A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase Singularities
We present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which initially contains several vortices at arbitrary locations. The method allows one to find the analytical solution for the dynamics of the Bose-Einstein condensate in a homogeneous medium and in a para...
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MDPI AG
2023-01-01
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| Series: | Condensed Matter |
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| Online Access: | https://www.mdpi.com/2410-3896/8/1/12 |
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| author | Sergi De María-García Albert Ferrando J. Alberto Conejero Pedro Fernández De Córdoba Miguel Ángel García-March |
| author_facet | Sergi De María-García Albert Ferrando J. Alberto Conejero Pedro Fernández De Córdoba Miguel Ángel García-March |
| author_sort | Sergi De María-García |
| collection | DOAJ |
| description | We present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which initially contains several vortices at arbitrary locations. The method allows one to find the analytical solution for the dynamics of the Bose-Einstein condensate in a homogeneous medium and in a parabolic trap, for the ideal non-interacting case. Secondly, the method allows one to obtain algebraic equations for the trajectories of the position of phase singularities present in the initial condensate along with time (the vortex lines). With these equations, one can predict quantities of interest, such as the time at which a vortex and an antivortex contained in the initial condensate will merge. For the homogeneous case, this method was introduced in the context of photonics. Here, we adapt it to the context of Bose-Einstein condensates, and we extend it to the trapped case for the first time. Also, we offer numerical simulations in the non-linear case, for repulsive and attractive interactions. We use a numerical split-step simulation of the non-linear Gross-Pitaevskii equation to determine how these trajectories and quantities of interest are changed by the interactions. We illustrate the method with several simple cases of interest, both in the homogeneous and parabolically trapped systems. |
| first_indexed | 2024-03-11T06:42:35Z |
| format | Article |
| id | doaj.art-3c2831b03b684989baaf72213187ab52 |
| institution | Directory Open Access Journal |
| issn | 2410-3896 |
| language | English |
| last_indexed | 2024-03-11T06:42:35Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Condensed Matter |
| spelling | doaj.art-3c2831b03b684989baaf72213187ab522023-11-17T10:26:48ZengMDPI AGCondensed Matter2410-38962023-01-01811210.3390/condmat8010012A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase SingularitiesSergi De María-García0Albert Ferrando1J. Alberto Conejero2Pedro Fernández De Córdoba3Miguel Ángel García-March4Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, SpainDepartment d’Optica, Universitat de València, Dr. Moliner, 50, E-46100 Burjassot (València), SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, SpainWe present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which initially contains several vortices at arbitrary locations. The method allows one to find the analytical solution for the dynamics of the Bose-Einstein condensate in a homogeneous medium and in a parabolic trap, for the ideal non-interacting case. Secondly, the method allows one to obtain algebraic equations for the trajectories of the position of phase singularities present in the initial condensate along with time (the vortex lines). With these equations, one can predict quantities of interest, such as the time at which a vortex and an antivortex contained in the initial condensate will merge. For the homogeneous case, this method was introduced in the context of photonics. Here, we adapt it to the context of Bose-Einstein condensates, and we extend it to the trapped case for the first time. Also, we offer numerical simulations in the non-linear case, for repulsive and attractive interactions. We use a numerical split-step simulation of the non-linear Gross-Pitaevskii equation to determine how these trajectories and quantities of interest are changed by the interactions. We illustrate the method with several simple cases of interest, both in the homogeneous and parabolically trapped systems.https://www.mdpi.com/2410-3896/8/1/12Bose-Einstein condensatesvorticesphase singularitiesnumerical method |
| spellingShingle | Sergi De María-García Albert Ferrando J. Alberto Conejero Pedro Fernández De Córdoba Miguel Ángel García-March A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase Singularities Condensed Matter Bose-Einstein condensates vortices phase singularities numerical method |
| title | A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase Singularities |
| title_full | A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase Singularities |
| title_fullStr | A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase Singularities |
| title_full_unstemmed | A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase Singularities |
| title_short | A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase Singularities |
| title_sort | method for the dynamics of vortices in a bose einstein condensate analytical equations of the trajectories of phase singularities |
| topic | Bose-Einstein condensates vortices phase singularities numerical method |
| url | https://www.mdpi.com/2410-3896/8/1/12 |
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