Adiabaticity And Stability Of The Ultracold Atom-molecule Dark State

The study of ultracold molecules connects both the fundamental theory and the most advanced experimental technique of physics, and has important theoretical and practical significance. The creation of ultracold molecues is not only an extension of atom cooling but also a challenge of cooling technique. Owing to the invalidation of laser cooling on molecules because of the lack of simple level structures, there has been explosive growth of interest in developing effective techniques for producing ultracold molecules in recent years. Currently, the ultracold molecules are generally obtained by coupling atoms in external fields. One effective, robust method is the stimulated Raman adiabatic passage. In this article, using quantum many-body and nonlinear theory, under the mean-field approximation, we investigate the adiabaticity and stability of the dark state in the atom-molecule conversion system in the stimulated Raman adiabatic passage.In the 1st chapter, we introduce the background about cold atomic and molecular physics, including the cooling techniques of atoms or molecules, the atomic Bose-Einstein Condensation, the ultracold degenerate Fermionic gas, the ultracold molecules, the molecular Bose-Einstein Condensation, and their experimental processes.In the 2nd chapter, we present the fundamental theory using to describe BEC dynamics. Starting with the second quantized Hamiltonian, we have worked out the Gross-Pitaevskii equations for the atomic and atom-molecule condensate systems under the meanfield approximation. Considering the effect of fluctuation, we also obtain the Bogoliubov equations of the collective excitation of the atomic and atom-molecule condensates. Then, we introduce a method to construct the equivalent classical Hamiltonian for quantum systems.In the 3rd chapter, by generalizing the definition of fidelity for the nonlinear system, we investigate the dynamics and adiabaticity of the population transfer for atom-molecule three-level A-system in a stimulated Raman adiabatic passage (STIRAP). We find that, when neglecting the interparticle interactions, the adiabatic fidelity for the coherent population trapping (CPT) state or dark state, as the function of the adiabatic parameter, approaches to unit in a power law. The power exponent, however, is much less than the prediction of the linear adiabatic theorem. We further discuss how to achieve higher adiabatic fidelity for the dark state through optimizing the external parameters of STIRAP.In the 4th chapter, the dynamical stability and adiabatic fidelity of the atom-homonuclear-trimer dark state of a condensate system in a stimulated Raman adiabatic passage aided by Feshbach resonance is investigated. It is found that the interparticle interactions may cause dynamical instability in some parameter regions. The conditions for the appearance of dynamical instability are obtained analytically. Taking ⁸⁷Rb condensate system as an example, we numerically give the unstable regions. Moreover, the adiabatic property of the dark state is also studied in terms of a newly defined adiabatic fidelity. It is shown that the nonlinear collisions have a negative effect on the adiabaticity of the dark state and hence reduce the conversion efficiency.In the 5 th chapter, we investigate the adiabaticity and dynamical stability of a dark state in a nonlinear atom-heteronuclear-trimer conversion that is implemented by a two-photon stimulated Raman adiabatic passage (STIRAP). We find that, as in the atom-homonuclear-trimer conversion system, the interparticle interactions may cause dynamical instability in some parameter regions. We analytically obtain the condition for the occurrence of the dynamical instability of the atom-trimer dark state. Taking the condensate system of ⁴¹K and ⁸⁷Rb as an example, we further plot the phase diagrams of the instability in the parameter plane. We also give the adiabatic condition for the dark state of this system. We demonstrate that, in the absence of the nonlinear collisions, the adiabatic condition for this nonlinear system only depends on the Rabi-frequency of the dimer-trimer coupling optical field, which is different from traditional STIRAP processes. Moreover, we generalize the fidelity to this system and use it to study the adiabaticity of the dark state. Based on our theoretical analysis, we propose a feasible two-photon STIRAP scheme that has better adiabaticity, less instability and therefore could yield high atom-trimer conversion efficiency.