Physical Review A

Decay of trapped ultracold alkali atoms by recombination

A. J. Moerdijk, H. M. J. M. Boesten, BOUDEWIJN J. VERHAAR

Published Feb 1, 1996• 110 citations

Abstract

Using the knowledge of two-body collision properties that has recently become available, we estimate the three-body recombination rate for doubly-spin-polarized ultracold gas samples of $^{7}\mathrm{Li}$, $^{23}\mathrm{Na}$ and $^{87}\mathrm{Rb}$ on the basis of the Jastrow approximation. We find that only recombination leading to the formation of the highest two-body bound states is important. The rate for the highest bound level with zero angular momentum is found to increase strongly with the absolute value of the two-body scattering length. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physreva.53.916

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Physical Review A

Decay of trapped ultracold alkali atoms by recombination

A. J. Moerdijk, H. M. J. M. Boesten, BOUDEWIJN J. VERHAAR

Published Feb 1, 1996• 110 citations

Publisher

Abstract

Using the knowledge of two-body collision properties that has recently become available, we estimate the three-body recombination rate for doubly-spin-polarized ultracold gas samples of

^{7}\mathrm{Li}

^{23}\mathrm{Na}

and

^{87}\mathrm{Rb}

on the basis of the Jastrow approximation. We find that only recombination leading to the formation of the highest two-body bound states is important. The rate for the highest bound level with zero angular momentum is found to increase strongly with the absolute value of the two-body scattering length. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physreva.53.916

Related papers

Three-Body Recombination of Ultracold Atoms to a Weakly Bound s Level

Peter O. Fedichev, M. W. Reynolds, Georgy V. Shlyapnikov

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We have studied hydrogen-hydrogen-alkali three-body systems in the adiabatic hyperspherical representation. For the spin-stretched case, there exists a single $X$ H molecular state when $X$ is one of the bosonic alkali atoms: $^{7}\mathrm{Li}$ , $^{23}\mathrm{Na}$ , $^{39}\mathrm{K}$ , $^{87}\mathrm{Rb}$ , or $^{133}\mathrm{Cs}$ . As a result, the only recombination process is the one that leads to formation of $X$ H molecules, $\text{H}+\text{H}+X\ensuremath{\rightarrow}X\text{H}+\text{H}$, and such molecules will be stable against vibrational relaxation. We have calculated the collision rates for recombination and collision-induced dissociation as well as the elastic cross sections for $\text{H}+X\text{H}$ collisions up to a temperature of 0.5 K, including the partial wave contributions from ${J}^{\ensuremath{\Pi}}={0}^{+}$ to ${5}^{\ensuremath{-}}$. We have also found that there is just one three-body bound state for such systems for ${J}^{\ensuremath{\Pi}}={0}^{+}$ and no bound states for higher angular momenta.We have studied hydrogen-hydrogen-alkali three-body systems in the adiabatic hyperspherical representation. For the spin-stretched case, there exists a single $X$H molecular state when $X$ is one of the bosonic alkali atoms: $^{7}\mathrm{Li}$, $^{23}\mathrm{Na}$, $^{39}\mathrm{K}$, $^{87}\mathrm{Rb}$, or $^{133}\mathrm{Cs}$. As a result, the only recombination process is the one that leads to formation of $X$H molecules, $\text{H}+\text{H}+X\ensuremath{\rightarrow}X\text{H}+\text{H}$, and such molecules will be stable against vibrational relaxation. We have calculated the collision rates for recombination and collision-induced dissociation as well as the elastic cross sections for $\text{H}+X\text{H}$ collisions up to a temperature of 0.5 K, including the partial wave contributions from ${J}^{\ensuremath{\Pi}}={0}^{+}$ to ${5}^{\ensuremath{-}}$. We have also found that there is just one three-body bound state for such systems for ${J}^{\ensuremath{\Pi}}={0}^{+}$ and no bound states for higher angular momenta.

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Hiroya Suno, Brett D. Esry

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Physical Review ADec 2, 200951 citations

Using the knowledge of two-body collision properties that has recently become available, we estimate the three-body recombination rate for doubly-spin-polarized ultracold gas samples of

^{7}\mathrm{Li}

^{23}\mathrm{Na}

and

^{87}\mathrm{Rb}

We discuss three-body recombination of ultracold atoms to a weakly bound

s

level. In this case, characterized by large and positive scattering length

a

for pair interaction, we find a repulsive effective potential for three-body collisions, which strongly reduces the recombination probability. In the zero temperature limit we obtain a universal relation, independent of the detailed shape of the interaction potential, for the (event) rate constant of three-body recombination: ${\ensuremath{\alpha}}_{\mathrm{rec}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3.9\ensuremath{\Elzxh}{a}^{4}/m$, where

m

is the atom mass.

a

. It grows as

{a}^{4}

for large

|a|,

with different mechanisms for

a<0

and

a>0

. Our calculations document a previously established mechanism that causes

{K}_{3}

to grow rapidly as the two-body scattering length

a

increases toward $+\ensuremath{\infty}$, and a new tunneling mechanism that produces an even stronger enhancement of

{K}_{3}

as $a\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$. The expectations based on these two mechanisms can be modified by quantum mechanical interference or resonance effects.

We have studied hydrogen-hydrogen-alkali three-body systems in the adiabatic hyperspherical representation. For the spin-stretched case, there exists a single

X

H molecular state when

X

is one of the bosonic alkali atoms:

^{7}\mathrm{Li}

^{23}\mathrm{Na}

^{39}\mathrm{K}

^{87}\mathrm{Rb}

, or

^{133}\mathrm{Cs}

. As a result, the only recombination process is the one that leads to formation of

X

H molecules, $\text{H}+\text{H}+X\ensuremath{\rightarrow}X\text{H}+\text{H}$, and such molecules will be stable against vibrational relaxation. We have calculated the collision rates for recombination and collision-induced dissociation as well as the elastic cross sections for

\text{H}+X\text{H}

collisions up to a temperature of 0.5 K, including the partial wave contributions from ${J}^{\ensuremath{\Pi}}={0}^{+}$ to ${5}^{\ensuremath{-}}$. We have also found that there is just one three-body bound state for such systems for ${J}^{\ensuremath{\Pi}}={0}^{+}$ and no bound states for higher angular momenta.

X=^{7}\text{L}\text{i}

^{23}\text{N}\text{a}

^{39}\text{K}

^{85}\text{R}\text{b}

, and

^{133}\text{C}\text{s}

, are calculated at nonzero collision energies by including not only zero total angular momentum,

J=0

, states but also

J>0

states. The three-body recombination rates show a relatively weak dependence on the alkali-metal species, differing from each other only by about one order of magnitude, except for the

^{4}\text{H}\text{e-}^{4}\text{H}\text{e-}^{23}\text{N}\text{a}

system.