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Two-dimensional Bose condensates in a harmonic trap

B. Tanatar

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

We study the condensate wave function of a two-dimensional Bose condensate in an harmonic trap potential using the recently proposed mean-field equation that takes into account the correct dimensionality effect. We compare our results with other approaches with various forms for the two-dimensional coupling. Our calculations show that by adjusting the parameter describing confinement in the third direction it is possible to obtain agreement between these models.

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Journal of Physics Conference Series•Dec 1, 2019•1 citation
We study the condensate wave function of a two-dimensional Bose condensate in an harmonic trap potential using the recently proposed mean-field equation that takes into account the correct dimensionality effect. We compare our results with other approaches with various forms for the two-dimensional coupling. Our calculations show that by adjusting the parameter describing confinement in the third direction it is possible to obtain agreement between these models.
We study the ground state properties of a two-dimensional Bose gas in an harmonic trap potential using the recently proposed mean-field equation that takes into account the correct dimensionality effect. In contrast to the three-dimensional case, the interaction term depends logarithmically on the scattering length and density. We compare our results with other approaches with various forms for the two-dimensional coupling. We also consider the vortex states and study the effects of density-dependent interactions on the formation of vortices.
The theory of Bose-Einstein condensation in a two-dimensional(2D) harmonic trap is developed from 2D Gross-Pitaevskii equation. The 2D interaction strength is obtained from a 2D collision theory. We show the realization of 2D condensation of trapped Bose atoms directly by obtaining the stable solutions for the condensate wave function from the 2D Gross-Pitaevskii equation. We calculate the ground-state energy of the 2D system, and also the wave function of the 2D vortex state. In particular, the 2D energy state becomes less stable than the 3D case with the number of trapped atoms. The results of the 2D Bose condensation are also compared with those of the well-known 3D case.
We study the interaction effects on the condensates by considering a model of one-dimensional bosons. The harmonic external potential allows for the formation of a condensate in these systems. Using a density-functional theory-type formalism we obtain an equation describing the condensate wave function in the limit of very strong interactions between the bosons. We then consider a model of strongly interacting two-component system of bosons and study its stability conditions. Similar to the weakly interacting case, the two-component system exhibits coexisting and segregated phases depending on system parameters.
We present an overview of our recent work describing the treatment of ultracold atomic Bose gases confined to two dimensions in a harmonic trap. We show how the gas goes through a number of regimes as the axially confining potential is increased and discuss the scattering properties of the gas in each of these regimes. We then use the formalism developed to investigate the phase-coherent Bose-Einstein condensate that is present in the trapped two-dimensional gas at temperatures that are low compared to the ideal gas critical temperature and to analyze the first-order coherence as a function of temperature. We identify the regime in which the gas loses its global phase coherence, although a macroscopic occupation of the ground state persists at a temperature well below the ideal gas critical temperature. We comment on the possible connection between this fluctuating regime and the Berezinskii-Kosterlitz-Thouless phase.
Abstract By using the one-dimensional canonical partition function, we modelled an ideal gas-like form of a set of Bose-Einstein condensates confined by a three-dimensional anisotropic parabolic trap. The model itself was constructed by taking the eigenenergies of the one-dimensional Gross-Pitaevskii equation in the longitudinal direction and enabling the harmonic volume as the inverse cube of average geometric trapping frequency to substitute the real volume. In this paper, we showed that the condensates form an ideal gas represented by its equation of state and have similar mature to Einstein’s solid-like model with the corrections in both the low and high temperatures in the internal energy formulations.