Elementary excitations of spinor Bose-Einstein condensates

Abstract

Since the first experiment realization of Bose-Einstein condensation in 1995, numerous theoretical and experimental work have been devoted to the research of ultracold system. Owing to the success of optical trapping, the magnetic field could be used to control the internal states. A lot of interesting phenomena arises from the interplay of multiple internal states and the so-called spinor system has attracted much attention.

Spin-orbit coupling is crucial to understand a wide range of physical phenomena, including atomic fine structure and topological insulators. Its manifestation in neutral cold atomic systems has opened a new avenue of research in condensed systems. The properties of homogeneous two-component condensate with spin-orbit coupling has been worked out in numerous literatures. However, there are few work studying the system with trap. In this thesis, we investigate the spin-orbit coupled condensate subjected to cigar-shaped harmonic trap. Within mean-field approximation, we obtain the system’s ground state phase diagram, elementary excitation and coherence. The excitation frequency vanishes and the condensate is fully coherent at the phase transition between spin-balance and -imbalance states. Both analytical and numerical solutions of Gross-Pitaevskii equations suggest the visibility of the Josephson oscillation and the reduction of coherence. Lastly, the analytical results in low chemical potential regime provide physical insights to understand the effects of spin-orbit coupling on both Josephson oscillation and phase transition.

Prompted by recent experiments of coherent spin dynamics in spin-1 condensate, it is important to know its underlying elementary excitations and response to external perturbation. In the last part of this thesis, we review the mean-field phase diagram and the critical Zeeman fields for both ferromagnetic and anti-ferromagnetic spin-1 Bose gases in uniform space. In particular, the ferromagnetic phase of anti-ferromagnetic gas is studied, its spin susceptibility and response to varying magnetic fields are discussed.