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Collective Excitation of Bose-Einstein Condensate of Bose Atoms with P\"Oschl-Teller Interaction

Avra Banerjee, Arnab Bhowmik, Dwipesh Majumder

Published Jan 1, 2024• 0 citations
Publisher
DOI
10.2139/ssrn.4876459

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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.

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ABSTRACT In this study, the dynamics of a quasi 1D Bose–Einstein condensate is investigated with the help of homotopy perturbation and Bernoulli sub‐equation function methods, and their effectiveness is compared. The quasi‐1D condensate, composed of interacting atoms at low temperatures and low densities, is modeled by the 1D Gross–Pitaevskii equation, which provides highly accurate results under the assumptions of mean‐field theory. In this context, the equation is considered both in the absence of a trap potential and in the presence of the Pöschl–Teller trap potential, which holds special significance in quantum mechanics. For the first time, the analysis of the 1D Gross–Pitaevski equation with the Pöschl–Teller trap potential is carried out using the Bernoulli sub‐equation function and homotopy perturbation methods.

Annalen der Physik•Feb 1, 2026•0 citations
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.
ABSTRACT In this study, the dynamics of a quasi 1D Bose–Einstein condensate is investigated with the help of homotopy perturbation and Bernoulli sub‐equation function methods, and their effectiveness is compared. The quasi‐1D condensate, composed of interacting atoms at low temperatures and low densities, is modeled by the 1D Gross–Pitaevskii equation, which provides highly accurate results under the assumptions of mean‐field theory. In this context, the equation is considered both in the absence of a trap potential and in the presence of the Pöschl–Teller trap potential, which holds special significance in quantum mechanics. For the first time, the analysis of the 1D Gross–Pitaevski equation with the Pöschl–Teller trap potential is carried out using the Bernoulli sub‐equation function and homotopy perturbation methods.