiabatic passage. Then we describe heat bath theory and Langevin equation which can be used to study the open system of atoms coupling to the cavity modes. Starting from the system of coupling system of two-level cold atomic gases with single cavity mode, we study the system ofΛ-type three-level cold atomic gases interacting with two cavity modes. Under the condition of large detuning, detailed analysis of the Langevin equation of cavity field operator and atomic field operator enables us to adiabatically eliminate the atomic particles on the upper level, and obtain the effective Hamiltonian of the system, which may be used to simulate the phase transition and the dynamics of two-component Bose-Hubbard model in two cavity modes.