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.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/0308281Physical Review LettersJan 28, 2004345 citations

On ground state of spinor Bose–Einstein condensates

Daomin Cao, I‐Liang Chern, Juncheng Wei

Nonlinear Differential Equations and Applications NoDEAFeb 7, 201143 citations

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.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:1109.0400Physical Review ANov 15, 201169 citations

Spin domains in ground-state Bose–Einstein condensates

J. Stenger, S. Inouye, Dan Stamper-Kurn +3 more

arXiv:cond-mat/9901072NatureNov 1, 19981,152 citations

Symmetry classification of spin-orbit-coupled spinor Bose-Einstein condensates

Zhi-Fang Xu, Yuki Kawaguchi, Li You +1 more

We develop a symmetry classification scheme to find ground states of pseudo-spin- $\frac{1}{2}$ , spin-1, and spin-2 spin-orbit-coupled spinor Bose-Einstein condensates and show that as the SO(2) symmetry of simultaneous spin and space rotations is broken into discrete cyclic groups, various types of lattice structures emerge in the absence of a lattice potential. Examples include two different kagome lattices for pseudo-spin- $\frac{1}{2}$ condensates and a nematic vortex lattice in which uniaxial and biaxial spin textures align alternatively for spin-2 condensates. For the pseudo-spin- $\frac{1}{2}$ system, although mean-field states always break time-reversal symmetry, there exists a time-reversal invariant many-body ground state, which is fragmented and expected to be observed in a microcondensate.We develop a symmetry classification scheme to find ground states of pseudo-spin-$\frac{1}{2}$, spin-1, and spin-2 spin-orbit-coupled spinor Bose-Einstein condensates and show that as the SO(2) symmetry of simultaneous spin and space rotations is broken into discrete cyclic groups, various types of lattice structures emerge in the absence of a lattice potential. Examples include two different kagome lattices for pseudo-spin-$\frac{1}{2}$ condensates and a nematic vortex lattice in which uniaxial and biaxial spin textures align alternatively for spin-2 condensates. For the pseudo-spin-$\frac{1}{2}$ system, although mean-field states always break time-reversal symmetry, there exists a time-reversal invariant many-body ground state, which is fragmented and expected to be observed in a microcondensate.

arXiv:1203.2005Physical Review ASep 26, 201274 citations

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.

We develop a symmetry classification scheme to find ground states of pseudo-spin-

\frac{1}{2}

, spin-1, and spin-2 spin-orbit-coupled spinor Bose-Einstein condensates and show that as the SO(2) symmetry of simultaneous spin and space rotations is broken into discrete cyclic groups, various types of lattice structures emerge in the absence of a lattice potential. Examples include two different kagome lattices for pseudo-spin-

\frac{1}{2}

condensates and a nematic vortex lattice in which uniaxial and biaxial spin textures align alternatively for spin-2 condensates. For the pseudo-spin-

\frac{1}{2}

system, although mean-field states always break time-reversal symmetry, there exists a time-reversal invariant many-body ground state, which is fragmented and expected to be observed in a microcondensate.