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arXiv:cond-mat/9808148 · Physical Review A

Exciting, cooling, and vortex trapping in a Bose-condensed gas

R. J. Marshall, G.H.C. New, Keith R. Burnett, Seok Jin Choi

Published Mar 1, 1999• 49 citations
arXivHTMLPDF

Abstract

A straightforward numerical technique, based on the Gross-Pitaevskii equation, is used to generate a self-consistent description of thermally excited states of a dilute boson gas. The process of evaporative cooling is then modeled by following the time evolution of the system using the same equation. It is shown that the subsequent rethermalization of the thermally excited state produces a cooler coherent condensate. Other results presented show that trapping vortex states with the ground state may be possible in a two-dimensional experimental environment.

DOI
10.1103/physreva.59.2085

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A straightforward numerical technique, based on the Gross-Pitaevskii equation, is used to generate a self-consistent description of thermally excited states of a dilute boson gas. The process of evaporative cooling is then modeled by following the time evolution of the system using the same equation. It is shown that the subsequent rethermalization of the thermally excited state produces a cooler coherent condensate. Other results presented show that trapping vortex states with the ground state may be possible in a two-dimensional experimental environment.
We introduce a technique to simulate the dynamics of a thermal dilute Bose gas. With the method of the nonequilibrium statistical operator, a correction to the Gross-Pitaevskii equation (GPE) is derived. This modification of the GPE describes spontaneous scattering processes. It regularizes the ultraviolet catastrophe and captures the dynamics of the particles at all energies, including the tail of the momentum distribution. We apply our model to the simulation of an evaporative cooling quench of a two-dimensional Bose gas.
Abstract We have devised a simulation method for studying the evaporative cooling process of trapped Bose-Einstein condensates at finite temperatures, leveraging the Zaremba-Nikuni-Griffin (ZNG) formalism. This framework incorporates the generalized Gross-Pitaevskii (GP) equation and a semiclassical kinetic equation governing the behavior of the thermal cloud. Our approach builds upon the numerical techniques pioneered by Jackson and Zaremba, which involve simulating the kinetic equation using test particles. A pivotal aspect of our method lies in emulating the evaporative cooling process by selectively removing test particles with high energy. Through extensive simulations, we demonstrate the efficacy of our approach in accurately describing condensate growth during evaporative cooling. Furthermore, we extend our simulations to investigate the formation of vortex lattices during evaporative cooling in the presence of a rotating thermal cloud. This comprehensive analysis provides valuable insights into the intricate dynamics of trapped Bose-Einstein condensates undergoing evaporative cooling processes.
In experiments, Bose-Einstein condensates are prepared by cooling a dilute Bose gas in a trap. After the phase transition has been reached, the trap is switched off and the evolution of the condensate observed. The evolution is macroscopically described by the Gross-Pitaevskii equation. On the microscopic level, the dynamics of Bose gases are described by the NNN-body Schrödinger equation. We review our article [BdS12] in which we construct a class of initial data in Fock space which are energetically close to the ground state and prove that their evolution approximately follows the Gross-Pitaevskii equation. The key idea is to model two-particle correlations with a Bogoliubov transformation.
Since dilute Bose gas condensates were first experimentally produced, the Gross-Pitaevskii equation has been successfully used as a descriptive tool. As a mean-field equation, it cannot by definition predict anything about the many-body quantum statistics of condensate. We show here that there are a class of dynamical systems where it cannot even make successful predictions about the mean-field behavior, starting with the process of evaporative cooling by which condensates are formed. Among others are parametric processes, such as photoassociation and dissociation of atomic and molecular condensates.
We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features of the vortex states, and its predictions agree well with available experimental results. We discuss various properties of a single vortex, including its structure, energy, dynamics, normal modes, and stability, as well as vortex arrays. When the nonuniform condensate contains a vortex, the excitation spectrum includes unstable (`anomalous') mode(s) with negative frequency. Trap rotation shifts the normal-mode frequencies and can stabilize the vortex. We consider the effect of thermal quasiparticles on vortex normal modes as well as possible mechanisms for vortex dissipation. Vortex states in mixtures and spinor condensates are also discussed.