Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation
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 fie...
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MDPI AG
2020-05-01
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| Online Access: | https://www.mdpi.com/1996-1944/13/10/2236 |
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| author | Lucas Carvalho Pereira Valter Aragão do Nascimento |
| author_facet | Lucas Carvalho Pereira Valter Aragão do Nascimento |
| author_sort | Lucas Carvalho Pereira |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T19:52:44Z |
| format | Article |
| id | doaj.art-9230a6879d8e40b7876bfc593c77c94d |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-10T19:52:44Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials |
| spelling | doaj.art-9230a6879d8e40b7876bfc593c77c94d2023-11-20T00:17:27ZengMDPI AGMaterials1996-19442020-05-011310223610.3390/ma13102236Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii EquationLucas Carvalho Pereira0Valter Aragão do Nascimento1Programa de Pós-Graduaçāo em Ciência dos Materiais, Instituto de Física, Universidade Federal de Mato Grosso do Sul, Campo Grande 79070-900, Mato Grosso do Sul, BrazilGroup of Spectroscopy and Bioinformatics Applied to Biodiversity and Health, School of Medicine, Postgraduation Program in Health and Development in the Midwest Region, Faculty of Medicine, Federal University of Mato Grosso do Sul, Campo Grande 79070-900, Mato Grosso do Sul, BrazilWe 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.https://www.mdpi.com/1996-1944/13/10/2236Bose–Einstein condensatesPöschl–Teller potentialvariational methodsplit-step Crank–Nicolson method |
| spellingShingle | Lucas Carvalho Pereira Valter Aragão do Nascimento Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation Materials Bose–Einstein condensates Pöschl–Teller potential variational method split-step Crank–Nicolson method |
| title | Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation |
| title_full | Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation |
| title_fullStr | Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation |
| title_full_unstemmed | Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation |
| title_short | Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation |
| title_sort | dynamics of bose einstein condensates subject to the poschl teller potential through numerical and variational solutions of the gross pitaevskii equation |
| topic | Bose–Einstein condensates Pöschl–Teller potential variational method split-step Crank–Nicolson method |
| url | https://www.mdpi.com/1996-1944/13/10/2236 |
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