Physical Review A

Singlet s -wave scattering lengths of Li6 and Li7

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

Published Jun 1, 1996• 51 citations

Abstract

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.

DOI: 10.1103/physreva.53.r3713

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Singlet s-wave scattering lengths of {sup 6}Li and {sup 7}Li

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Photoassociative Spectroscopy of Collisions Between Ultracold Lithium Atoms

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

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Physical Review A

Singlet s -wave scattering lengths of Li6 and Li7

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

Published Jun 1, 1996• 51 citations

Publisher

Abstract

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.

DOI: 10.1103/physreva.53.r3713

Related papers

Singlet s-wave scattering lengths of {sup 6}Li and {sup 7}Li

E. Abraham, W. I. McAlexander, Jordan M. Gerton

Ultracold collisional interactions are crucial to both the dynamical evolution and the steady-state behavior of systems designed to observe Bose-Einstein condensation, and are relevant to the advances in high precision measurements, and the creation of more highly accurate atomic clocks based on laser-cooled neutral atoms. An important parameter for understanding these collisions is the s-wave scattering length {alpha}, which can be determined from accurate knowledge of the two-body interaction potential. Photoassociation of ultracold lithium atoms into bound vibrational levels of the A{sup 1}{Sigma}{sub u}{sup +} excited state is used to probe the X{sup 1}{Sigma}{sub g}{sup +} ground state interaction potential of {sup 6}Li{sub 2} and {sup 7}Li{sub 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 scattering length. The authors present 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 scattering lengths for collisions involving {sup 7}Li atoms in different hyperfine states.Ultracold collisional interactions are crucial to both the dynamical evolution and the steady-state behavior of systems designed to observe Bose-Einstein condensation, and are relevant to the advances in high precision measurements, and the creation of more highly accurate atomic clocks based on laser-cooled neutral atoms. An important parameter for understanding these collisions is the s-wave scattering length {alpha}, which can be determined from accurate knowledge of the two-body interaction potential. Photoassociation of ultracold lithium atoms into bound vibrational levels of the A{sup 1}{Sigma}{sub u}{sup +} excited state is used to probe the X{sup 1}{Sigma}{sub g}{sup +} ground state interaction potential of {sup 6}Li{sub 2} and {sup 7}Li{sub 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 scattering length. The authors present 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 scattering lengths for collisions involving {sup 7}Li atoms in different hyperfine states.

Bulletin of the American Physical SocietyMay 1, 19960 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

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

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

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.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.

Physical Review AMay 1, 1997190 citations

Sympathetic cooling of Li6 atoms

Frank A. van Abeelen, BOUDEWIJN J. VERHAAR, A. J. Moerdijk

We use recently measured cold photoassociation and two-photon data to extract the singlet and triplet accumulated radial phases of interacting ground-state lithium atoms. Using the resulting values we predict scattering lengths, Feshbach resonances, and exchange decay rates for cold collisions between $^{7}\mathrm{Li}$ and $^{6}\mathrm{Li}$ atoms that are of interest for the possibility of sympathetic cooling of $^{6}\mathrm{Li}$ and for the coexistence of the bosonic and fermionic quantum-degenerate phases of $^{7}\mathrm{Li}$ and $^{6}\mathrm{Li}$ . In addition, we calculate scattering lengths and exchange decay rates for cold collisions between identical lithium isotopes in different hyperfine states. These quantities are used to examine the possibilities of coexisting $^{7}\mathrm{Li}$ Bose condensates and of evaporatively cooling coexisting $^{6}\mathrm{Li}$ subsystems.We use recently measured cold photoassociation and two-photon data to extract the singlet and triplet accumulated radial phases of interacting ground-state lithium atoms. Using the resulting values we predict scattering lengths, Feshbach resonances, and exchange decay rates for cold collisions between $^{7}\mathrm{Li}$ and $^{6}\mathrm{Li}$ atoms that are of interest for the possibility of sympathetic cooling of $^{6}\mathrm{Li}$ and for the coexistence of the bosonic and fermionic quantum-degenerate phases of $^{7}\mathrm{Li}$ and $^{6}\mathrm{Li}$. In addition, we calculate scattering lengths and exchange decay rates for cold collisions between identical lithium isotopes in different hyperfine states. These quantities are used to examine the possibilities of coexisting $^{7}\mathrm{Li}$ Bose condensates and of evaporatively cooling coexisting $^{6}\mathrm{Li}$ subsystems.

Physical Review AJun 1, 199746 citations

Ground-state scattering lengths for potassium isotopes determined by double-resonance photoassociative spectroscopy of ultracold 39K

Haijin Wang, Anguel Nikolov, J. R. Ensher +9 more

We use double-resonance photoassociative spectroscopy of ultracold ${}^{39}\mathrm{K}$ atoms to precisely determine the triplet $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free ${}^{39}\mathrm{K}$ atoms to the pure long-range ${0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}=0,{J}^{\ensuremath{'}}=2)$ level is followed by stimulated emission to high-lying levels of the $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potential. The binding energies of levels within 5 GHz below the lowest ground-state ${4s}_{1/2}{(f}_{a}{=1)+4s}_{1/2}{(f}_{b}=1)$ hyperfine asymptote are measured by both trap loss and ionization detection. The locations of these near-threshold hyperfine-coupled molecular levels allow us to constrain the triplet potential and thereby determine the triplet scattering length. The result for ${}^{39}\mathrm{K},$ ${a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}$ ${(1a}_{0}=0.0529177 \mathrm{nm}),$ is a factor of $\ensuremath{\sim}5$ improvement over previous determinations and establishes that a large ${}^{39}\mathrm{K}$ Bose-Einstein condensate will not be stable.We use double-resonance photoassociative spectroscopy of ultracold ${}^{39}\mathrm{K}$ atoms to precisely determine the triplet $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free ${}^{39}\mathrm{K}$ atoms to the pure long-range ${0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}=0,{J}^{\ensuremath{'}}=2)$ level is followed by stimulated emission to high-lying levels of the $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potential. The binding energies of levels within 5 GHz below the lowest ground-state ${4s}_{1/2}{(f}_{a}{=1)+4s}_{1/2}{(f}_{b}=1)$ hyperfine asymptote are measured by both trap loss and ionization detection. The locations of these near-threshold hyperfine-coupled molecular levels allow us to constrain the triplet potential and thereby determine the triplet scattering length. The result for ${}^{39}\mathrm{K},$ ${a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}$ ${(1a}_{0}=0.0529177 \mathrm{nm}),$ is a factor of $\ensuremath{\sim}5$ improvement over previous determinations and establishes that a large ${}^{39}\mathrm{K}$ Bose-Einstein condensate will not be stable.

Physical Review AOct 12, 200062 citations

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

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.

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 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.

^{7}\mathrm{Li}

and

^{6}\mathrm{Li}

atoms that are of interest for the possibility of sympathetic cooling of

^{6}\mathrm{Li}

and for the coexistence of the bosonic and fermionic quantum-degenerate phases of

^{7}\mathrm{Li}

and

^{6}\mathrm{Li}

. In addition, we calculate scattering lengths and exchange decay rates for cold collisions between identical lithium isotopes in different hyperfine states. These quantities are used to examine the possibilities of coexisting

^{7}\mathrm{Li}

Bose condensates and of evaporatively cooling coexisting

^{6}\mathrm{Li}

subsystems.

We use double-resonance photoassociative spectroscopy of ultracold

{}^{39}\mathrm{K}

atoms to precisely determine the triplet $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free

{}^{39}\mathrm{K}

atoms to the pure long-range ${0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}=0,{J}^{\ensuremath{'}}=2)$ level is followed by stimulated emission to high-lying levels of the $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potential. The binding energies of levels within 5 GHz below the lowest ground-state

{4s}_{1/2}{(f}_{a}{=1)+4s}_{1/2}{(f}_{b}=1)

hyperfine asymptote are measured by both trap loss and ionization detection. The locations of these near-threshold hyperfine-coupled molecular levels allow us to constrain the triplet potential and thereby determine the triplet scattering length. The result for

{}^{39}\mathrm{K},

${a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}$

{(1a}_{0}=0.0529177 \mathrm{nm}),

is a factor of $\ensuremath{\sim}5$ improvement over previous determinations and establishes that a large

{}^{39}\mathrm{K}

Bose-Einstein condensate will not be stable.

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.