Physical Review Letters

Prospects for Bose-Einstein Condensation in Atomic Li7 and Na23

A. J. Moerdijk, BOUDEWIJN J. VERHAAR

Published Jul 25, 1994• 64 citations

Abstract

We have determined the scattering length of the ground state $^{7}\mathrm{Li}$ + $^{7}\mathrm{Li}$ singlet potential from spectroscopic data on the highest $S=0$ bound states. Combining this with a previously obtained triplet value we find the first example of an alkali atom hyperfine state (the $^{7}\mathrm{Li}$ $F=1$, ${M}_{F}=\ensuremath{-}1$ state) for which the scattering length is positive. This implies a stable Bose condensate in future attempts to realize Bose-Einstein condensation in a magnetically trapped ultracold gas sample. We also predict magnetic-field-dependent resonances in the collision between atoms in the hyperfine state studied.

DOI: 10.1103/physrevlett.73.518

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Physical Review Letters

Prospects for Bose-Einstein Condensation in Atomic Li7 and Na23

A. J. Moerdijk, BOUDEWIJN J. VERHAAR

Published Jul 25, 1994• 64 citations

Publisher

Abstract

We have determined the scattering length of the ground state

^{7}\mathrm{Li}

^{7}\mathrm{Li}

singlet potential from spectroscopic data on the highest

S=0

bound states. Combining this with a previously obtained triplet value we find the first example of an alkali atom hyperfine state (the

^{7}\mathrm{Li}

F=1

{M}_{F}=\ensuremath{-}1

state) for which the scattering length is positive. This implies a stable Bose condensate in future attempts to realize Bose-Einstein condensation in a magnetically trapped ultracold gas sample. We also predict magnetic-field-dependent resonances in the collision between atoms in the hyperfine state studied.

DOI: 10.1103/physrevlett.73.518

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Spectroscopic determination of the s-wave scattering length of lithium

E. Abraham, W. L. McAlexander, Charles A. Sackett +1 more

Two-photon photoassociation of colliding ultracold ${}^{7}$ Li atoms is used to probe the $^{3}\ensuremath{\Sigma}_{u}^{+}(a)$ ground state of ${}^{7}$ L ${\mathrm{i}}_{2}$ . The binding energy of the least-bound state of this triplet potential, $\ensuremath{\upsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10$, is found to be $12.47\ifmmode\pm\else\textpm\fi{}0.04$ GHz. This spectroscopic information establishes that the $s$ -wave scattering length for ${}^{7}$ Li atoms in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ , ${m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ state is $(\ensuremath{-}27.3\ifmmode\pm\else\textpm\fi{}0.8){a}_{0}$. The negative sign of the scattering length has important implications as to whether atoms at this doubly spin-polarized state can undergo a Bose-Einstein condensation.Two-photon photoassociation of colliding ultracold ${}^{7}$Li atoms is used to probe the $^{3}\ensuremath{\Sigma}_{u}^{+}(a)$ ground state of ${}^{7}$L${\mathrm{i}}_{2}$. The binding energy of the least-bound state of this triplet potential, $\ensuremath{\upsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10$, is found to be $12.47\ifmmode\pm\else\textpm\fi{}0.04$ GHz. This spectroscopic information establishes that the $s$-wave scattering length for ${}^{7}$Li atoms in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$, ${m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ state is $(\ensuremath{-}27.3\ifmmode\pm\else\textpm\fi{}0.8){a}_{0}$. The negative sign of the scattering length has important implications as to whether atoms at this doubly spin-polarized state can undergo a Bose-Einstein condensation.

Quantum Electronics and Laser Science ConferenceMay 22, 19955 citations

We have determined the scattering length of the ground state

^{7}\mathrm{Li}

^{7}\mathrm{Li}

singlet potential from spectroscopic data on the highest

S=0

bound states. Combining this with a previously obtained triplet value we find the first example of an alkali atom hyperfine state (the

^{7}\mathrm{Li}

F=1

{M}_{F}=\ensuremath{-}1

We have improved the theoretical triplet ground-state potential of

^{7}\mathrm{Li}_{2}

by means of an inverse perturbation analysis, and find that the diatomic scattering length for

^{7}\mathrm{Li}

atoms in the F=2,

{\mathit{m}}_{\mathit{F}}

=2 ground-state hyperfine level is negative. The consequences of this result for achieving Bose-Einstein condensation in a trapped ultracold

^{7}\mathrm{Li}

gas sample are addressed.

{\mathrm{Cs}}_{2}

in three-body collisions. We find that, on the basis of these conditions, the prospects for observing Bose-Einstein condensation are favorable for a gas of ground-state Cs atoms in the highest state of the lowest hyperfine manifold. In all calculated elastic and inelastic two-body rates we find a pronounced resonance structure, which can be understood in terms of the interplay between the singlet-triplet interaction and the hyperfine, Zeeman, and magnetic dipole interactions. The experimental observation of these resonances may help to eliminate present uncertainties about interaction potentials.

We have determined properties of cold

^{39}\mathrm{K}

^{39}\mathrm{K}

and

^{41}\mathrm{K}

^{41}\mathrm{K}

collisions by a multichannel inverted perturbation approach applied to spectroscopic data of highly excited

^{39}\mathrm{K}

singlet and triplet bound states. We predict positive scattering lengths for the

^{39}\mathrm{K}

^{39}\mathrm{K}

and

^{41}\mathrm{K}

^{41}\mathrm{K}

singlet potentials, as well as for the

^{41}\mathrm{K}

^{41}\mathrm{K}

triplet potential, and a negative value for

^{39}\mathrm{K}

^{39}\mathrm{K}

triplet scattering. From a study of the magnetic field dependence we conclude that

^{41}\mathrm{K}

may be a bosonic atom with a Feshbach resonance in the magnetic field range where these atoms can be trapped in the

f=1

, ${m}_{f}=\ensuremath{-}1$ hyperfine state, thus providing a possibility to switch between stable and instable condensates in a Bose-Einstein condensation experiment.

{}^{133}\mathrm{Cs}

and in

{}^{135}\mathrm{Cs}

Two-photon photoassociation of colliding ultracold

{}^{7}

Li atoms is used to probe the $^{3}\ensuremath{\Sigma}_{u}^{+}(a)$ ground state of

{}^{7}

{\mathrm{i}}_{2}

. The binding energy of the least-bound state of this triplet potential, $\ensuremath{\upsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10$, is found to be $12.47\ifmmode\pm\else\textpm\fi{}0.04$ GHz. This spectroscopic information establishes that the

s

-wave scattering length for

{}^{7}

Li atoms in the

F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2

{m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2

state is $(\ensuremath{-}27.3\ifmmode\pm\else\textpm\fi{}0.8){a}_{0}$. The negative sign of the scattering length has important implications as to whether atoms at this doubly spin-polarized state can undergo a Bose-Einstein condensation.