Introduction A lecturer in second year once told our class that the goal of physics was to predict the future. This is child’s play for linear, well-behaved systems away from the deathly touch of chaos, but for most systems — especially those transitioning between phases — this is not so trivial. Symmetry breaking phase transitions are a fundamental physical process that appears in scenarios ranging from superfluid helium to the early dynamics of the universe. In this thesis we look at the equilibriation dynamics of spinor Bose-Einstein condensates (BECs). First theorized by S. N. Bose in 1924 and experimentally realized in 1995, Bose-Einstein condensation is a highly coherent state of matter that provides us with an extremely unique opportunity. BECs have highly tunable interactions that we can control using Feshbach resonances. In addition, they equilibriate slowly — spinor condensates slower still. These systems give us a unique chance to perform a quantum quench and actually watch the system reorganize itself. When we “quench” a system, we change its parameters on a timescale much shorter than its healing time — much like a blacksmith dipping a hot sword into cold water. In a quantum spinor system it’s a magnetic field, instead of temperature, that we dial back. This translates to exponentially growing excitations that manifest themselves as magnetic domains. This structure comes about from the spontaneously broken symmetry by quantum fluctuations during a quench through a multicritical point; a phase transition. Previous work on quenched spinor condensates has found that some dynamics are reasonably well described by a linearized theory (which we introduce in the next chapter). In 2011, in an investigation into thermalization dynamics, Barnett et al. concluded that the quenched system does not thermalize at all. Instead it reaches a quasisteady (“prethermalized”) phase, with domains that grow randomly over time. Interestingly enough, such prethermalized regimes also turn up in atomic superfluids. In this work we explore the results seen by Barnett et al. for a two-dimensional spin-1 condensate. Simulation code is developed from the ground up, tested by reproducing experimentally known phenomena, and finally used to investigate quenching dynamics. We make use of the spinor Gross-Pitaevskii equations, and Bogoliubov theory to analytically explore instabilities around a quench. Our goals for this research are to a) develop working code that accurately simulates an interacting spin1 Bose system; b) reproduce the results of Barnett et al.’s 2011 paper; c) investigate the effect on domain formation of different quench depths; and d) determine the boundaries of different quench regimes, if any. In chapter 2, we outline the background theory needed to begin our investigation. Included is an overview of the different ground state phases and spin dynamics in a spinor condensate, so that we may develop an initial intuition for these highly quantum systems. Chapter 3 discusses the numerical essentials of our project — how we developed our code and the tests to justify it. Finally, chapter 4 goes through the simulation results.
This is my thesis for my Honours project! :)