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:0909.0489 · Physical Review A

Spin-dependent inelastic collisions in spin-2 Bose-Einstein condensates

賢 東條, Tarō Hayashi, Tatsuyoshi Tanabe, Takuya Hirano, Yuki Kawaguchi, Hiroki Saito, Masahito Ueda

Published Oct 12, 2009• 52 citations
arXivHTMLPDF

Abstract

We studied spin-dependent two-body inelastic collisions in $F=2$ $^{87}\text{R}\text{b}$ Bose-Einstein condensates both experimentally and theoretically. The $^{87}\text{R}\text{b}$ condensates were confined in an optical trap and selectively prepared in various spin states in the $F=2$ manifold at a magnetic field of 3.0 G. The measured atom loss rates depend on the spin states of colliding atoms. We measured two fundamental loss coefficients for two-body inelastic collisions with total spins of 0 and 2. The loss coefficients determine the loss rates of all the spin pairs. The experimental results for mixtures of all spin combinations are in good agreement with numerical solutions of the Gross-Pitaevskii equations that include the effect of a magnetic field gradient.

DOI
10.1103/physreva.80.042704

Related papers

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

Quantum many-body analysis of spin-2 bosons with two-body inelastic decay

Takeshi Takahashi, Hiroki Saito

Bose-Einstein condensates of $^{87}\mathrm{Rb}$ atoms with a hyperfine spin of 2 are open quantum systems, where the atoms are lost through two-body inelastic collisions. In this dissipation process, a collision channel with total spin of 4 is forbidden by angular momentum conservation, which results in magnetization of the atoms remaining in the condensate. Here, we investigate the quantum many-body properties of spin-2 bosons that undergo two-body atomic loss. We show that the system finally reaches a steady state, which is a mixture of the states with maximum total spins. In addition, we find that a nonclassical steady state can be obtained by applying and quenching the quadratic Zeeman field.

arXiv:2510.10050•Physical Review A•Apr 6, 2026•0 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

Giant Spin Relaxation of an Ultracold Cesium Gas

Johannes Söding, David Guéry-Odelin, Pierre Desbiolles +2 more

We have measured the rate of inelastic collisions in a cloud of doubly polarized ground-state cesium atoms ( ${F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$) confined in a magnetic trap for temperatures $T$ between 8 and $70\ensuremath{\mu}\mathrm{K}$. We find a two-body rate coefficient varying as ${T}^{\ensuremath{-}0.63}$. At 8 $\ensuremath{\mu}\mathrm{K}$ it reaches $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}$ which is 3 orders of magnitude larger than predicted, ruling out a Bose-Einstein condensation of Cs in this internal state.

Physical Review Letters•Mar 2, 1998•105 citations

Magnetic-field-dependent trap loss of ultracold metastable helium

Joseph Steven Borbely, Rob van Rooij, Steven Knoop +1 more

We have experimentally studied the magnetic-field dependence of the decay of a Bose-Einstein condensate of metastable ${}^{4}$He atoms confined in an optical dipole trap, for atoms in the $m=+1$ and $m=\ensuremath{-}1$ magnetic substates, and up to 450 G. Our measurements confirm longstanding calculations of the two-body loss rate coefficient that show an increase above 50 G. We demonstrate that for $m=\ensuremath{-}1$ atoms decay is due to three-body recombination only, with a three-body loss rate coefficient of $6.5{(0.4)}_{\mathrm{stat}}{(0.6)}_{\mathrm{sys}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}$ cm${}^{6}$s${}^{\ensuremath{-}1}$, which is interesting in the context of universal few-body theory. We have also searched for a recently predicted $d$-wave Feshbach resonance, but did not observe it.

arXiv:1111.5829•Physical Review A•Feb 14, 2012•16 citations

Collisions between Ultracold Molecules and Atoms in a Magnetic Trap

Sarunas Jurgilas, A. Chakraborty, C. J. H. Rich +7 more

We prepare mixtures of ultracold CaF molecules and Rb atoms in a magnetic trap and study their inelastic collisions. When the atoms are prepared in the spin-stretched state and the molecules in the spin-stretched component of the first rotationally excited state, they collide inelastically with a rate coefficient k_{2}=(6.6±1.5)×10^{-11} cm^{3}/s at temperatures near 100 μK. We attribute this to rotation-changing collisions. When the molecules are in the ground rotational state we see no inelastic loss and set an upper bound on the spin-relaxation rate coefficient of k_{2}<5.8×10^{-12} cm^{3}/s with 95% confidence. We compare these measurements to the results of a single-channel loss model based on quantum defect theory. The comparison suggests a short-range loss parameter close to unity for rotationally excited molecules, but below 0.04 for molecules in the rotational ground state.

arXiv:2101.01580•Physical Review Letters•Apr 13, 2021•51 citations
We studied spin-dependent two-body inelastic collisions in F=2F=2F=2 87Rb^{87}\text{R}\text{b}87Rb Bose-Einstein condensates both experimentally and theoretically. The 87Rb^{87}\text{R}\text{b}87Rb condensates were confined in an optical trap and selectively prepared in various spin states in the F=2F=2F=2 manifold at a magnetic field of 3.0 G. The measured atom loss rates depend on the spin states of colliding atoms. We measured two fundamental loss coefficients for two-body inelastic collisions with total spins of 0 and 2. The loss coefficients determine the loss rates of all the spin pairs. The experimental results for mixtures of all spin combinations are in good agreement with numerical solutions of the Gross-Pitaevskii equations that include the effect of a magnetic field gradient.
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.
Bose-Einstein condensates of 87Rb^{87}\mathrm{Rb}87Rb atoms with a hyperfine spin of 2 are open quantum systems, where the atoms are lost through two-body inelastic collisions. In this dissipation process, a collision channel with total spin of 4 is forbidden by angular momentum conservation, which results in magnetization of the atoms remaining in the condensate. Here, we investigate the quantum many-body properties of spin-2 bosons that undergo two-body atomic loss. We show that the system finally reaches a steady state, which is a mixture of the states with maximum total spins. In addition, we find that a nonclassical steady state can be obtained by applying and quenching the quadratic Zeeman field.
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 have measured the rate of inelastic collisions in a cloud of doubly polarized ground-state cesium atoms ( F=mF=4{F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4F=mF​=4) confined in a magnetic trap for temperatures TTT between 8 and $70\ensuremath{\mu}\mathrm{K}$. We find a two-body rate coefficient varying as ${T}^{\ensuremath{-}0.63}$. At 8 $\ensuremath{\mu}\mathrm{K}$ it reaches $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}$ which is 3 orders of magnitude larger than predicted, ruling out a Bose-Einstein condensation of Cs in this internal state.
We have experimentally studied the magnetic-field dependence of the decay of a Bose-Einstein condensate of metastable 4{}^{4}4He atoms confined in an optical dipole trap, for atoms in the m=+1m=+1m=+1 and $m=\ensuremath{-}1$ magnetic substates, and up to 450 G. Our measurements confirm longstanding calculations of the two-body loss rate coefficient that show an increase above 50 G. We demonstrate that for $m=\ensuremath{-}1$ atoms decay is due to three-body recombination only, with a three-body loss rate coefficient of $6.5{(0.4)}_{\mathrm{stat}}{(0.6)}_{\mathrm{sys}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}$ cm6{}^{6}6s${}^{\ensuremath{-}1}$, which is interesting in the context of universal few-body theory. We have also searched for a recently predicted ddd-wave Feshbach resonance, but did not observe it.
We prepare mixtures of ultracold CaF molecules and Rb atoms in a magnetic trap and study their inelastic collisions. When the atoms are prepared in the spin-stretched state and the molecules in the spin-stretched component of the first rotationally excited state, they collide inelastically with a rate coefficient k_{2}=(6.6±1.5)×10^{-11} cm^{3}/s at temperatures near 100 μK. We attribute this to rotation-changing collisions. When the molecules are in the ground rotational state we see no inelastic loss and set an upper bound on the spin-relaxation rate coefficient of k_{2}<5.8×10^{-12} cm^{3}/s with 95% confidence. We compare these measurements to the results of a single-channel loss model based on quantum defect theory. The comparison suggests a short-range loss parameter close to unity for rotationally excited molecules, but below 0.04 for molecules in the rotational ground state.