Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation

• Published in: Materials Vol. 13; no. 10; p. 2236
• Main Authors: Pereira, Lucas Carvalho, Nascimento, Valter Aragão do
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 13.05.2020; MDPI
• Subjects: Bose-Einstein condensates; Chemical potential; Cigars; Condensed matter physics; Fermi gases; Fluids; Mathematical models; Molecular physics; Optical lattices; Physical properties; Physics; Quantum dots; Solid state physics; Superfluidity; Superlattices; Trapping; Pöschl–Teller potential; variational method; split-step Crank–Nicolson method; Bose–Einstein condensates
• ISSN: 1996-1944; 1996-1944
• DOI: 10.3390/ma13102236

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.