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:physics/0104013 · Physical Review A

Nature of spinor Bose-Einstein condensates in rubidium

Nille N. Klausen, John L. Bohn, Chris H. Greene

Published Oct 2, 2001• 166 citations
arXivHTMLPDF

Abstract

We perform detailed close-coupling calculations for the rubidium isotopes ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ to ascertain the nature of their spinor Bose-Einstein condensates. These calculations predict that the spinor condensate for the spin-1 boson ${}^{87}\mathrm{Rb}$ has a ferromagnetic nature. The spinor condensates for the spin-2 bosons ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb},$ however, are both predicted to be polar. The nature of a spin-1 condensate hinges critically on the sign of the difference between the s-wave scattering lengths for total spins 0 and 2 while the nature of a spin-2 condensate depends on the values of the differences between s-wave scattering lengths for the total spins 0, 2, and 4. These scattering lengths were extracted previously and found to have overlapping uncertainties for all three cases, thus leaving the nature of the spinor condensates ambiguous. The present study exploits a refined uncertainty analysis of the scattering lengths based on recently improved result from experimental work by Roberts et al., which permits us to extract an unambiguous result for the nature of the ground state spinor condensates.

DOI
10.1103/physreva.64.053602

Related papers

Observation of a strongly ferromagnetic spinor Bose-Einstein condensate

SeungJung Huh, Kyungtae Kim, Kiryang Kwon +1 more

We report the observation of strongly ferromagnetic F = 1 spinor Bose-Einstein condensates of 7 Li atoms.The condensates are generated in an optical dipole trap without using magnetic Feshbach resonances, so that the condensates have internal spin degrees of freedom.Studying the nonequilibrium spin dynamics, we have measured the ferromagnetic spin interaction energy and determined the s-wave scattering length difference among total spin f channels to be a f =2a f =0 = -18(3) Bohr radius.This strong collision-channel dependence leads to a large variation in the condensate size with different spin composition.We were able to excite a radial monopole mode after a spin-flip transition between the |m F = 0 and |m F = 1 spin states.From the experiments, we estimated the scattering length ratio a f =2 /a f =0 = 0.27(6), and determined a f =2 = 7(2) and a f =0 = 25(5) Bohr radii, respectively.The results indicate the spin-dependent interaction energy of our system is as large as 46% of the condensate chemical potential.

arXiv:2006.06228•Physical Review Research•Sep 23, 2020•45 citations

Spinor Bose Condensates in Optical Traps

Tin-Lun Ho

We show that in an optical trap the ground states of spin-1 bosons such as ${}^{23}\mathrm{Na}$, ${}^{39}\mathrm{K}$, and ${}^{87}\mathrm{Rb}$ can be either ferromagnetic or ``polar" states, depending on the scattering lengths in different angular momentum channels. The collective modes of these states have very different spin character and spatial distributions. While ordinary vortices are stable in the polar state, only those with unit circulation are stable in the ferromagnetic state. The ferromagnetic state also has coreless (or Skyrmion) vortices like those of ${}^{3}\mathrm{He}\ensuremath{-}A$.

arXiv:cond-mat/9803231•Physical Review Letters•Jul 27, 1998•1,552 citations

Dynamics of F=2 Spinor Bose-Einstein Condensates

H. Schmaljohann, M. Erhard, Jochen Kronjäger +6 more

We experimentally investigate and analyze the rich dynamics in $F=2$ spinor Bose-Einstein condensates of $^{87}\mathrm{R}\mathrm{b}$. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular, we measure conversion rates in the range of ${10}^{\ensuremath{-}12}\text{ }\text{ }{\mathrm{c}\mathrm{m}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for spin-changing collisions within the $F=2$ manifold and spin-dependent loss rates in the range of ${10}^{\ensuremath{-}13}\text{ }\text{ }{\mathrm{c}\mathrm{m}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for hyperfine-changing collisions. We observe polar behavior in the $F=2$ ground state of $^{87}\mathrm{R}\mathrm{b}$, while we find the $F=1$ ground state to be ferromagnetic. We further see a magnetization for condensates prepared with nonzero total spin.

arXiv:cond-mat/0308281•Physical Review Letters•Jan 28, 2004•345 citations

Ferromagnetic phase transition in spinor Bose gases

Qiang Gu

The achievement in cooling alkali atomic gases, such as $^{87}$Rb, $^{23}$Na and $^{7}$Li, to quantum degeneracy opens up a way to study magnetism in spinor bosons, because these constituent atoms usually have a hyperfine spin degree of freedom. This article reviews several basic problems related to the ferromagnetic phase transition in spinor atomic Bose gases from a theoretical perspective. After a brief discussion on various possible origins of the ferromagnetic interaction, the phase diagram of the ferromagnetically coupled spinor bosons is investigated. It is found that the ferromagnetic transition occurs always above Bose-Einstein condensation and the Bose condensate is fully polarized. The low-lying collective excitations of the spinor condensate, including spin and density modes, are discussed. The spectrum of the density mode is of the Bogliubov form and the spin wave spectrum has a $k^2$-formed dispersion relation at long wavelengths. The spin-wave stiffness coefficient contains contribut

arXiv:cond-mat/0512693•Dec 29, 2005•0 citations

Phase diagrams of F=2 spinor Bose-Einstein condensates

Cristian V. Ciobanu, Sungkit Yip, Tin-Lun Ho

We show that there are three possible phases for a spin-2 spinor Bose condensate, one more compared to the spin-1 case. The order parameters of these phases are the spontaneous magnetization and the singlet pair amplitude. Current estimates of scattering lengths show that all three phases have realizations in optically trapped alkali atoms. There is also a one-to-one correspondence between the structure of a spin-2 spinor Bose condensate and that of a d-wave BCS superfluid.

arXiv:cond-mat/9908018•Physical Review A•Feb 11, 2000•230 citations

Theory of spin-2 Bose-Einstein condensates: Spin correlations, magnetic response, and excitation spectra

Masahito Ueda, Masato Koashi

The ground states of Bose-Einstein condensates (BECs) of spin-2 bosons are classified into three distinct phases (ferromagnetic, ``antiferromagnetic,'' and cyclic) depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the thermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied magnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ``pairs'' undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ``trios'' condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.

arXiv:cond-mat/0203052•Physical Review A•May 29, 2002•163 citations
We perform detailed close-coupling calculations for the rubidium isotopes 85Rb{}^{85}\mathrm{Rb}85Rb and 87Rb{}^{87}\mathrm{Rb}87Rb to ascertain the nature of their spinor Bose-Einstein condensates. These calculations predict that the spinor condensate for the spin-1 boson 87Rb{}^{87}\mathrm{Rb}87Rb has a ferromagnetic nature. The spinor condensates for the spin-2 bosons 85Rb{}^{85}\mathrm{Rb}85Rb and 87Rb,{}^{87}\mathrm{Rb},87Rb, however, are both predicted to be polar. The nature of a spin-1 condensate hinges critically on the sign of the difference between the s-wave scattering lengths for total spins 0 and 2 while the nature of a spin-2 condensate depends on the values of the differences between s-wave scattering lengths for the total spins 0, 2, and 4. These scattering lengths were extracted previously and found to have overlapping uncertainties for all three cases, thus leaving the nature of the spinor condensates ambiguous. The present study exploits a refined uncertainty analysis of the scattering lengths based on recently improved result from experimental work by Roberts et al., which permits us to extract an unambiguous result for the nature of the ground state spinor condensates.
We report the observation of strongly ferromagnetic F = 1 spinor Bose-Einstein condensates of 7 Li atoms.The condensates are generated in an optical dipole trap without using magnetic Feshbach resonances, so that the condensates have internal spin degrees of freedom.Studying the nonequilibrium spin dynamics, we have measured the ferromagnetic spin interaction energy and determined the s-wave scattering length difference among total spin f channels to be a f =2a f =0 = -18(3) Bohr radius.This strong collision-channel dependence leads to a large variation in the condensate size with different spin composition.We were able to excite a radial monopole mode after a spin-flip transition between the |m F = 0 and |m F = 1 spin states.From the experiments, we estimated the scattering length ratio a f =2 /a f =0 = 0.27(6), and determined a f =2 = 7(2) and a f =0 = 25(5) Bohr radii, respectively.The results indicate the spin-dependent interaction energy of our system is as large as 46% of the condensate chemical potential.
We show that in an optical trap the ground states of spin-1 bosons such as 23Na{}^{23}\mathrm{Na}23Na, 39K{}^{39}\mathrm{K}39K, and 87Rb{}^{87}\mathrm{Rb}87Rb can be either ferromagnetic or ``polar" states, depending on the scattering lengths in different angular momentum channels. The collective modes of these states have very different spin character and spatial distributions. While ordinary vortices are stable in the polar state, only those with unit circulation are stable in the ferromagnetic state. The ferromagnetic state also has coreless (or Skyrmion) vortices like those of ${}^{3}\mathrm{He}\ensuremath{-}A$.
We experimentally investigate and analyze the rich dynamics in F=2F=2F=2 spinor Bose-Einstein condensates of 87Rb^{87}\mathrm{R}\mathrm{b}87Rb. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular, we measure conversion rates in the range of ${10}^{\ensuremath{-}12}\text{ }\text{ }{\mathrm{c}\mathrm{m}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for spin-changing collisions within the F=2F=2F=2 manifold and spin-dependent loss rates in the range of ${10}^{\ensuremath{-}13}\text{ }\text{ }{\mathrm{c}\mathrm{m}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for hyperfine-changing collisions. We observe polar behavior in the F=2F=2F=2 ground state of 87Rb^{87}\mathrm{R}\mathrm{b}87Rb, while we find the F=1F=1F=1 ground state to be ferromagnetic. We further see a magnetization for condensates prepared with nonzero total spin.
The achievement in cooling alkali atomic gases, such as 87^{87}87Rb, 23^{23}23Na and 7^{7}7Li, to quantum degeneracy opens up a way to study magnetism in spinor bosons, because these constituent atoms usually have a hyperfine spin degree of freedom. This article reviews several basic problems related to the ferromagnetic phase transition in spinor atomic Bose gases from a theoretical perspective. After a brief discussion on various possible origins of the ferromagnetic interaction, the phase diagram of the ferromagnetically coupled spinor bosons is investigated. It is found that the ferromagnetic transition occurs always above Bose-Einstein condensation and the Bose condensate is fully polarized. The low-lying collective excitations of the spinor condensate, including spin and density modes, are discussed. The spectrum of the density mode is of the Bogliubov form and the spin wave spectrum has a k2k^2k2-formed dispersion relation at long wavelengths. The spin-wave stiffness coefficient contains contribut
The ground states of Bose-Einstein condensates (BECs) of spin-2 bosons are classified into three distinct phases (ferromagnetic, ``antiferromagnetic,'' and cyclic) depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the thermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied magnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ``pairs'' undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ``trios'' condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.