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

Spin evolution in ultracold quantum gases

H. Schmaljohann, Erhard, M., Kronjäger, J., Kottke, M., S. van Staa, J. Arlt, Kai Bongs, K. Sengstock

Published Sep 1, 2004• 0 citations
OpenAlex

Abstract

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.

Related papers

Magnetism in ultracold quantum gases

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

We study the static and dynamic magnetic properties of ultracold quantum gases, in particular the spinor physics of F = 1 and F = 2 Bose-Einstein condensates of 87Rb atoms. Our data lead to the conclusion, that the F = 2 ground state of 87Rb is polar, while we find the F = 1 ground state to be ferromagnetic. The dynamics of spinor systems is linked to an interplay between coherent mean-field interactions, losses and interactions with atoms in the thermal cloud. Within this rich parameter space we observe indications for coherent spinor dynamics and novel thermalization regimes.

Journal of Modern Optics•Jun 18, 2004•2 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

Spinor Bose-Einstein gases

G. Edward Marti, Dan Stamper-Kurn

In a spinor Bose-Einstein gas, the non-zero hyperfine spin of the gas becomes an accessible degree of freedom. At low temperature, such a gas shows both magnetic and superfluid order, and undergoes both density and spin dynamics. These lecture notes present a general overview of the properties of spinor Bose-Einstein gases. The notes are divided in five sections. In the first, we summarize basic properties of multi-component quantum fluids, focusing on the specific case of spinor Bose-Einstein gases and the role of rotational symmetry in defining their properties. Second, we consider the magnetic state of a spinor Bose-Einstein gas, highlighting effects of thermodynamics and Bose-Einstein statistics and also of spin-dependent interactions between atoms. In the third section, we discuss methods for measuring the properties of magnetically ordered quantum gases and present newly developed schemes for spin-dependent imaging. We then discuss the dynamics of spin mixing in which the spin composition of the gas evolves through the spin-dependent interactions within the gas. We discuss spin mixing first from a microscopic perspective, and then advance to discussing collective and beyond-mean-field dynamics. The fifth section reviews recent studies of the magnetic excitations of quantum-degenerate spinor Bose gases. We conclude with some perspectives on future directions for research.

arXiv:1511.01575•Nov 5, 2015•3 citations

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

Yujiro Eto, Hitoshi Shibayama, Hiroki Saito +1 more

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.

arXiv:1707.02660•Physical Review A•Feb 13, 2018•17 citations

Investigating non-equilibrium phenomena in spinor antiferromagnetic Bose-Einstein condensates

Anshuman Vinit

This thesis discusses non-equilibrium phenomena in antiferromagnetic spinor quantum gases. We investigate, both experimentally and theoretically, the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition. A microwave dressing field was used as a novel tool to access the polar to antiferrmagnetic quantum phase transition at the quadratic Zeeman shift, q=0. By performing instantaneous quenches across the phase transition,a dynamical instability was induced in the atomic cloud. This lead to pair formation and rapid amplification of spin +/-1 atoms through spin-mixing collisions. The spatial ordering kinetics in the vicinity of the phase transition was quantified by performing the local spin measurement. The coarsening dynamics was observed for the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud. Rich nonequilibrium behavior was observed in the form of growth and decay of both nematic and magnetic spin waves, following the quench. The spatiotemporal evolution was characterized through two particle correlations between atoms in each pair of spin states, which revealed dramatic differences between the dynamics of the spin correlations and those of the spin populations. \nFinally, we demonstrate the remarkable influence of linear Zeeman term on non-equilibrium dynamics of spinor Bose-Einstein condensates. We show that contrary to prior understanding magnetic field gradient actually suppresses the tendency of spin 0 state to separate into spin +/-1 state. This reconciles the Bogoliubov discrepancies and leads to a dramatic sharpening of the transition point, resulting in a resolution at the 1 Hz level. Our results point to the use of dynamics, rather than equilibrium quantities for high precision measurements of phase transitions in quantum gases.

•Aug 3, 2016•0 citations

Magnetic field dependence of the dynamics of Rb87 spin-2 Bose-Einstein condensates

T. Kuwamoto, K. Araki, T. Eno +1 more

We experimentally studied the spin-dependent collision dynamics of $^{87}\mathrm{Rb}$ spin-2 Bose-Einstein condensates confined in an optical trap. The condensed atoms were initially populated in the $\ensuremath{\mid}F=2,{m}_{F}=0⟩$ state, and their time evolutions in the trap were measured in the presence of external magnetic field strengths ranging from 0.1 to $3.0\phantom{\rule{0.3em}{0ex}}\mathrm{G}$. The atom loss rate due to inelastic two-body collisions was found to be $1.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{3}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Spin mixing in the $F=2$ manifold developed dramatically for the first few tens of milliseconds, and the oscillations in the population distribution between different magnetic components were observed over a limited range of magnetic field strengths. The antiferromagnetic property of this system was deduced from the magnetic field dependence on the evolution of relative populations for each ${m}_{F}$ component.

Physical Review A•Jun 8, 2004•172 citations
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 study the static and dynamic magnetic properties of ultracold quantum gases, in particular the spinor physics of F = 1 and F = 2 Bose-Einstein condensates of 87Rb atoms. Our data lead to the conclusion, that the F = 2 ground state of 87Rb is polar, while we find the F = 1 ground state to be ferromagnetic. The dynamics of spinor systems is linked to an interplay between coherent mean-field interactions, losses and interactions with atoms in the thermal cloud. Within this rich parameter space we observe indications for coherent spinor dynamics and novel thermalization regimes.
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.
In a spinor Bose-Einstein gas, the non-zero hyperfine spin of the gas becomes an accessible degree of freedom. At low temperature, such a gas shows both magnetic and superfluid order, and undergoes both density and spin dynamics. These lecture notes present a general overview of the properties of spinor Bose-Einstein gases. The notes are divided in five sections. In the first, we summarize basic properties of multi-component quantum fluids, focusing on the specific case of spinor Bose-Einstein gases and the role of rotational symmetry in defining their properties. Second, we consider the magnetic state of a spinor Bose-Einstein gas, highlighting effects of thermodynamics and Bose-Einstein statistics and also of spin-dependent interactions between atoms. In the third section, we discuss methods for measuring the properties of magnetically ordered quantum gases and present newly developed schemes for spin-dependent imaging. We then discuss the dynamics of spin mixing in which the spin composition of the gas evolves through the spin-dependent interactions within the gas. We discuss spin mixing first from a microscopic perspective, and then advance to discussing collective and beyond-mean-field dynamics. The fifth section reviews recent studies of the magnetic excitations of quantum-degenerate spinor Bose gases. We conclude with some perspectives on future directions for research.
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.
This thesis discusses non-equilibrium phenomena in antiferromagnetic spinor quantum gases. We investigate, both experimentally and theoretically, the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition. A microwave dressing field was used as a novel tool to access the polar to antiferrmagnetic quantum phase transition at the quadratic Zeeman shift, q=0. By performing instantaneous quenches across the phase transition,a dynamical instability was induced in the atomic cloud. This lead to pair formation and rapid amplification of spin +/-1 atoms through spin-mixing collisions. The spatial ordering kinetics in the vicinity of the phase transition was quantified by performing the local spin measurement. The coarsening dynamics was observed for the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud. Rich nonequilibrium behavior was observed in the form of growth and decay of both nematic and magnetic spin waves, following the quench. The spatiotemporal evolution was characterized through two particle correlations between atoms in each pair of spin states, which revealed dramatic differences between the dynamics of the spin correlations and those of the spin populations. \nFinally, we demonstrate the remarkable influence of linear Zeeman term on non-equilibrium dynamics of spinor Bose-Einstein condensates. We show that contrary to prior understanding magnetic field gradient actually suppresses the tendency of spin 0 state to separate into spin +/-1 state. This reconciles the Bogoliubov discrepancies and leads to a dramatic sharpening of the transition point, resulting in a resolution at the 1 Hz level. Our results point to the use of dynamics, rather than equilibrium quantities for high precision measurements of phase transitions in quantum gases.
We experimentally studied the spin-dependent collision dynamics of 87Rb^{87}\mathrm{Rb}87Rb spin-2 Bose-Einstein condensates confined in an optical trap. The condensed atoms were initially populated in the $\ensuremath{\mid}F=2,{m}_{F}=0⟩$ state, and their time evolutions in the trap were measured in the presence of external magnetic field strengths ranging from 0.1 to 3.0G3.0\phantom{\rule{0.3em}{0ex}}\mathrm{G}3.0G. The atom loss rate due to inelastic two-body collisions was found to be $1.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{3}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Spin mixing in the F=2F=2F=2 manifold developed dramatically for the first few tens of milliseconds, and the oscillations in the population distribution between different magnetic components were observed over a limited range of magnetic field strengths. The antiferromagnetic property of this system was deduced from the magnetic field dependence on the evolution of relative populations for each mF{m}_{F}mF​ component.