Physical Review A

Sympathetic cooling of 85Rb and 87Rb

Immanuel Bloch, Markus Greiner, Olaf Mandel, Theodor W. Hänsch, Tilman Esslinger

Published Jul 10, 2001• 75 citations

Abstract

We demonstrate sympathetic cooling between magnetically trapped ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ atoms. Up to $6\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${}^{85}\mathrm{Rb}$ atoms are cooled via elastic collisions with a reservoir of $8\ifmmode\times\else\texttimes\fi{}{10}^{8}$ ${}^{87}\mathrm{Rb}$ atoms. The temperature of the binary atomic ensemble is adjusted by using radio-frequency evaporation of ${}^{87}\mathrm{Rb}.$ Temperatures as low as $T=100 \mathrm{nK}$ have been realized in the binary ensemble. Through a cross-dimensional mixing approach we have been able to measure the interspecies ${}^{87}\mathrm{Rb}{\ensuremath{-}}^{85}\mathrm{Rb}$ scattering cross section $\ensuremath{\sigma}=1.52(34)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15} {\mathrm{m}}^{2}.$

DOI: 10.1103/physreva.64.021402

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Physical Review A

Sympathetic cooling of 85Rb and 87Rb

Immanuel Bloch, Markus Greiner, Olaf Mandel, Theodor W. Hänsch, Tilman Esslinger

Published Jul 10, 2001• 75 citations

Publisher

Abstract

We demonstrate sympathetic cooling between magnetically trapped

{}^{85}\mathrm{Rb}

and

{}^{87}\mathrm{Rb}

atoms. Up to

6\ifmmode\times\else\texttimes\fi{}{10}^{6}

{}^{85}\mathrm{Rb}

atoms are cooled via elastic collisions with a reservoir of

8\ifmmode\times\else\texttimes\fi{}{10}^{8}

{}^{87}\mathrm{Rb}

atoms. The temperature of the binary atomic ensemble is adjusted by using radio-frequency evaporation of

{}^{87}\mathrm{Rb}.

Temperatures as low as

T=100 \mathrm{nK}

have been realized in the binary ensemble. Through a cross-dimensional mixing approach we have been able to measure the interspecies

{}^{87}\mathrm{Rb}{\ensuremath{-}}^{85}\mathrm{Rb}

scattering cross section

\ensuremath{\sigma}=1.52(34)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15} {\mathrm{m}}^{2}.

DOI: 10.1103/physreva.64.021402

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arXiv:cond-mat/0011291Physical Review AJun 8, 2001142 citations

We demonstrate sympathetic cooling between magnetically trapped

{}^{85}\mathrm{Rb}

and

{}^{87}\mathrm{Rb}

atoms. Up to

6\ifmmode\times\else\texttimes\fi{}{10}^{6}

{}^{85}\mathrm{Rb}

atoms are cooled via elastic collisions with a reservoir of

8\ifmmode\times\else\texttimes\fi{}{10}^{8}

{}^{87}\mathrm{Rb}

atoms. The temperature of the binary atomic ensemble is adjusted by using radio-frequency evaporation of

{}^{87}\mathrm{Rb}.

Temperatures as low as

T=100 \mathrm{nK}

have been realized in the binary ensemble. Through a cross-dimensional mixing approach we have been able to measure the interspecies

{}^{87}\mathrm{Rb}{\ensuremath{-}}^{85}\mathrm{Rb}

scattering cross section

\ensuremath{\sigma}=1.52(34)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15} {\mathrm{m}}^{2}.

We report on measurements of the collisional properties of a mixture of

^{133}\mathrm{Cs}

and

^{87}\mathrm{Rb}

atoms in a magnetic trap at $\ensuremath{\mu}\mathrm{K}$ temperatures. By selectively evaporating the Rb atoms using a radio-frequency field, we achieved sympathetic cooling of Cs down to a few $\ensuremath{\mu}\mathrm{K}$. The interspecies collisional cross section was determined through rethermalization measurements, leading to good agreement with a theoretical prediction of

595{a}_{0}

for the triplet

s

-wave scattering length for Rb in the $\ensuremath{\mid}F=2,{m}_{F}=2⟩$ and Cs in the $\ensuremath{\mid}F=4,{m}_{F}=4⟩$ magnetic states. We briefly speculate on the prospects for reaching the Bose-Einstein condensation of Cs inside a magnetic trap through sympathetic cooling.

We present a model for the collisional properties of a mixture of

^{133}\mathrm{Cs}

and

^{87}\mathrm{Rb}

atoms in a magnetic trap at $\ensuremath{\mu}\mathrm{K}$ temperatures. The experimental sequence we model corresponds to a selective evaporation of the Rb atoms using a radio-frequency field, leading to sympathetic cooling of the Cs atoms or, if selective evaporation is carried out fast, to a difference in temperature between the two atomic species. In the latter case, the two atomic clouds reached an equilibrium temperature starting from an Rb temperature lower than that of Cs. By supposing that each atomic cloud was in thermal equilibrium we modeled this rethermalization process through differential equations for the two atomic temperatures. An alternative approach was based on the Monte Carlo simulations of the individual collisional processes. The sympathetic cooling and the rethermalization were analyzed in terms of the inter-species collisional cross-section.

F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

, ${m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$ hyperfine state was determined to be $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ c

{\mathrm{m}}^{2}

, which implies a positive value of the scattering length.

s

-wave scattering length. Together with trajectory calculations, these differential cross sections are used to simulate the cooling of the molecules, the heating of the atoms, and the loss of atoms from the trap. We show that a hard-sphere collision model based on an energy-dependent momentum transport cross section accurately predicts the molecule cooling rate but underestimates the rates of atom heating and loss. Our simulations suggest that Rb is a more effective coolant than Li for ground-state molecules, and that the cooling dynamics is less sensitive to the exact value of the

s

-wave scattering length when Rb is used. Using realistic experimental parameters, we find that molecules can be sympathetically cooled to $100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in about 10 s. By applying evaporative cooling to the atoms, the cooling rate can be increased and the final temperature of the molecules can be reduced to $1 \ensuremath{\mu}\mathrm{K}$ within 30 s.

Sympathetic cooling of two atomic isotopes is experimentally investigated. Using forced evaporation of a bosonic

{}^{7}\mathrm{Li}

gas in a magnetic trap, a sample of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{5}$

{}^{6}\mathrm{Li}

fermions has been sympathetically cooled to $9(3) \ensuremath{\mu}\mathrm{K},$ corresponding to

2.2(0.8)

times the Fermi temperature. The measured rate constant for two-body inelastic collisions of the

{}^{7}\mathrm{Li}

|2,2〉

state at low magnetic field is ${1.0}_{\ensuremath{-}0.5}^{+0.8}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14} {\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}.$