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Physical Review A

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

Haijin Wang, Anguel Nikolov, J. R. Ensher, P. L. Gould, Edward E. Eyler, William C. Stwalley, J. P. Burke, John L. Bohn, Chris H. Greene, Eite Tiesinga, Carl J. Williams, Paul S. Julienne

Published Oct 12, 2000• 62 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.62.052704

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We use double-resonance photoassociative spectroscopy of ultracold 39K{}^{39}\mathrm{K}39K atoms to precisely determine the triplet a3\ensuremathΣu+a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}a3\ensuremathΣu+​ scattering length for the various isotopes of potassium. Photoassociation of free 39K{}^{39}\mathrm{K}39K atoms to the pure long-range 0g\ensuremath−(v\ensuremath′=0,J\ensuremath′=2){0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}=0,{J}^{\ensuremath{'}}=2)0g\ensuremath−​(v\ensuremath′=0,J\ensuremath′=2) level is followed by stimulated emission to high-lying levels of the a3\ensuremathΣu+a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}a3\ensuremathΣu+​ potential. The binding energies of levels within 5 GHz below the lowest ground-state 4s1/2(fa=1)+4s1/2(fb=1){4s}_{1/2}{(f}_{a}{=1)+4s}_{1/2}{(f}_{b}=1)4s1/2​(fa​=1)+4s1/2​(fb​=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 39K,{}^{39}\mathrm{K},39K, at=\ensuremath−33\ifmmode±\else\textpm\fi5a0{a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}at​=\ensuremath−33\ifmmode±\else\textpm\fi5a0​ (1a0=0.0529177nm),{(1a}_{0}=0.0529177 \mathrm{nm}),(1a0​=0.0529177nm), is a factor of \ensuremath∼5\ensuremath{\sim}5\ensuremath∼5 improvement over previous determinations and establishes that a large 39K{}^{39}\mathrm{K}39K Bose-Einstein condensate will not be stable.
The field of laser cooling and trapping of atoms has had a profound impact on many areas of atomic, molecular and optical science. In particular, ultracold atoms colliding in magneto-optical traps typically have relative kinetic energies of 300muK(sim7MHz)300\\mu K (\\sim 7 MHz)300muK(sim7MHz), so free-bound absorption lines are as sharp as bound-bound lines. Moreover, because of very long range centrifugal barriers, only a few collisional partial waves are important (Jprimeprime=0,1J^{\\prime\\prime} = 0, 1Jprimeprime=0,1 and 2 in our work on 39K^{39}K39K). Such photoassociative free-bound absorption allows observation of ``pure long-range molecule'' states (Re=28R_{e} = 28Re​=28 and 39 {\\AA} in 39K2^{39}K_{2}39K2​) as well as long-range levels of known short range states with outer classical turning points of sim20−250AA\\sim 20 - 250 {\\AA}sim20−250AA. Such spectra have been observed by ``trap loss'' (decrease in atomic fluorescence), molecular ionization, and fragment ionization. Optical-optical double resonance (OODR), e.g. through the ``Franck-Condon windows'' of the ``pure long-range'' states, produces readily assignable spectra at higher asymptotes as well. Further extensions of ultracold photoassociative spectroscopy and applications to determination of long range potentials, atomic properties, and Bose-Einstein condensate stability will be presented.
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)].
We have determined the scattering lengths for collisions between the different isotopes of two potassium atoms in singlet and triplet molecular states of K2{\mathrm{K}}_{2}K2​. We show that for the two bosonic species 39K{}^{39}\mathrm{K}39K and 41K{}^{41}\mathrm{K}41K the scattering lengths are positive, hence, leading to stable condensates. The fermionic isotope 40K{}^{40}\mathrm{K}40K also has positive scattering lengths, but the triplet value is nearly zero, hence, a quasi-non-interacting fermionic gas. We also give results for the interspecies collisions. We conclude that double condensates of 39K{}^{39}\mathrm{K}39K and 41K{}^{41}\mathrm{K}41K are possible for purely spin-polarized atoms, and sympathetic cooling between the bosonic 39K{}^{39}\mathrm{K}39K and the fermionic 40K{}^{40}\mathrm{K}40K will be efficient due to low spin-flip rates and a sizable interspecies scattering length.
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.
The hyperfine-state-selected scattering properties of potassium atoms at ultralow temperatures are calculated using interaction potentials gleaned from an analysis of recent photoassociation data. We predict that the small, probably negative value of the 39K{}^{39}\mathrm{K}39K triplet scattering length will hamper efforts to produce a Bose-Einstein condensate, unless experiments utilize a broad, accessible magnetic Feshbach resonance. The large positive value calculated for the 41K{}^{41}\mathrm{K}41K triplet scattering length makes it a better candidate for condensation at zero magnetic field. The fermionic isotope 40K{}^{40}\mathrm{K}40K is also predicted to have a large, positive scattering length for elastic collisions between spin states of experimental interest, implying that it can be efficiently evaporatively cooled to the quantum degenerate regime. In addition, certain spin states possess Feshbach resonances that may enable tuning of its interatomic interactions, possibly leading to the formation of Cooper pairs.
Threshold scattering properties of 39K{}^{39}\mathrm{K}39K 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., C6=3800{C}_{6}=3800C6​=3800 a.u.