Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0611171 · Physical Review A

Symmetry and inert states of spin Bose-Einstein condensates

Sungkit Yip

Published Feb 28, 2007• 40 citations
arXivHTMLPDF

Abstract

We construct the list of all possible inert states of spin Bose-Einstein condensates for $S\ensuremath{\le}4$. In doing so, we also obtain their symmetry properties. These results are applied to classify line defects of spin condensates in zero magnetic field.

DOI
10.1103/physreva.75.023625

Related papers

Symmetry classification of spinor Bose-Einstein condensates

Yuki Kawaguchi, Masahito Ueda

We propose a method for systematically finding ground states of spinor Bose-Einstein condensates by utilizing the symmetry properties of the system. By this method, we can find not only an inert state, whose symmetry is maximal in the manifold under consideration, but also a noninert state, which has lower symmetry and depends on the parameters in the Hamiltonian. We establish the symmetry-classification method for the spin-1, 2, and 3 cases at zero magnetic field, and find an additional phase in the last case. The properties of the vortices in the spin-3 system are also discussed.

arXiv:1109.0400•Physical Review A•Nov 15, 2011•69 citations

Inert states of spin-5 and spin-6 Bose–Einstein condensates

Marcin Fizia, Krzysztof Sacha

In this paper, we consider spinor Bose–Einstein condensates with spin f = 5 and f = 6 in the presence and absence of an external magnetic field at the mean field level. We calculate all of the so-called inert states of these systems. Inert states are a very unique class of stationary states because they remain stationary while Hamiltonian parameters change. Their existence comes from Michel’s theorem. For illustration of symmetry properties of the inert states we use a method that allows for the classification of the systems as a polyhedron with 2 f vertices proposed by Barnett et al (2006 Phys. Rev. Lett. 97 180412).

arXiv:1108.6042•Journal of Physics A Mathematical and Theoretical•Jan 11, 2012•6 citations

Spinor Bose-Einstein Condensates and Topological Defects

Mäkelä, Harri

This thesis concentrates on the topological defects of spin-1 and spin-2 Bose-Einstein condensates, the ground states of spin-3 condensates, and the inert states of spinor condensates with arbitrary spin. Our work is based on the description of a spinor condensate of spin-S atoms in terms of a state vector of a spin-S particle. The results of the homotopy theory are used to study the existence and structure of the topological defects in spinor condensates. We construct examples of defects, study their energetics, and examine how their stability is affected by the presence of an external magnetic field. The ground states of spin-3 condensates are calculated using analytical and numerical means. Special emphasis is put on the ground states of a chromium condensate, whose dependence on the magnetic dipole-dipole interaction is studied. A simple geometrical method for the calculation of inert states of spinor condensates is presented. This method is used to find candidates for the ground states of spin-S condensates.

•Nov 14, 2007•0 citations

Topological defects in spinor condensates

H M kel, Yang Zhang, Kalle‐Antti Suominen

We investigate the structure of topological defects in the ground states of spinor Bose–Einstein condensates with spin F = 1 or F = 2. The type and number of defects are determined by calculating the first and second homotopy groups of the order-parameter space. The order-parameter space is identified with a set of degenerate ground state spinors. Because the structure of the ground state depends on whether or not there is an external magnetic field applied to the system, defects are sensitive to the magnetic field. We study both cases and find that the defects in zero and non-zero field are different.

arXiv:cond-mat/0305497•Journal of Physics A Mathematical and General•Jul 29, 2003•53 citations

Homotopy Theory of Topological Defects in Spinor Condensates

Yunbo Zhang, H. Mäkelä, Kalle‐Antti Suominen

We investigate the topological defects in atomic spin-1 and spin-2 Bose-Einstein condensates by applying the homotopy group theory. With this rigorous approach we clarify the previously controversial identification of symmetry groups and order parameter spaces for the spin-1 case, and show that the spin-2 case provides a rare example of a physical system with non-Abelian line defects, and the possibility to have winding numbers of 1/3 and its multiples.

arXiv:cond-mat/0305489•May 21, 2003•0 citations

Ground-state phases of a mixture of spin-1 and spin-2 Bose-Einstein condensates

Naoki Irikura, Yujiro Eto, Takuya Hirano +1 more

We investigate the ground-state phases of a mixture of spin-1 and spin-2 Bose-Einstein condensates at zero magnetic field. In addition to the intraspin interactions, two spin-dependent interaction coefficients are introduced to describe the interspin interaction. We systematically explore the wide parameter space, and obtain phase diagrams containing a rich variety of phases. For example, there exists a phase in which the spin-1 and spin-2 vectors are tilted relative to each other breaking the axial symmetry.

arXiv:1712.05111•Physical Review A•Feb 13, 2018•20 citations
We construct the list of all possible inert states of spin Bose-Einstein condensates for S\ensuremath≤4S\ensuremath{\le}4S\ensuremath≤4. In doing so, we also obtain their symmetry properties. These results are applied to classify line defects of spin condensates in zero magnetic field.
We propose a method for systematically finding ground states of spinor Bose-Einstein condensates by utilizing the symmetry properties of the system. By this method, we can find not only an inert state, whose symmetry is maximal in the manifold under consideration, but also a noninert state, which has lower symmetry and depends on the parameters in the Hamiltonian. We establish the symmetry-classification method for the spin-1, 2, and 3 cases at zero magnetic field, and find an additional phase in the last case. The properties of the vortices in the spin-3 system are also discussed.
In this paper, we consider spinor Bose–Einstein condensates with spin f = 5 and f = 6 in the presence and absence of an external magnetic field at the mean field level. We calculate all of the so-called inert states of these systems. Inert states are a very unique class of stationary states because they remain stationary while Hamiltonian parameters change. Their existence comes from Michel’s theorem. For illustration of symmetry properties of the inert states we use a method that allows for the classification of the systems as a polyhedron with 2 f vertices proposed by Barnett et al (2006 Phys. Rev. Lett. 97 180412).
This thesis concentrates on the topological defects of spin-1 and spin-2 Bose-Einstein condensates, the ground states of spin-3 condensates, and the inert states of spinor condensates with arbitrary spin. Our work is based on the description of a spinor condensate of spin-S atoms in terms of a state vector of a spin-S particle. The results of the homotopy theory are used to study the existence and structure of the topological defects in spinor condensates. We construct examples of defects, study their energetics, and examine how their stability is affected by the presence of an external magnetic field. The ground states of spin-3 condensates are calculated using analytical and numerical means. Special emphasis is put on the ground states of a chromium condensate, whose dependence on the magnetic dipole-dipole interaction is studied. A simple geometrical method for the calculation of inert states of spinor condensates is presented. This method is used to find candidates for the ground states of spin-S condensates.
We investigate the structure of topological defects in the ground states of spinor Bose–Einstein condensates with spin F = 1 or F = 2. The type and number of defects are determined by calculating the first and second homotopy groups of the order-parameter space. The order-parameter space is identified with a set of degenerate ground state spinors. Because the structure of the ground state depends on whether or not there is an external magnetic field applied to the system, defects are sensitive to the magnetic field. We study both cases and find that the defects in zero and non-zero field are different.
We investigate the ground-state phases of a mixture of spin-1 and spin-2 Bose-Einstein condensates at zero magnetic field. In addition to the intraspin interactions, two spin-dependent interaction coefficients are introduced to describe the interspin interaction. We systematically explore the wide parameter space, and obtain phase diagrams containing a rich variety of phases. For example, there exists a phase in which the spin-1 and spin-2 vectors are tilted relative to each other breaking the axial symmetry.