Spin structures of the ground states of four body bound systems with spin 3 cold atoms

Abstract We consider the case that four spin-3 atoms are confined in an optical trap. The temperature is so low that the spatial degrees of freedom have been frozen. Exact numerical and analytical solutions for the spin-states have been both obtained. Two kinds of phase-diagrams for the ground state...

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Autores principales:	Y. M. Liu, C. G. Bao
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/483bafb14bc94e7cbe94fd722e3f2899
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spelling	oai:doaj.org-article:483bafb14bc94e7cbe94fd722e3f28992021-12-02T19:13:48ZSpin structures of the ground states of four body bound systems with spin 3 cold atoms10.1038/s41598-021-97521-y2045-2322https://doaj.org/article/483bafb14bc94e7cbe94fd722e3f28992021-09-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-97521-yhttps://doaj.org/toc/2045-2322Abstract We consider the case that four spin-3 atoms are confined in an optical trap. The temperature is so low that the spatial degrees of freedom have been frozen. Exact numerical and analytical solutions for the spin-states have been both obtained. Two kinds of phase-diagrams for the ground states (g.s.) have been plotted. In general, the eigen-states with the total-spin S (a good quantum number) can be expanded in terms of a few basis-states $$f_{S,i}$$ f S , i . Let $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ be the probability of a pair of spins coupled to $$\lambda =0, 2, 4$$ λ = 0 , 2 , 4 , and 6 in the $$f_{S,i}$$ f S , i state. Obviously, when the strength $$g_{\lambda }$$ g λ of the $$\lambda $$ λ -channel is more negative, the basis-state with the largest $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ would be more preferred by the g.s.. When two strengths are more negative, the two basis-states with the two largest probabilities would be more important components. Thus, based on the probabilities, the spin-structures (described via the basis-states) can be understood. Furthermore, all the details in the phase-diagrams, say, the critical points of transition, can also be explained. Note that, for $$f_{S,i}$$ f S , i , $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ is completely determined by symmetry. Thus, symmetry plays a very important role in determining the spin-structure of the g.s..Y. M. LiuC. G. BaoNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-8 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Y. M. Liu C. G. Bao Spin structures of the ground states of four body bound systems with spin 3 cold atoms
description	Abstract We consider the case that four spin-3 atoms are confined in an optical trap. The temperature is so low that the spatial degrees of freedom have been frozen. Exact numerical and analytical solutions for the spin-states have been both obtained. Two kinds of phase-diagrams for the ground states (g.s.) have been plotted. In general, the eigen-states with the total-spin S (a good quantum number) can be expanded in terms of a few basis-states $$f_{S,i}$$ f S , i . Let $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ be the probability of a pair of spins coupled to $$\lambda =0, 2, 4$$ λ = 0 , 2 , 4 , and 6 in the $$f_{S,i}$$ f S , i state. Obviously, when the strength $$g_{\lambda }$$ g λ of the $$\lambda $$ λ -channel is more negative, the basis-state with the largest $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ would be more preferred by the g.s.. When two strengths are more negative, the two basis-states with the two largest probabilities would be more important components. Thus, based on the probabilities, the spin-structures (described via the basis-states) can be understood. Furthermore, all the details in the phase-diagrams, say, the critical points of transition, can also be explained. Note that, for $$f_{S,i}$$ f S , i , $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ is completely determined by symmetry. Thus, symmetry plays a very important role in determining the spin-structure of the g.s..
format	article
author	Y. M. Liu C. G. Bao
author_facet	Y. M. Liu C. G. Bao
author_sort	Y. M. Liu
title	Spin structures of the ground states of four body bound systems with spin 3 cold atoms
title_short	Spin structures of the ground states of four body bound systems with spin 3 cold atoms
title_full	Spin structures of the ground states of four body bound systems with spin 3 cold atoms
title_fullStr	Spin structures of the ground states of four body bound systems with spin 3 cold atoms
title_full_unstemmed	Spin structures of the ground states of four body bound systems with spin 3 cold atoms
title_sort	spin structures of the ground states of four body bound systems with spin 3 cold atoms
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/483bafb14bc94e7cbe94fd722e3f2899
work_keys_str_mv	AT ymliu spinstructuresofthegroundstatesoffourbodyboundsystemswithspin3coldatoms AT cgbao spinstructuresofthegroundstatesoffourbodyboundsystemswithspin3coldatoms
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Spin structures of the ground states of four body bound systems with spin 3 cold atoms

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