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/0610071 · Physical Review A

Ground states of spin-3 Bose-Einstein condensates for conserved magnetization

H. Mäkelä, Kalle‐Antti Suominen

Published Mar 21, 2007• 37 citations
arXivHTMLPDF

Abstract

We calculate the ground states and ground state phase diagrams of Bose-Einstein condensates of spin-3 atoms under the assumption of conserved magnetization. We especially concentrate on the ground states of a $^{52}\mathrm{Cr}$ condensate. In $^{52}\mathrm{Cr}$ the magnetic dipole-dipole interaction enables magnetization changing collisions, but in a strong magnetic field these are suppressed. In the calculation of the phase diagrams we neglect the contribution from the dipole-dipole interaction, but discuss its effects at the end of the paper. We show that the ground state of a $^{52}\mathrm{Cr}$ condensate does not seem to depend on whether or not the dipole-dipole interaction is taken into attention.

DOI
10.1103/physreva.75.033610

Related papers

Spontaneous Demagnetization of a Dipolar Spinor Bose Gas in an Ultralow Magnetic Field

Benjamin Pasquiou, É. Maréchal, G. Bismut +4 more

We study the spinor properties of S = 3 (52)Cr condensates, in which dipole-dipole interactions allow changes in magnetization. We observe a demagnetization of the Bose-Einstein condensate (BEC) when the magnetic field is quenched below a critical value corresponding to a phase transition between a ferromagnetic and a nonpolarized ground state, which occurs when spin-dependent contact interactions overwhelm the linear Zeeman effect. The critical field is increased when the density is raised by loading the BEC in a deep 2D optical lattice. The magnetization dynamics is set by dipole-dipole interactions.

arXiv:1103.4819•Physical Review Letters•Jun 23, 2011•115 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

Spin-3 Chromium Bose-Einstein Condensates

Luis Santos, Tilman Pfau

We analyze the physics of spin-3 Bose-Einstein condensates, and, in particular, the new physics expected in ongoing experiments with condensates of chromium atoms. We first discuss the ground-state properties, which, depending on still unknown chromium parameters, and for low magnetic fields, can present various types of phases. We also discuss the spinor dynamics in chromium spinor condensates, which present significant qualitative differences when compared to other spinor condensates. In particular, dipole-induced spin relaxation may lead for low magnetic fields to transfer of spin into angular momentum similar to the well-known Einstein-de Haas effect. Additionally, a rapid large transference of population between distant magnetic states also becomes possible.

arXiv:cond-mat/0510634•Physical Review Letters•May 16, 2006•190 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

Metastable spin-phase diagrams in antiferromagnetic Bose-Einstein condensates

Eduardo Serrano-Ensástiga, Francisco Mireles

Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this paper, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of self-consistency methods. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase in temperature induces a traceable shift of the ferromagnetic-polar transition boundary, behavior previously not noted by self-consistent mean-field calculations.

arXiv:2109.01986•Physical Review A•Dec 13, 2021•4 citations

Dynamics of quantum phases in a spinor condensate

S. Yi, Özgür Esat Müstecaplıoğlu, Li You

We discuss the quantum phases and their diffusion dynamics in a spinor-1 atomic Bose-Einstein condensate. For ferromagnetic interactions, we obtain the exact ground-state distribution of the phases associated with the total atom number $(N),$ the total magnetization $(\mathcal{M}),$ and the alignment (or hypercharge) (Y) of the system. The mean-field ground state is stable against fluctuations of atom numbers in each of the spin components, and the phases associated with the order parameter for each spin components diffuse while dynamically recovering the two broken continuous symmetries [U(1) and SO(2)] when N and $\mathcal{M}$ are conserved, as in current experiments. We discuss the implications to the quantum dynamics due to an external (homogeneous) magnetic field. We also comment on the case of a spinor-1 condensate with antiferromagnetic interactions.

arXiv:cond-mat/0302464•Physical Review A•Jul 30, 2003•18 citations
We calculate the ground states and ground state phase diagrams of Bose-Einstein condensates of spin-3 atoms under the assumption of conserved magnetization. We especially concentrate on the ground states of a 52Cr^{52}\mathrm{Cr}52Cr condensate. In 52Cr^{52}\mathrm{Cr}52Cr the magnetic dipole-dipole interaction enables magnetization changing collisions, but in a strong magnetic field these are suppressed. In the calculation of the phase diagrams we neglect the contribution from the dipole-dipole interaction, but discuss its effects at the end of the paper. We show that the ground state of a 52Cr^{52}\mathrm{Cr}52Cr condensate does not seem to depend on whether or not the dipole-dipole interaction is taken into attention.
We study the spinor properties of S = 3 (52)Cr condensates, in which dipole-dipole interactions allow changes in magnetization. We observe a demagnetization of the Bose-Einstein condensate (BEC) when the magnetic field is quenched below a critical value corresponding to a phase transition between a ferromagnetic and a nonpolarized ground state, which occurs when spin-dependent contact interactions overwhelm the linear Zeeman effect. The critical field is increased when the density is raised by loading the BEC in a deep 2D optical lattice. The magnetization dynamics is set by dipole-dipole interactions.
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 analyze the physics of spin-3 Bose-Einstein condensates, and, in particular, the new physics expected in ongoing experiments with condensates of chromium atoms. We first discuss the ground-state properties, which, depending on still unknown chromium parameters, and for low magnetic fields, can present various types of phases. We also discuss the spinor dynamics in chromium spinor condensates, which present significant qualitative differences when compared to other spinor condensates. In particular, dipole-induced spin relaxation may lead for low magnetic fields to transfer of spin into angular momentum similar to the well-known Einstein-de Haas effect. Additionally, a rapid large transference of population between distant magnetic states also becomes possible.
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.
Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this paper, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of self-consistency methods. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase in temperature induces a traceable shift of the ferromagnetic-polar transition boundary, behavior previously not noted by self-consistent mean-field calculations.
We discuss the quantum phases and their diffusion dynamics in a spinor-1 atomic Bose-Einstein condensate. For ferromagnetic interactions, we obtain the exact ground-state distribution of the phases associated with the total atom number (N),(N),(N), the total magnetization (M),(\mathcal{M}),(M), and the alignment (or hypercharge) (Y) of the system. The mean-field ground state is stable against fluctuations of atom numbers in each of the spin components, and the phases associated with the order parameter for each spin components diffuse while dynamically recovering the two broken continuous symmetries [U(1) and SO(2)] when N and M\mathcal{M}M are conserved, as in current experiments. We discuss the implications to the quantum dynamics due to an external (homogeneous) magnetic field. We also comment on the case of a spinor-1 condensate with antiferromagnetic interactions.