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Bulletin of the American Physical Society

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

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

Published May 1, 1996• 0 citations
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Abstract

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.

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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.
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 6Li2^{6}\mathrm{Li}_{2}6Li2​ and 7Li2^{7}\mathrm{Li}_{2}7Li2​. It had been predicted that the sss-wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive sss-wave scattering length. We report the observation of this novel effect, and use the location of the minimum to precisely determine the singlet sss-wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the minima for collisions involving 7Li^{7}\mathrm{Li}7Li atoms in different hyperfine states.
The spectra of the high-lying vibrational levels of the Asp1Sigmasbspu+A\\sp1\\Sigma\\sbsp{u}{+}Asp1Sigmasbspu+ and 1sp3Sigmasbspg+1\\sp3\\Sigma\\sbsp{g}{+}1sp3Sigmasbspg+ singly excited states of both sp6rmLisb2\\sp6\\rm Li\\sb2sp6rmLisb2 and sp7rmLisb2\\sp7\\rm Li\\sb2sp7rmLisb2 are obtained via photoassociation of colliding ultracold atoms confined in a magneto-optical trap. The least bound state of the asp3Sigmasbspu+a\\sp3\\Sigma\\sbsp{u}{+}asp3Sigmasbspu+ ground state potential, obtained by two-photon photoassociative spectroscopy, is also presented for both sp7rmLisb2\\sp7\\rm Li\\sb2sp7rmLisb2 and sp6rmLisb2\\sp6\\rm Li\\sb2sp6rmLisb2. 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.
Two-photon photoassociation of colliding ultracold 7{}^{7}7Li atoms is used to probe the $^{3}\ensuremath{\Sigma}_{u}^{+}(a)$ ground state of 7{}^{7}7Li2{\mathrm{i}}_{2}i2​. 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 sss-wave scattering length for 7{}^{7}7Li atoms in the F=2F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2F=2, mF=2{m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2mF​=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{}^{7}7Li atoms is used to probe the $^{3}\ensuremath{\Sigma}_{u}^{+}(a)$ ground state of 7{}^{7}7Li2{\mathrm{i}}_{2}i2​. 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 sss-wave scattering length for 7{}^{7}7Li atoms in the F=2F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2F=2, mF=2{m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2mF​=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.
The paper reports on a new measurement method of the s-wave scattering length of metastable helium atoms by photoassociation (PA) technique. Lightshifts of the PA resonance lines are measured, which results from the coupling of a bound state in the excited state potential and the continuum of scattering states above the ground state potential. Ultracold molecules are formed by photoassociation from spin-polarized metastable helium atoms, which are trapped in a magnetic trap and cooled down to a temperature of 16 /spl mu/K by evaporative cooling technique. The PA laser is red detuned to the atomic D0 line (2/sup 3/S-2/sup 3/P/sub 0/) and scanned around the bound state levels in the purely long-range 0/sub 0//sup +/ potential to provide precise PA spectra.
We present spectroscopic measurements of seven vibrational levels v=29−−35v=29--35v=29−−35 of the $A({1}^{1}{\ensuremath{\Sigma}}_{u}^{+})$ excited state of Li2{}_{2}2​ molecules by the photoassociation of a degenerate Fermi gas of 6{}^{6}6Li atoms. The absolute uncertainty of our measurements is $\ifmmode\pm\else\textpm\fi{}0.000\phantom{\rule{0.16em}{0ex}}02$ cm${}^{\ensuremath{-}1}$ ($\ifmmode\pm\else\textpm\fi{}600$ kHz) and we use these new data to further refine an analytic potential for this state. This work provides high accuracy photoassociation resonance locations essential for the eventual high-resolution mapping of the $X({1}^{1}{\ensuremath{\Sigma}}_{g}^{+})$ state enabling further improvements to the sss-wave scattering length determination of Li and enabling the eventual creation of ultracold ground-state 6{}^{6}6Li2{}_{2}2​ molecules.