Physical Review A

Triplet s-wave resonance in Li6 collisions and scattering lengths of Li6 and Li7

E. R. I. Abraham, W. I. McAlexander, Jordan M. Gerton, Randall G. Hulet, Robin Côté, A. Dalgarno

Published May 1, 1997• 190 citations

Abstract

The triplet s-wave scattering length of $^{6}\mathrm{Li}$ is determined using two-photon photoassociative spectroscopy of the diatomic a${\mathrm{}}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathrm{u}}^{+}$ state of $^{6}\mathrm{Li}_{2}$. The measured binding energy of the highest-lying bound state, combined with knowledge of the potential, determines the s-wave scattering length to be (-2160\ifmmode\pm\else\textpm\fi{}250)${\mathrm{a}}_{0}$, where ${\mathrm{a}}_{0}$ is the Bohr radius. This extraordinarily large scattering length signifies a near-threshold resonance. A complete table of singlet and triplet scattering lengths for collisions involving $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ determined from this and our previous spectroscopic investigations is given.

DOI: 10.1103/physreva.55.r3299

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Singlet s -wave scattering lengths of Li6 and Li7

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Physical Review A

Triplet s-wave resonance in Li6 collisions and scattering lengths of Li6 and Li7

E. R. I. Abraham, W. I. McAlexander, Jordan M. Gerton, Randall G. Hulet, Robin Côté, A. Dalgarno

Published May 1, 1997• 190 citations

Publisher

Abstract

The triplet s-wave scattering length of

^{6}\mathrm{Li}

is determined using two-photon photoassociative spectroscopy of the diatomic a

{\mathrm{}}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathrm{u}}^{+}

state of

^{6}\mathrm{Li}_{2}

. The measured binding energy of the highest-lying bound state, combined with knowledge of the potential, determines the s-wave scattering length to be (-2160\ifmmode\pm\else\textpm\fi{}250)

{\mathrm{a}}_{0}

, where

{\mathrm{a}}_{0}

is the Bohr radius. This extraordinarily large scattering length signifies a near-threshold resonance. A complete table of singlet and triplet scattering lengths for collisions involving

^{6}\mathrm{Li}

and

^{7}\mathrm{Li}

determined from this and our previous spectroscopic investigations is given.

DOI: 10.1103/physreva.55.r3299

Related papers

Singlet s -wave scattering lengths of Li6 and Li7

E. R. I. Abraham, W. I. McAlexander, Jordan M. Gerton +3 more

Photoassociation of ultracold lithium atoms into bound vibrational levels of the $A^{1}\ensuremath{\Sigma}_{u}^{+}$ excited state is used to probe the $X^{1}\ensuremath{\Sigma}_{g}^{+}$ ground-state interaction potential of $^{6}\mathrm{Li}_{2}$ and $^{7}\mathrm{Li}_{2}$ . It had been predicted that the $s$ -wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive $s$ -wave scattering length. We report the observation of this novel effect, and use the location of the minimum to precisely determine the singlet $s$ -wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the minima for collisions involving $^{7}\mathrm{Li}$ atoms in different hyperfine states.Photoassociation of ultracold lithium atoms into bound vibrational levels of the $A^{1}\ensuremath{\Sigma}_{u}^{+}$ excited state is used to probe the $X^{1}\ensuremath{\Sigma}_{g}^{+}$ ground-state interaction potential of $^{6}\mathrm{Li}_{2}$ and $^{7}\mathrm{Li}_{2}$. It had been predicted that the $s$-wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive $s$-wave scattering length. We report the observation of this novel effect, and use the location of the minimum to precisely determine the singlet $s$-wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the minima for collisions involving $^{7}\mathrm{Li}$ atoms in different hyperfine states.

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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.

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Feshbach resonances in fermionic Li6

Christian H. Schunck, Martin W. Zwierlein, Claudiu Andrei Stan +6 more

Feshbach resonances in $^{6}\mathrm{Li}$ were experimentally studied and theoretically analyzed. In addition to two previously known $s$ -wave resonances, three $p$ -wave resonances were found. Four of these resonances are narrow and yield a precise value of the singlet scattering length. The position of the broad $s$ -wave resonance near $83\phantom{\rule{0.3em}{0ex}}\mathrm{mT}$ is mostly sensitive to the triplet potential. It was previously determined in a molecule-dissociation experiment for which we, here, discuss systematic shifts.Feshbach resonances in $^{6}\mathrm{Li}$ were experimentally studied and theoretically analyzed. In addition to two previously known $s$-wave resonances, three $p$-wave resonances were found. Four of these resonances are narrow and yield a precise value of the singlet scattering length. The position of the broad $s$-wave resonance near $83\phantom{\rule{0.3em}{0ex}}\mathrm{mT}$ is mostly sensitive to the triplet potential. It was previously determined in a molecule-dissociation experiment for which we, here, discuss systematic shifts.

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Determination of 39K scattering lengths using photoassociation spectroscopy of the 0g− state

James P. Burke, Chris H. Greene, John L. Bohn +3 more

Threshold scattering properties of ${}^{39}\mathrm{K}$ atoms are extracted from a line-shape analysis of photoassociation data. Specifically, we consider the rovibrational levels ${(v}^{\ensuremath{'}}=0--6)$ populated in the photoassociation process $\mathrm{K}(4S)+\mathrm{K}(4S)+\ensuremath{\Elzxh}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}{\mathrm{K}}_{2}^{*}[{0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}{,J}^{\ensuremath{'}})].$ The measured spectra exhibit several general trends, including large ${J}^{\ensuremath{'}}=2$ linewidths, large relative ${J}^{\ensuremath{'}}=4$ peak intensities, and odd rotational lines which are weak or missing. The even ${J}^{\ensuremath{'}}$ features signal the presence of a d-wave shape resonance in the ground-state collisions. The combination of spectral features allows us to place the following limits on the ground-state singlet and triplet scattering lengths, ${a}_{s}{=140}_{\ensuremath{-}9}^{+6}$ a.u. and ${a}_{t}=\ensuremath{-}17\ensuremath{-}{0.045(C}_{6}\ensuremath{-}{C}_{6})\ifmmode\pm\else\textpm\fi{}25$ a.u., ${C}_{6}=3800$ a.u.Threshold scattering properties of ${}^{39}\mathrm{K}$ atoms are extracted from a line-shape analysis of photoassociation data. Specifically, we consider the rovibrational levels ${(v}^{\ensuremath{'}}=0--6)$ populated in the photoassociation process $\mathrm{K}(4S)+\mathrm{K}(4S)+\ensuremath{\Elzxh}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}{\mathrm{K}}_{2}^{*}[{0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}{,J}^{\ensuremath{'}})].$ The measured spectra exhibit several general trends, including large ${J}^{\ensuremath{'}}=2$ linewidths, large relative ${J}^{\ensuremath{'}}=4$ peak intensities, and odd rotational lines which are weak or missing. The even ${J}^{\ensuremath{'}}$ features signal the presence of a d-wave shape resonance in the ground-state collisions. The combination of spectral features allows us to place the following limits on the ground-state singlet and triplet scattering lengths, ${a}_{s}{=140}_{\ensuremath{-}9}^{+6}$ a.u. and ${a}_{t}=\ensuremath{-}17\ensuremath{-}{0.045(C}_{6}\ensuremath{-}{C}_{6})\ifmmode\pm\else\textpm\fi{}25$ a.u., ${C}_{6}=3800$ a.u.

Physical Review ADec 1, 199935 citations

Photoassociative Spectroscopy of Collisions Between Ultracold Lithium Atoms

E. Abraham

The spectra of the high-lying vibrational levels of the $A\\sp1\\Sigma\\sbsp{u}{+}$ and $1\\sp3\\Sigma\\sbsp{g}{+}$ singly excited states of both $\\sp6\\rm Li\\sb2$ and $\\sp7\\rm Li\\sb2$ are obtained via photoassociation of colliding ultracold atoms confined in a magneto-optical trap. The least bound state of the $a\\sp3\\Sigma\\sbsp{u}{+}$ ground state potential, obtained by two-photon photoassociative spectroscopy, is also presented for both $\\sp7\\rm Li\\sb2$ and $\\sp6\\rm Li\\sb2$ . The vibrational levels have resolved hyperfine structure, whose relative energy splittings and transition strengths are accurately modeled. The photoassociative spectra are used to precisely determine both the singlet and triplet s-wave scattering lengths for both isotopes, which are important parameters in systems designed to observe quantum degenerate effects and Bose-Einstein condensation.The spectra of the high-lying vibrational levels of the $A\\sp1\\Sigma\\sbsp{u}{+}$ and $1\\sp3\\Sigma\\sbsp{g}{+}$ singly excited states of both $\\sp6\\rm Li\\sb2$ and $\\sp7\\rm Li\\sb2$ are obtained via photoassociation of colliding ultracold atoms confined in a magneto-optical trap. The least bound state of the $a\\sp3\\Sigma\\sbsp{u}{+}$ ground state potential, obtained by two-photon photoassociative spectroscopy, is also presented for both $\\sp7\\rm Li\\sb2$ and $\\sp6\\rm Li\\sb2$. The vibrational levels have resolved hyperfine structure, whose relative energy splittings and transition strengths are accurately modeled. The photoassociative spectra are used to precisely determine both the singlet and triplet s-wave scattering lengths for both isotopes, which are important parameters in systems designed to observe quantum degenerate effects and Bose-Einstein condensation.

Jan 1, 19960 citations

The triplet s-wave scattering length of

^{6}\mathrm{Li}

is determined using two-photon photoassociative spectroscopy of the diatomic a

{\mathrm{}}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathrm{u}}^{+}

state of

^{6}\mathrm{Li}_{2}

. The measured binding energy of the highest-lying bound state, combined with knowledge of the potential, determines the s-wave scattering length to be (-2160\ifmmode\pm\else\textpm\fi{}250)

{\mathrm{a}}_{0}

, where

{\mathrm{a}}_{0}

is the Bohr radius. This extraordinarily large scattering length signifies a near-threshold resonance. A complete table of singlet and triplet scattering lengths for collisions involving

^{6}\mathrm{Li}

and

^{7}\mathrm{Li}

determined from this and our previous spectroscopic investigations is given.

^{6}\mathrm{Li}_{2}

and

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

. It had been predicted that the

s

-wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive

s

-wave scattering length. We report the observation of this novel effect, and use the location of the minimum to precisely determine the singlet

s

-wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the minima for collisions involving

^{7}\mathrm{Li}

atoms in different hyperfine states.

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.

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}

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

Feshbach resonances in

^{6}\mathrm{Li}

were experimentally studied and theoretically analyzed. In addition to two previously known

s

-wave resonances, three

p

-wave resonances were found. Four of these resonances are narrow and yield a precise value of the singlet scattering length. The position of the broad

s

-wave resonance near

83\phantom{\rule{0.3em}{0ex}}\mathrm{mT}

is mostly sensitive to the triplet potential. It was previously determined in a molecule-dissociation experiment for which we, here, discuss systematic shifts.

Threshold scattering properties of

{}^{39}\mathrm{K}

atoms are extracted from a line-shape analysis of photoassociation data. Specifically, we consider the rovibrational levels ${(v}^{\ensuremath{'}}=0--6)$ populated in the photoassociation process $\mathrm{K}(4S)+\mathrm{K}(4S)+\ensuremath{\Elzxh}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}{\mathrm{K}}_{2}^{*}[{0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}{,J}^{\ensuremath{'}})].$ The measured spectra exhibit several general trends, including large ${J}^{\ensuremath{'}}=2$ linewidths, large relative ${J}^{\ensuremath{'}}=4$ peak intensities, and odd rotational lines which are weak or missing. The even ${J}^{\ensuremath{'}}$ features signal the presence of a d-wave shape resonance in the ground-state collisions. The combination of spectral features allows us to place the following limits on the ground-state singlet and triplet scattering lengths, ${a}_{s}{=140}_{\ensuremath{-}9}^{+6}$ a.u. and ${a}_{t}=\ensuremath{-}17\ensuremath{-}{0.045(C}_{6}\ensuremath{-}{C}_{6})\ifmmode\pm\else\textpm\fi{}25$ a.u.,

{C}_{6}=3800

a.u.

The spectra of the high-lying vibrational levels of the

A\\sp1\\Sigma\\sbsp{u}{+}

and

1\\sp3\\Sigma\\sbsp{g}{+}

singly excited states of both

\\sp6\\rm Li\\sb2

and

\\sp7\\rm Li\\sb2

are obtained via photoassociation of colliding ultracold atoms confined in a magneto-optical trap. The least bound state of the

a\\sp3\\Sigma\\sbsp{u}{+}

ground state potential, obtained by two-photon photoassociative spectroscopy, is also presented for both

\\sp7\\rm Li\\sb2

and

\\sp6\\rm Li\\sb2

. The vibrational levels have resolved hyperfine structure, whose relative energy splittings and transition strengths are accurately modeled. The photoassociative spectra are used to precisely determine both the singlet and triplet s-wave scattering lengths for both isotopes, which are important parameters in systems designed to observe quantum degenerate effects and Bose-Einstein condensation.