Spin-10 Spinor Bose-Einstein Condensates

Abstract

Spinor Bose-Einstein Condensates enable the study of various phenomena such as coherent spin dynamics, quantum phase transitions, topological structures and spin-textures. While there has been significant progress in the theoretical and experimental understanding of spinor BECs with a few sub-levels, there is very little work done for systems with spin f > 3. Experimentally, spinor BECs with f > 3 have not been obtained. The above fact, along with recent works in ultracold Dysprosium atoms, which host a metastable state having total angular momentum J = 10, motivated us to take on the spin-10 BEC. Spinor BECs get significantly more complex as we move to higher spins, with additional tensors appearing in the interaction Hamiltonians of the system, and the dynamical equations being dependent on a much larger number of terms. Lots of parallels can be drawn to multi-level atoms due to the high internal spin degrees of freedom. Due to the completely unexplored nature of this system, we attempt to establish foundational knowledge in this thesis, paving the way for in depth analyses of specific aspects in the future. We examine the full Hamiltonian and the Gross-Pitaevskii equations governing the time dynamics of the system. The Bogoliubov spectrum contains 2 f +1 terms for a spin- f system, and governs the behaviour under elementary excitations in the system. We provide a general method for finding the full energy spectrum for two phases of the spin- f system, namely the ferromagnetic and polar phases. The methods used in this thesis are easily generalizable, and we hope this sets the foundation for additional theoretical work in higher spin condensates in general.