Theoretical Studies On Several Novel Quantum Phenomena In Ultracold Atomic Systems

Bose-Einstein condensates (BECs) exist at the confluence of several physical fields, which have been exhibiting many novel phenomena in the last decade. The realization of BECs in experiment have opened up the exploration of novel quan-tum phenomena in a qualitatively new regime. In this dissertation, we first review the main experimental developments and the elementary theory approaches on BECs. Then we present our studies on several novel quantum phenomena in the rotating and molecular BECs.In the averaged vortex approximation, a fast rotating BEC in an anharmonic potential is studied in variational method. We prove that the multiply-quantized vortex can be generated in such a system. Many puzzling phenomena presented in experiment are also explained. Then we study the effect of an applied electric field on a rotating BEC in a harmonic trap. We find that the system becomes more stable in the presence of electric field because it suppresses the energy of the system. The electric field can also bring out a shift to both the vortex lattice and the particle distribution. When the rotation frequency of the system is near the frequency of the harmonic potential, the shift induced by the electric field may be detected according to our advice.We study the effects of an optically induced gauge field in cold atoms show-ing that the laser with time-dependent amplitudes can induce non-Abelian gauge fields, where the scalar fields are obtained directly rather than through a pro-jecting process. Some features of the Landau levels and the ground-state phase diagram of a rotating system for a concrete gauge field are also discussed. We show that such a simple gauge field can make the picture of rotating BECs more fascinating.We theoretically study how to convert two-species atoms into molecules through the technique of Stimulated Raman adiabatic passage (STIRAP) aided by Feshbach resonance. Taking the mixture of 40K and 87Rb as an example, we show that the technique of STIRAP aided by Feshbach resonance can efficiently convert Bose-Fermi mixtures into molecules, which is contrast to the case of the bare Feshbach resonance. We also study the conversion of fermionic atoms in two different hyperfine states into molecules showing that the technique of STIRAP aided by Feshbach resonance is more effective than the bare Feshbach resonance for 6Li atoms rather than 40K atoms. We introduce a adiabatic fidelity for a coherent population trapping (CPT) state to characterize the adiabatic property of the system and explain why the atom-to-molecule conversion efficiencies for 40K and 6Li are distinctly different with the help of the adiabatic fidelity of CPT state.Based on the single-particle density matrix, we investigate some dynamical properties of a partly coherent BEC in double wells. We show that the amplitude of Rabi oscillation decreases with the reduction of coherence degree for a non-interacting system. Considering the interaction between atoms, we also study the adiabatic evolution of the ground state for the partly coherent BEC by the numerical method.