Phase Transition Dynamics of Quenched Spinor Bose-Einstein Condensates with Antiferromagnetic Interactions

Abstract

Understanding non-equilibrium systems are challenging, because they are usually accompanied by either strong time-dependent perturbations or non-vanishing energy and mass flows. Many efforts have been made to study the far-from-equilibrium dynamics by extending the statistical frame of an equilibrium system. One promising progress has been made in the field of phase transition dynamics near a critical point. The significant questions for phase transition dynamics contain how the many-body system evolves into a newly ordered state and how many excitations occurs. It is well known that the scaling behavior in the vicinity of a critical point is determined by the correlation length, the dimension of the system, and the symmetry of an order parameter in the thermal equilibrium. This scaling hypothesis can be extended to the dynamic scaling hypothesis of an out-of-equilibrium system across a phase transition. At the end of the evolution, topological defects are formed as a result of excitations.<br/> <br/> One typical protocol is a quantum quench that explores a non-equilibrium system across a phase transition by suddenly changing the systems Hamiltonian. However, for a many-body quantum system, the time-evolution of far-from-equilibrium system is extremely complicated for study in either an analytical or numerical way, which requires an experimental approach. Ultracold atomic gases provide a good platform to study these non-equilibrium dynamics in a highly controllable and well-isolated manner with sufficiently long coherent time.<br/> <br/> In this thesis, we introduce some methods to induce non-equilibrium dynamics through quenched phase transition in a quasi-2D spinor Bose-Einstein condensate (BEC) with antiferromagnetic interactions. We then discuss its evolution. There are two ground states for an antiferromagnetic spinor BEC depending on the quadratic Zeeman energy, q: the easy-axis polar (EAP) phase for q>0 and the easy-plane polar (EPP) phase for q<0. The microwave dressing technique allow us to access both positive and negative values of q.<br/> <br/> A BEC, initially prepared in the EAP state, becomes dynamically unstable when the q suddenly changes to negative. The EAP-to-EPP phase transition occurs through the transverse magnon excitations according to the mean-field theory. In addition, the dynamical instability is scaled with the quench depth of