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Springer proceedings in physics

Two Component Bose–Einstein Condensate in a Pöschl–Teller Potential

Nilanjan Kundu, Utpal Roy

Published Jan 1, 2019• 0 citations
Publisher
DOI
10.1007/978-981-13-9969-5_12

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We present for the first time an approach about Bose-Einstein condensates made up of atoms with attractive interatomic interactions confined to the Pöschl-Teller hyperbolic potential. In this paper, we consider a Bose-Einstein condensate confined in a cigar-shaped, and it was modeled by the mean field equation known as the Gross-Pitaevskii equation. An analytical (variational method) and numerical (two-step Crank-Nicolson) approach is proposed to study the proposed model of interatomic interaction. The solutions of the one-dimensional Gross-Pitaevskii equation obtained in this paper confirmed, from a theoretical point of view, the possibility of the Pöschl-Teller potential to confine Bose-Einstein condensates. The chemical potential as a function of the depth of the Pöschl-Teller potential showed a behavior very similar to the cases of Bose-Einstein condensates and superfluid Fermi gases in optical lattices and optical superlattices. The results presented in this paper can open the way for several applications in atomic and molecular physics, solid state physics, condensed matter physics, and material sciences.
This paper presents the numerical and variational solutions of the 1D Schrödinger Equation submitted to the Pöschl-Teller potential. The methods used were the Variational Method and the Finite Difference Method. They were presented in a didactic and detailed way with the purpose of instructing both undergraduate and graduate students, about the applicability and effectiveness of the aforementioned methods. We use the Pöschl-Teller potential due to the fact that it is little explored in the books of Quantum Mechanics used in undergraduation courses and also because of its diverse applications, such as in Bose-Einstein condensates, waveguides, topological defects in field theory and so on. We conclude this paper comparing the variational and numerical solutions with the analytical solution and present the advantages of each method.