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Physical Review A

Precise atomic radiative lifetime via photoassociative spectroscopy of ultracold lithium

W. I. McAlexander, E. R. I. Abraham, Nicholas W. M. Ritchie, Carl J. Williams, Henk T. C. Stoof, Randall G. Hulet

Published Feb 1, 1995• 123 citations
Publisher

Abstract

We have obtained spectra of the high-lying vibrational levels of the ${1}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state of $^{6}\mathrm{Li}_{2}$ via photoassociation of ultracold $^{6}\mathrm{Li}$ atoms confined in a magneto-optical trap. The ${1}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state of the diatomic molecule correlates to a 2${\mathit{S}}_{1/2}$ state atom plus a 2${\mathit{P}}_{1/2}$ state atom. The long-range part of the molecular interaction potential for this state depends on the 2P atomic radiative lifetime. By calculating the energy eigenvalues of a model potential for the ${1}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state and fitting them to the experimentally measured vibrational levels, we have extracted a value for the 2P lifetime of 26.99\ifmmode\pm\else\textpm\fi{}0.16 ns. The precision is currently limited by the accuracy of a region of the model potential provided by ab initio calculations.

DOI
10.1103/physreva.51.r871

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We have obtained spectra of the high-lying vibrational levels of the {1}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+} state of 6Li2^{6}\mathrm{Li}_{2}6Li2​ via photoassociation of ultracold 6Li^{6}\mathrm{Li}6Li atoms confined in a magneto-optical trap. The {1}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+} state of the diatomic molecule correlates to a 2S1/2{\mathit{S}}_{1/2}S1/2​ state atom plus a 2P1/2{\mathit{P}}_{1/2}P1/2​ state atom. The long-range part of the molecular interaction potential for this state depends on the 2P atomic radiative lifetime. By calculating the energy eigenvalues of a model potential for the {1}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+} state and fitting them to the experimentally measured vibrational levels, we have extracted a value for the 2P lifetime of 26.99\ifmmode\pm\else\textpm\fi{}0.16 ns. The precision is currently limited by the accuracy of a region of the model potential provided by ab initio calculations.
Spectroscopy of the high-lying vibrational levels of the 1sp3Sigmasbspg+1\\sp3\\Sigma\\sbsp{g}{+}1sp3Sigmasbspg+ and 1sp1Sigmasbspu+1\\sp1\\Sigma\\sbsp{u}{+}1sp1Sigmasbspu+ states of both rmsp6Lisb2\\rm\\sp6Li\\sb2rmsp6Lisb2 and rmsp7Lisb2\\rm\\sp7Li\\sb2rmsp7Lisb2 has been accomplished via photoassociation of ultracold atomic lithium confined in a magneto-optical trap. Both these molecular states correlate to 2Ssb1/22S\\sb{1/2}2Ssb1/2 plus 2Psb1/22P\\sb{1/2}2Psb1/2 free atomic states. The long range part of these molecular potentials depends on the 2P atomic radiative lifetime. Accurate models were constructed for both the 1sp3Sigmasbspg+1\\sp3\\Sigma\\sbsp{g}{+}1sp3Sigmasbspg+ and 1sp1Sigmasbspu+1\\sp1\\Sigma\\sbsp{u}{+}1sp1Sigmasbspu+ potentials. By fitting these models to the experimentally measured vibrational levels observed in rmsp6Lisb2\\rm\\sp6Li\\sb2rmsp6Lisb2 and rmsp7Lisb2\\rm\\sp7Li\\sb2rmsp7Lisb2, we have been able to extract a value for the 2P lifetime of lithium. Fitting to the absolute values of the data gives a value of 26.99 pm\\pmpm 0.16 ns whereas fitting to differences in the spectral features gives a value of 27.04 pm\\pmpm 0.18 ns. While both values agree with previous work, improvements made in the potential models would enable this analysis to resolve the current discrepancy between experiment and theory.
We have obtained high-lying vibrational spectra for the rm1sp3Sigmasbspg+\\rm 1\\sp3\\Sigma\\sbsp{g}{+}rm1sp3Sigmasbspg+ and rm1sp1Sigmasbspu+\\rm 1\\sp1\\Sigma\\sbsp{u}{+}rm1sp1Sigmasbspu+ excited states of both rmsp7Lisb2\\rm \\sp7Li\\sb2rmsp7Lisb2 and rmsp6Lisb2\\rm \\sp6Li\\sb2rmsp6Lisb2 via photoassociation of colliding ultracold lithium atoms confined in a magneto-optical trap. Photoassociative spectroscopy of ultracold atoms is a powerful tool for probing molecular states near the dissociation energy that are inaccessible by other methods. For an ultracold lithium vapor, the distribution of unbound ground state energies is so small that precise free-bound spectroscopy is possible. Molecular hyperfine structure is resolved. We calculate accurate dissociation energies for both the rm1sp3Sigmasbspg+\\rm 1\\sp3\\Sigma\\sbsp{g}{+}rm1sp3Sigmasbspg+ and rm1sp1Sigmasbspu+\\rm 1\\sp1\\Sigma\\sbsp{u}{+}rm1sp1Sigmasbspu+ excited states of Lisb2\\sb2sb2. A model potential is constructed from a combination of experimental and theoretical information, and used to assign vibrational quantum numbers. We observe rotational structure and assign rotational quantum numbers.
Rovibrational levels (v=0--30) of the ${0}_{\mathrm{g}}^{\mathrm{\ensuremath{-}}}$ ``pure long-range'' state of 39K2^{39}\mathrm{K}_{2}39K2​ are observed by photoassociative spectroscopy of ultracold potassium atoms prepared in a high-density magneto-optical trap. The measured molecular binding energies are used to precisely determine the long-range dipole-dipole potential constant ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$ of the K(4s)+K(4p) asymptote and the radiative lifetime of the 4p state. We determine ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$=-5.456(9) zJ nm3{\mathrm{nm}}^{3}nm3 (-8.445(14) a.u.), \ensuremath{\tau}(42{\mathrm{}}^{2}2P3/2{\mathrm{P}}_{3\mathrm{/}2}P3/2​)=26.34(5) ns, and \ensuremath{\tau}(42{\mathrm{}}^{2}2P1/2{\mathrm{P}}_{1\mathrm{/}2}P1/2​)=26.69(5) ns. Our result is a significant improvement in precision over previous lifetime measurements and agrees well with the recent fast-beam experiment [U. Volz and H. Schmoranzer, Phys. Scr. T65, 48 (1996)].
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.
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We have obtained spectra of the high-lying vibrational levels of the A1Σu+ and 13Σg+states of both 6Li2 and 7Li2 via photoassociation of colliding ultracold atoms confined to a magneto-optical trap. Because of the low collision energies (∼1 mK), very high spectroscopic resolution is realized, and sensitivity is greatest for the usually difficult to access long-range states. Binding energies relative to the center of gravity of the resolved hyperfine structure are given for the A1Σu+ vibrational levels v =62–88 for 6Li2 and v=65–97 for 7Li2, and the 13Σg+ vibrational levels v=56–84 for 6Li2 and v=62–90 for 7Li2. These are extremely long-range levels with outer classical turning points ranging from 25 a0 to 220 a0, where a0 is the Bohr radius. The spectra arise mainly from s-wave collisions, and therefore exhibit little rotational structure.