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The problem of understanding how a coherent, macroscopic Bose-Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly-interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation, and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases.
The entanglement between spatial regions in an interacting Bose-Einstein condensate is investigated using a quantum field theoretic formalism. Regions that are small compared to the healing length are governed by a non-relativistic quantum field theo
Nambu-Goldstone modes in immiscible two-component Bose-Einstein condensates are studied theoretically. In a uniform system, a flat domain wall is stabilized and then the translational invariance normal to the wall is spontaneously broken in addition
We explore the time evolution of quasi-1D two component Bose-Einstein condensates (BECs) following a quench from one component BECs with a ${rm U}(1)$ order parameter into two component condensates with a ${rm U}(1)shorttimes{rm Z}_2$ order parameter
Equilibrium vortex formation in rotating binary Bose gases with a rotating frequency higher than the harmonic trapping frequency is investigated theoretically. We consider the system being evaporatively cooled to form condensates and a combined numer
We present experimental observations and numerical simulations of nonequilibrium spatial structures in a trapped Bose-Einstein condensate subject to oscillatory perturbations. In experiment, first, there appear collective excitations, followed by qua