Summary form only given. Bosonic stimulation as the principal mechanism for the growth of a Bose-Einstein condensate was first introduced and quantitatively evaluated by Gardiner et al., and this was subsequently experimentally verified by Miesner et al. Although agreement between experiment and theory is not perfect, it is clear that the predicted mechanism of stimulated emission into the condensate is indeed the principal cause of condensate growth.
Summary form only given. Bosonic stimulation as the principal mechanism for the growth of a Bose-Einstein condensate was first introduced and quantitatively evaluated by Gardiner et al., and this was subsequently experimentally verified by Miesner et al. Although agreement between experiment and theory is not perfect, it is clear that the predicted mechanism of stimulated emission into the condensate is indeed the principal cause of condensate growth.
A detailed analysis of the growth of a Bose-Einstein condensate is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose-stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. [Phys. Rev. Lett. 79, 1793 (1997); 81, 5266 (1998)]. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan, Svistunov, and Shlyapnikov (Zh. Eksp. Teor. Fiz. 101, 528 (1992) [Sov. Phys. JETP 75, 387 (1992)]), for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modeling of growth implicitly gives a model of the spatial shape of the density profile of the condensate-vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi-shaped condensate. Our method gives substantially different results for condensate numbers and temperatures obtained from phenomenological fits, but fits the published column density data very well.
We extend the earlier model of condensate growth of Davis et al (Davis M J, Gardiner C W and Ballagh R J 2000 Phys. Rev. A 62 063608) to include the effect of gravity in a magnetic trap. We carry out calculations to model the experiment reported by Köhl et al (Köhl M, Davis M J, Gardiner C W, Hänsch T and Esslinger T 2001 Preprint cond-mat/0106642) who study the formation of a rubidium Bose-Einstein condensate for a range of evaporative cooling parameters. We find that, in the regime where our model is valid, the theoretical curves agree with all the experimental data with no fitting parameters. However, for the slowest cooling of the gas the theoretical curve deviates significantly from the experimental curves. It is possible that this discrepancy may be related to the formation of a quasicondensate.
We extend earlier models of the growth of a Bose-Einstein condensate c.w. [Gardiner et al., Phys. Rev. Lett. 79, 1793 (1997); e-print cond-mat/9801027; Phys. Rev. Lett. 81, 5266 (1998)] to include the full dynamical effects of the thermal cloud by numerically solving a modified quantum Boltzmann equation. We determine the regime in which the assumptions of the simple model of Gardiner et al. [Phys. Rev. Lett. 81, 5266 (1998)] are a reasonable approximation, and compare our results with those that were earlier compared with experimental data. We find good agreement with our earlier modeling, except at higher condensate fractions, for which a significant speedup is found. We also investigate the effect of the final temperature on condensate growth, and find that this has a surprisingly small effect. The particular discrepancy between theory and experiment found in our earlier model remains, since the speedup found in these computations does not occur in the parameter regime specified in the experiment.
Summary form only given. Quantum theory predicts that Bose-Einstein condensation (BEC) of a spatially homogeneous gas with attractive interactions is precluded by a conventional phase transition into either a liquid or solid. When confined to a trap, however, such a condensate can form provided that its occupation number No does not exceed a limiting value. The stability limit is determined by a balance between self-attraction and a repulsion arising from position-momentum uncertainty under conditions of spatial confinement. Near the stability limit, self-attraction can overwhelm the repulsion, causing the condensate to collapse. Growth of the condensate, therefore, is punctuated by intermittent collapses, which are triggered either by macroscopic quantum tunneling or thermal fluctuation. The data presented here are the first direct observations of the growth and collapse of Bose Einstein condensates with attractive interactions.
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. Introduction The equilibrium phase diagram of the dilute Bose gas exhibits a continuous phase transition between condensed and noncondensed phases. The order parameter characteristic of the condensed phase vanishes above some critical temperature T c and grows continuously with decreasing temperature below this critical point. However, the dynamical process of condensate formation has proved to be a challenging phenomenon to address both theoretically and experimentally. This formation process is a crucial aspect of Bose systems and of direct relevance to all condensates discussed in this book, despite their evident system-specific properties. Important questions leading to intense discussions in the early literature include the time scale for condensate formation and the role of inhomogeneities and finite-size effects in “closed” systems. These issues are related to the concept of spontaneous symmetry breaking, its causes, and implications for physical systems (see, for example, Chapter 5 by Snoke and Daley). In this chapter, we give an overview of the dynamics of condensate formation and describe the present understanding provided by increasingly well-controlled cold-atom experiments and corresponding theoretical advances over the past twenty years. We focus on the growth of BECs in cooled Bose gases, which, from a theoretical standpoint, requires a suitable nonequilibrium formalism.