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:1707.02660 · Physical Review A

Spinor dynamics in a mixture of spin-1 and spin-2 Bose-Einstein condensates

Yujiro Eto, Hitoshi Shibayama, Hiroki Saito, Takuya Hirano

Published Feb 13, 2018• 17 citations
arXivHTMLPDF

Abstract

The spinor dynamics of Bose-Einstein condensates of $^{87}\mathrm{Rb}$ atoms with hyperfine spins of 1 and 2 are investigated. A mixture of spinor condensates is generated in the transversely polarized spin-1 and the longitudinally polarized spin-2 states using simultaneous Ramsey interferometry. In the subsequent dynamics, temporal modulation of spin-1 magnetization is observed in the spinor mixture due to the spin-dependent interaction with the spin-2 component. By comparison with numerical simulations based on the Gross-Pitaevskii equation, we find that the observed nonferromagnetic dynamics reflect the ground-state properties of the spinor mixture.

DOI
10.1103/physreva.97.021602

Related papers

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

Spin evolution in ultracold quantum gases

H. Schmaljohann, Erhard, M., Kronjäger, J. +5 more

We discuss the static and dynamic magnetic properties of cold quantum gas systems. In particular, we investigate and analyze the ground state properties and dynamics of F = 2 spinor Bose-Einstein condensates of 87Rb. The rich physics of these systems is governed by an interplay between mean-field-driven spin dynamics and hyperfine-changing losses in addition to interactions with atoms in the thermal cloud. We find conversion rates on the order of 10-12 cm3 s-1 for spin-changing collisions within the F = 2 manifold and spin-dependent loss rates on the order of 10-13 cm3 s-1 for hyperfine-changing collisions. Our data leads to the conclusion that the F = 2 ground state of 87Rb is polar, while we measure the F = 1 ground state to be ferromagnetic. As remarkable features in the spin dynamics we observe spinor oscillations and a delayed formation of new mF-condensate components.

•Sep 1, 2004•0 citations

Observation of Dipole-Induced Spin Texture in an Rb87 Bose-Einstein Condensate

Yujiro Eto, Hiroki Saito, Takuya Hirano

We report the formation of spin texture resulting from the magnetic dipole-dipole interaction in a spin-2 87Rb Bose-Einstein condensate. The spinor condensate is prepared in the transversely polarized spin state and the time evolution is observed under a magnetic field of 90 mG with a gradient of 3 mG/cm using Stern-Gerlach imaging. The experimental results are compared with numerical simulations of the Gross-Pitaevskii equation, which reveals that the observed spatial modulation of the longitudinal magnetization is due to the spin precession in an effective magnetic field produced by the dipole-dipole interaction. These results show that the dipole-dipole interaction has considerable effects even on spinor condensates of alkali metal atoms.

arXiv:1402.7071•Physical Review Letters•May 9, 2014•54 citations

Quenched binary Bose-Einstein condensates: Spin-domain formation and coarsening

S. De, Daniel L. Campbell, Rodney Price +3 more

We explore the time evolution of two-component Bose-Einstein condensates (BECs), quasi one dimensional with respect to their spinor dynamics, following a quench from one component BECs with a $\mathrm{U}(1)$ order parameter into two-component condensates with a $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single-component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifying any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin-polarized domains, which are far from the system's ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is consistent with our fully three-dimensional stochastic-projected Gross--Pitaevskii calculation.

arXiv:1211.3127•Physical Review A•Mar 25, 2014•65 citations

Population and phase dynamics of F=1 spinor condensates in an external magnetic field

Dimas Rodrigues Romano, E. J. V. de Passos

We show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor $F=1$ Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicate the absence of metastability.

Physical Review A•Oct 12, 2004•31 citations

Population and phase dynamics of F=1 spinor condensates in an external magnetic field

Dimas Rodrigues Romano, E. J. V. de Passos

We show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor F=1 Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicates the absence of metastability.

arXiv:cond-mat/0408069•Aug 3, 2004•1 citation
The spinor dynamics of Bose-Einstein condensates of 87Rb^{87}\mathrm{Rb}87Rb atoms with hyperfine spins of 1 and 2 are investigated. A mixture of spinor condensates is generated in the transversely polarized spin-1 and the longitudinally polarized spin-2 states using simultaneous Ramsey interferometry. In the subsequent dynamics, temporal modulation of spin-1 magnetization is observed in the spinor mixture due to the spin-dependent interaction with the spin-2 component. By comparison with numerical simulations based on the Gross-Pitaevskii equation, we find that the observed nonferromagnetic dynamics reflect the ground-state properties of the spinor mixture.
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.
We discuss the static and dynamic magnetic properties of cold quantum gas systems. In particular, we investigate and analyze the ground state properties and dynamics of F = 2 spinor Bose-Einstein condensates of 87Rb. The rich physics of these systems is governed by an interplay between mean-field-driven spin dynamics and hyperfine-changing losses in addition to interactions with atoms in the thermal cloud. We find conversion rates on the order of 10-12 cm3 s-1 for spin-changing collisions within the F = 2 manifold and spin-dependent loss rates on the order of 10-13 cm3 s-1 for hyperfine-changing collisions. Our data leads to the conclusion that the F = 2 ground state of 87Rb is polar, while we measure the F = 1 ground state to be ferromagnetic. As remarkable features in the spin dynamics we observe spinor oscillations and a delayed formation of new mF-condensate components.
We report the formation of spin texture resulting from the magnetic dipole-dipole interaction in a spin-2 87Rb Bose-Einstein condensate. The spinor condensate is prepared in the transversely polarized spin state and the time evolution is observed under a magnetic field of 90 mG with a gradient of 3 mG/cm using Stern-Gerlach imaging. The experimental results are compared with numerical simulations of the Gross-Pitaevskii equation, which reveals that the observed spatial modulation of the longitudinal magnetization is due to the spin precession in an effective magnetic field produced by the dipole-dipole interaction. These results show that the dipole-dipole interaction has considerable effects even on spinor condensates of alkali metal atoms.
We explore the time evolution of two-component Bose-Einstein condensates (BECs), quasi one dimensional with respect to their spinor dynamics, following a quench from one component BECs with a U(1)\mathrm{U}(1)U(1) order parameter into two-component condensates with a $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single-component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifying any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin-polarized domains, which are far from the system's ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is consistent with our fully three-dimensional stochastic-projected Gross--Pitaevskii calculation.
We show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor F=1F=1F=1 Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicate the absence of metastability.
We show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor F=1 Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicates the absence of metastability.