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Physical Review A

Strongly interacting one-dimensional Bose-Einstein condensates in harmonic traps

B. Tanatar, K. Erkan

Published Oct 9, 2000• 22 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.62.053601

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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.
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We study the Bose-Einstein condensation phenomenon in a two-dimensional (2D) system of bosons subjected to a harmonic-oscillator-type confining potential. The interaction among the 2D bosons is described by a \ensuremath{\delta} function in configuration space. Solving the Gross-Pitaevskii equation within the two-fluid model we calculate the condensate fraction, ground-state energy, and specific heat of the system. Our results indicate that interacting bosons have similar behavior to those of an ideal system for weak interactions.
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We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactl y soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives quite accurate description of the system in the limit of weak interactions.