Non-equilibrium dynamics and novel quantum phases of multicomponent ultracold atoms

Advances in the field of ultracold atomic gases have demonstrated the ability to isolate and tunably control the interactions between a large number of particles. This opens many novel challenges for condensed matter physics. For multicomponent systems when the particles have internal states, interactions determine how the internal and spatial degrees of freedom organize into different ordered phases. This thesis is concerned with the types of ordering that occur and the dynamics of how ordering emerges in multicomponent ultracold atoms.;Multicomponent atoms trapped in an optical lattice provide an ideal testing ground for quantum magnetism. We begin by analyzing one of the simplest such models, the Ising spin chain. We study the coherent quantum dynamics of this system as it is driven across a quantum critical point separating the ordered and disordered phase via an exact solution. Then we consider quantum noise analysis as a measurement tool adapted to the unique capabilities of ultracold atomic systems. For the Ising spin chain, we show the full distribution of the transverse magnetization has direct signatures of the ordered and disordered phase not captured by low order moments such as the average or standard deviation.;Next we turn to pairing in fermionic atoms. For fermionic atoms with two components and attractive local interactions, pairing was first described by Bardeen, Cooper, and Schrieffer. We generalize these results to multicomponent systems realizable with cold atoms. General symmetry arguments allow us to classify possible types of pairing as well as characterize the phase transitions separating them.;Finally, we study how magnetic ordering emerges in multicomponent spinor condensates. We begin by analyzing the collective mode spectrum and demonstrate how small fluctuations can develop dynamical instabilities and drive the non-equilibrium dynamics. Such instabilities may arise through externally imposed spiral order in the magnetization or through intrinsic dipolar interactions. We then present an effective low-energy theory for spinor condensates and find analytical solutions in the absence of dipolar interactions. These solutions give insight into the numerical solutions in the presence of dipolar interactions obtained via a systematic symmetry analysis.