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Physical Review A

Precise determination of the dipole matrix element and radiative lifetime of the K39 4p state by photoassociative spectroscopy

H. Wang, J. Li, X. T. Wang, Carl J. Williams, P. L. Gould, William C. Stwalley

Published Mar 1, 1997• 93 citations
Publisher

Abstract

Rovibrational levels (v=0--30) of the ${0}_{\mathrm{g}}^{\mathrm{\ensuremath{-}}}$ ``pure long-range'' state of $^{39}\mathrm{K}_{2}$ 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 ${\mathrm{nm}}^{3}$ (-8.445(14) a.u.), \ensuremath{\tau}(4${\mathrm{}}^{2}$${\mathrm{P}}_{3\mathrm{/}2}$)=26.34(5) ns, and \ensuremath{\tau}(4${\mathrm{}}^{2}$${\mathrm{P}}_{1\mathrm{/}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)].

DOI
10.1103/physreva.55.r1569

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Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The g− pure long-range state and the long-range potential constants

H. Wang, P. L. Gould, William C. Stwalley

This paper reports on a comprehensive study of the long-range interaction of the K39(4s)+39K(4p) asymptotic system. We present a detailed discussion of the R-dependent angular momentum couplings and correlation between the Hund’s case (a) and case (c) molecular states. Analytical expressions for the 16 adiabatic Hund’s case (c) long-range potential curves are derived including the higher order dispersion forces and the effects of retardation. Experimentally, six Hund’s case (c) long-range molecular states (0u+, 1g, and 0g− dissociating to the 4 2S1/2+4 2P3/2 asymptote and 0u+, 1g, and 0g− to the 4 2S1/2+4 2P1/2 limit) are observed with rovibrational resolution by photoassociative spectroscopy of ultracold K39 atoms in a high density magneto-optical trap (MOT). Among the six observed long-range states, the upper 0g− “pure long-range” state has negligible short-range chemical exchange contributions and the measured molecular binding energies (v=0–26) are used to precisely determine the long-range potential constants of the 4s+4p interaction. We determine: C3Π=8.436(14) a.u., C3Σ=16.872(28) a.u., C6Π=6272(94) a.u., and C6Σ=9365(141) a.u.. Molecular constants for the three special pure long-range states, the 0g− and 1u (dissociating to the 4 2P3/2 limit and with potential minimum) and the 1u (dissociating to the 4 2P1/2 and with potential maximum), are reported. The internal consistency of the theoretical model used in this work is confirmed by the excellent agreement between the long-range potential curve of the 1g state obtained in present work (from the 0g− state) and the long-range portion of the RKR potential curve of the 1 1Πg state previously determined by conventional molecular spectroscopy. The radiative lifetime of the K 4p state derived from the dipole–dipole interaction constant C3Π is also in excellent agreement with a recent fast-beam measurement.

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•Jan 1, 1995•0 citations

Photoassociative spectroscopy of ultracold K39 atoms in a high-density vapor-cell magneto-optical trap

H. Wang, P. L. Gould, William C. Stwalley

We have performed photoassociative spectroscopy of ultracold potassium atoms in a high-density vapor-cell magneto-optical trap (MOT) in which atoms are confined predominantly in "dark" hyperfine levels that do not interact with the trapping light. Three well-resolved vibrational series (one strong and two weak) of the $^{39}\mathrm{K}_{2}$ molecule are observed within 8 ${\mathrm{cm}}^{\ensuremath{-}1}$ below the $4^{2}P_{\frac{3}{2}}$ atomic limit. One of the series is identified as the ${0}_{g}^{\ensuremath{-}}$ pure long-range state and the other two are assigned to the ${0}_{u}^{+}$ and ${1}_{g}$ states. These photoassociative spectra are obtained by measuring reductions in the trap fluorescence due to trap loss induced by an intense photoassociation laser. By using a vapor-cell-dark MOT technique, we achieve atomic densities greater than ${10}^{11}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, increasing our trap loss signals by an order of magnitude compared to a normal MOT.

Physical Review A•Mar 1, 1996•88 citations

Optical-Optical Double Resonance Photoassociative Spectroscopy of Ultracold 39 K Atoms near Highly Excited Asymptotes

H. Wang, X.T. Wang, P. L. Gould +1 more

We report the first observation of optical-optical double resonance photoassociative spectroscopy of ultracold ${}^{39}$K atoms near the highly excited $^{39}K(4s)+^{39}K(4d,5d,6d,6s,7s)$ asymptotes in a high density magneto-optical trap. Using the ${v}^{\ensuremath{'}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ level of the ${0}_{g}^{\ensuremath{-}}$ ``pure long-range'' state (a localized long-range Franck-Condon window) as the intermediate state, we observe simple and assignable rovibrational progressions dissociating to these asymptotes. The dominant long-range potential constants are determined. Line broadening, presumably due to autoionization, and rotational excitations due to strong field effects are observed.

Physical Review Letters•Jun 2, 1997•46 citations
Rovibrational levels (v=0--30) of the 0g\ensuremath−{0}_{\mathrm{g}}^{\mathrm{\ensuremath{-}}}0g\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 C3\ensuremathΠ{\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}C3\ensuremathΠ​ of the K(4s)+K(4p) asymptote and the radiative lifetime of the 4p state. We determine C3\ensuremathΠ{\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}C3\ensuremathΠ​=-5.456(9) zJ nm3{\mathrm{nm}}^{3}nm3 (-8.445(14) a.u.), \ensuremath{\tau}(4{\mathrm{}}^{2}$${\mathrm{P}}_{3\mathrm{/}2})=26.34(5) ns, and \ensuremath{\tau}(4{\mathrm{}}^{2}$${\mathrm{P}}_{1\mathrm{/}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)].
This paper reports on a comprehensive study of the long-range interaction of the K39(4s)+39K(4p) asymptotic system. We present a detailed discussion of the R-dependent angular momentum couplings and correlation between the Hund’s case (a) and case (c) molecular states. Analytical expressions for the 16 adiabatic Hund’s case (c) long-range potential curves are derived including the higher order dispersion forces and the effects of retardation. Experimentally, six Hund’s case (c) long-range molecular states (0u+, 1g, and 0g− dissociating to the 4 2S1/2+4 2P3/2 asymptote and 0u+, 1g, and 0g− to the 4 2S1/2+4 2P1/2 limit) are observed with rovibrational resolution by photoassociative spectroscopy of ultracold K39 atoms in a high density magneto-optical trap (MOT). Among the six observed long-range states, the upper 0g− “pure long-range” state has negligible short-range chemical exchange contributions and the measured molecular binding energies (v=0–26) are used to precisely determine the long-range potential constants of the 4s+4p interaction. We determine: C3Π=8.436(14) a.u., C3Σ=16.872(28) a.u., C6Π=6272(94) a.u., and C6Σ=9365(141) a.u.. Molecular constants for the three special pure long-range states, the 0g− and 1u (dissociating to the 4 2P3/2 limit and with potential minimum) and the 1u (dissociating to the 4 2P1/2 and with potential maximum), are reported. The internal consistency of the theoretical model used in this work is confirmed by the excellent agreement between the long-range potential curve of the 1g state obtained in present work (from the 0g− state) and the long-range portion of the RKR potential curve of the 1 1Πg state previously determined by conventional molecular spectroscopy. The radiative lifetime of the K 4p state derived from the dipole–dipole interaction constant C3Π is also in excellent agreement with a recent fast-beam measurement.
We present a detailed study of the ${0}_{g}^{\ensuremath{-}}{(P}_{3/2})$ pure long-range electronic state of the 87Rb2{}^{87}{\mathrm{Rb}}_{2}87Rb2​ molecule. The high-resolution spectral data provided by photoassociative spectroscopy of 87Rb2{}^{87}{\mathrm{Rb}}_{2}87Rb2​ is analyzed by using the generalized simulated annealing method. The dipole matrix element of the 5p5p5p 87Rb{}^{87}\mathrm{Rb}87Rb atomic state and other effective asymptotic parameters for the ${0}_{g}^{\ensuremath{-}}{(P}_{3/2})$ long-range state are determined and a complete analytical description of the potential well is obtained. We extract a radiative lifetime of the 5P3/2{5P}_{3/2}5P3/2​ and 5P1/2{5P}_{1/2}5P1/2​ states equal to 26.25(8) ns and 27.75(8) ns, respectively, with a precision (0.3%) comparable to atomic physics experiment.
We have obtained spectra of the high-lying vibrational levels of the 13{1}^{3}13${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ 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 13{1}^{3}13${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ 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 13{1}^{3}13${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ 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 performed photoassociative spectroscopy of ultracold potassium atoms in a high-density vapor-cell magneto-optical trap (MOT) in which atoms are confined predominantly in "dark" hyperfine levels that do not interact with the trapping light. Three well-resolved vibrational series (one strong and two weak) of the 39K2^{39}\mathrm{K}_{2}39K2​ molecule are observed within 8 ${\mathrm{cm}}^{\ensuremath{-}1}$ below the 42P324^{2}P_{\frac{3}{2}}42P23​​ atomic limit. One of the series is identified as the ${0}_{g}^{\ensuremath{-}}$ pure long-range state and the other two are assigned to the 0u+{0}_{u}^{+}0u+​ and 1g{1}_{g}1g​ states. These photoassociative spectra are obtained by measuring reductions in the trap fluorescence due to trap loss induced by an intense photoassociation laser. By using a vapor-cell-dark MOT technique, we achieve atomic densities greater than 1011{10}^{11}1011 ${\mathrm{cm}}^{\ensuremath{-}3}$, increasing our trap loss signals by an order of magnitude compared to a normal MOT.
We report the first observation of optical-optical double resonance photoassociative spectroscopy of ultracold 39{}^{39}39K atoms near the highly excited 39K(4s)+39K(4d,5d,6d,6s,7s)^{39}K(4s)+^{39}K(4d,5d,6d,6s,7s)39K(4s)+39K(4d,5d,6d,6s,7s) asymptotes in a high density magneto-optical trap. Using the ${v}^{\ensuremath{'}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ level of the ${0}_{g}^{\ensuremath{-}}$ ``pure long-range'' state (a localized long-range Franck-Condon window) as the intermediate state, we observe simple and assignable rovibrational progressions dissociating to these asymptotes. The dominant long-range potential constants are determined. Line broadening, presumably due to autoionization, and rotational excitations due to strong field effects are observed.