Quantum kinetic theory. VI. The growth of a Bose-Einstein condensate

Abstract

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 ͑1997͒; 81, 5266 ͑1998͔͒. 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 ͑1992͒ ͓Sov. Phys. JETP 75, 387 ͑1992͔͒…, 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.

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

“…Other approaches to incorporate the thermal cloud include Stoof's nonequilibrium theory based on quantum kinetic theory [514][515][516][517] and Gardiner-Zoller's quantum kinetic master equation using techniques borrowed from quantum optics [518][519][520][521][522][523][524]. Also, efforts to include stochastic effects have been considered in Ref.…”

Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials

“…For the purpose of comparing the influence of the slab length on the thermalization dynamics, we choose the same logarithmic scale for all vertical axes. The discussion before (137) showed that exact agreement with the Maxwell-Boltzmann distribution is only achieved for z → ∞, whereas the contribution to thermalization is most pronounced where the particle density is highest, i. e. in the first half of the slab.…”

“…As a consequence, we expect the particle flux incident on the slab to equilibrate towards the distribution (137), provided the slab is sufficiently long. However, before scrutinizing this prediction numerically, we come back to the diagrammatic Gross-Pitaevskii equation: In which limit does our result (123) reproduce the stable coherent state described by the Gross-Pitaevskii equation, rather than thermalization?…”

“…In a series of papers by Gardiner and Zoller and co-workers, the concept of a quantum kinetic theory has been introduced [132][133][134][135][136][137][138], see also [139]. Whereas [132] generally introduces the main concept (without an external potential), the following papers focus on applications of the theory and simulations of relevant experimental scenarios.…”

Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: An example of an antidamped Josephson junction

“…A relevant-and analytically tractable-mean-field model that has recently gained attention in the study of temperatureinduced dissipation of dark solitons [18,20,[22][23][24][25] is the so-called dissipative Gross-Pitaevskii equation (DGPE). This model, which was first introduced phenomenologically [26] and later was justified from a microscopic perspective [27], has also been used in other works to describe, e.g., decoherence [28] and growth [29] of BECs, damping of collective excitations of BECs [30], vortex lattice growth [31,32], vortex dynamics [33][34][35][36], and dynamics of quasicondensates [37]. In the case of dark solitons, the DGPE model can describe accurately finite-temperature-induced soliton decay: results stemming from a perturbative study of soliton dynamics in the framework of the DGPE, compares favorably to ones obtained by the more accurate stochastic Gross-Pitaevskii model [20,22,23] (the latter, is a grand-canonical theory of thermal BECs, containing damping and noise terms which describe interactions of low-energy atoms with a high-energy thermal reservoir-see, e.g., Refs.…”