Singularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates

Abstract An approach is proposed to solve the coupled Gross-Pitaevskii equations (CGP) of the 3-species BEC in an analytical way under the Thomas-Fermi approximation (TFA). It was found that, when the strength of a kind of interaction increases and crosses over a critical value, a specific type of s...

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Autores principales:	Y. M. Liu, Y. Z. He, C. G. Bao
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/8d327c3726944ca2b575653f1f2f9251
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spelling	oai:doaj.org-article:8d327c3726944ca2b575653f1f2f92512021-12-02T15:05:33ZSingularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates10.1038/s41598-017-06843-32045-2322https://doaj.org/article/8d327c3726944ca2b575653f1f2f92512017-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-06843-3https://doaj.org/toc/2045-2322Abstract An approach is proposed to solve the coupled Gross-Pitaevskii equations (CGP) of the 3-species BEC in an analytical way under the Thomas-Fermi approximation (TFA). It was found that, when the strength of a kind of interaction increases and crosses over a critical value, a specific type of state-transition will occur and will cause a jump in the total energy. Due to the jump, the energy of the lowest symmetric state becomes considerably higher. This leaves a particular opportunity for the lowest asymmetric state to replace the symmetric states as the ground state. It was further found that the critical values are related to the singularity of either the matrix or a sub-matrix of the CGP. These critical values are not arising from the TFA but inherent in the CGP, and they can be analytically expressed. Furthermore, a model (in which two kinds of atoms separated from each other asymmetrically) has been proposed for the evaluation of the energy of the lowest asymmetric state. With this model the emergence of the asymmetric ground state is numerically confirmed under the TFA. The theoretical formalism of this paper is quite general and can be generalized for BEC with more than three species.Y. M. LiuY. Z. HeC. G. BaoNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-10 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Y. M. Liu Y. Z. He C. G. Bao Singularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates
description	Abstract An approach is proposed to solve the coupled Gross-Pitaevskii equations (CGP) of the 3-species BEC in an analytical way under the Thomas-Fermi approximation (TFA). It was found that, when the strength of a kind of interaction increases and crosses over a critical value, a specific type of state-transition will occur and will cause a jump in the total energy. Due to the jump, the energy of the lowest symmetric state becomes considerably higher. This leaves a particular opportunity for the lowest asymmetric state to replace the symmetric states as the ground state. It was further found that the critical values are related to the singularity of either the matrix or a sub-matrix of the CGP. These critical values are not arising from the TFA but inherent in the CGP, and they can be analytically expressed. Furthermore, a model (in which two kinds of atoms separated from each other asymmetrically) has been proposed for the evaluation of the energy of the lowest asymmetric state. With this model the emergence of the asymmetric ground state is numerically confirmed under the TFA. The theoretical formalism of this paper is quite general and can be generalized for BEC with more than three species.
format	article
author	Y. M. Liu Y. Z. He C. G. Bao
author_facet	Y. M. Liu Y. Z. He C. G. Bao
author_sort	Y. M. Liu
title	Singularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates
title_short	Singularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates
title_full	Singularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates
title_fullStr	Singularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates
title_full_unstemmed	Singularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates
title_sort	singularity in the matrix of the coupled gross-pitaevskii equations and the related state-transitions in three-species condensates
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/8d327c3726944ca2b575653f1f2f9251
work_keys_str_mv	AT ymliu singularityinthematrixofthecoupledgrosspitaevskiiequationsandtherelatedstatetransitionsinthreespeciescondensates AT yzhe singularityinthematrixofthecoupledgrosspitaevskiiequationsandtherelatedstatetransitionsinthreespeciescondensates AT cgbao singularityinthematrixofthecoupledgrosspitaevskiiequationsandtherelatedstatetransitionsinthreespeciescondensates
_version_	1718388779125833728

Singularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates

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