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Physical Review A

Predissociation induced by ungerade-gerade symmetry breaking in the B1Πu state of the 6Li7Li molecule

Nadia Bouloufa-Maafa, Patrice Cacciani, Viatcheslav Kokoouline, Françoise Masnou-Seeuws, Raymond J. Vetter, Li Li

Published Mar 19, 2001• 12 citations
Publisher

Abstract

Unlike the ${}^{6}{\mathrm{Li}}^{6}\mathrm{Li}$ and ${}^{7}{\mathrm{Li}}^{7}\mathrm{Li}$ isotopomers, the ${}^{6}{\mathrm{Li}}^{7}\mathrm{Li}$ molecule exhibits surprisingly high dissociation rates for the levels that lie just above the dissociation limit of the $B{}^{1}{\ensuremath{\Pi}}_{u}$ state. As shown by Cacciani and Kokoouline [Phys. Rev. Lett. 84, 5296 (2000)] they can be attributed to a coupling between the $B{}^{1}{\ensuremath{\Pi}}_{u}$ and $1{}^{1}{\ensuremath{\Pi}}_{g}$ states, through the breaking of the ungerade-gerade symmetry. Systematic measurements of these dissociation rates have been performed by discriminating atomic fluorescence from molecular fluorescence in a sub-Doppler experiment involving a beam of lithium dimers and a cw tunable laser beam. Calculations of dissociation rates have been performed in the framework of a perturbative approach, by solving the coupled Schr\"odinger equations through the use of the mapped Fourier grid representation method. Measured and calculated dissociation rates are in excellent agreement for a unique value of the coupling strength $h=0.144$ ${\mathrm{cm}}^{\ensuremath{-}1}.$

DOI
10.1103/physreva.63.042507

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Unlike the 6Li6Li{}^{6}{\mathrm{Li}}^{6}\mathrm{Li}6Li6Li and 7Li7Li{}^{7}{\mathrm{Li}}^{7}\mathrm{Li}7Li7Li isotopomers, the 6Li7Li{}^{6}{\mathrm{Li}}^{7}\mathrm{Li}6Li7Li molecule exhibits surprisingly high dissociation rates for the levels that lie just above the dissociation limit of the B1\ensuremathΠuB{}^{1}{\ensuremath{\Pi}}_{u}B1\ensuremathΠu​ state. As shown by Cacciani and Kokoouline [Phys. Rev. Lett. 84, 5296 (2000)] they can be attributed to a coupling between the B1\ensuremathΠuB{}^{1}{\ensuremath{\Pi}}_{u}B1\ensuremathΠu​ and 11\ensuremathΠg1{}^{1}{\ensuremath{\Pi}}_{g}11\ensuremathΠg​ states, through the breaking of the ungerade-gerade symmetry. Systematic measurements of these dissociation rates have been performed by discriminating atomic fluorescence from molecular fluorescence in a sub-Doppler experiment involving a beam of lithium dimers and a cw tunable laser beam. Calculations of dissociation rates have been performed in the framework of a perturbative approach, by solving the coupled Schr"odinger equations through the use of the mapped Fourier grid representation method. Measured and calculated dissociation rates are in excellent agreement for a unique value of the coupling strength h=0.144h=0.144h=0.144 cm\ensuremath−1.{\mathrm{cm}}^{\ensuremath{-}1}.cm\ensuremath−1.
Experimental observations of dissociative attachment in lithium are described. Using laser excitation of a supersonic lithium beam a population of metastable vibrationally excited lithium molecules has been created. A cold-electron population (0.13 eV) has been created by laser photoionization of lithium atoms, and the attachment of these electrons has been studied as a function of molecular state. The dissociative attachment rate constant does not vary significantly for Li2{\mathrm{Li}}_{2}Li2​(X) between v\ensuremath{\sim}10 and v\ensuremath{\sim}13, states which lie above the attachment energy threshold, nor is there significant rotational variation between J\ensuremath{\sim}0 and J\ensuremath{\sim}20. The rate constant for dissociative attachment to these states for thermal electrons at \ensuremath{\sim}0.05 eV has been measured to be (2\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ cm3{\mathrm{cm}}^{3}cm3 sec $^{\mathrm{\ensuremath{-}}1}$.
The treatment of the dynamics of ultracold molecules requires new theoretical tools. Previous work of the present authors [J. Chem. Phys. 110, 9865 (1999)] for calculation of vibrational levels by a Fourier grid representation with use of adaptative coordinates is generalized here to the treatment of the bound-continuum interaction in a two-channel problem. Two numerical methods are presented: a time-dependent method using a Chebyshev propagator to compute the correlation function and a time-independent method with diagonalization of a Hamiltonian that includes an absorbing optical potential. In both cases the adaptative coordinate is defined by a numerical rather than an analytical procedure. Lifetimes are reported for the predissociated levels of the Rb2{\mathrm{Rb}}_{2}Rb2​ and Cs20u+(ns+np2P3/2){\mathrm{Cs}}_{2}{0}_{u}^{+}{(ns+np}^{2}{P}_{3/2})Cs2​0u+​(ns+np2P3/2​) spectra, where n=5,6.n=5,6.n=5,6. The two numerical methods give similar results. The lifetimes increase with the vibrational quantum number proportionally to the classical vibration period estimated from the Le Roy--Bernstein law for an asymptotic ${R}^{\ensuremath{-}3}$ potential, and the energy variation can be fitted to an analytical formula. The results are shown to be very sensitive to the molecular parameters, potentials, and couplings. The measured width of 8.5 GHz reported by Cline et al. [Phys. Rev. Lett. 73, 632 (1994)] for one predissociated level of 87Rb2{}^{87}{\mathrm{Rb}}_{2}87Rb2​ is reproduced. A strong isotopic effect is found for the rubidium dimer, the lifetimes of 85Rb2{}^{85}{\mathrm{Rb}}_{2}85Rb2​ and 87Rb2{}^{87}{\mathrm{Rb}}_{2}87Rb2​ levels differing by a factor of 3. Finally, we present a third approach, in the framework of a generalized two-channel quantum-defect theory, where lifetimes are determined by extrapolation of parameters fitted to Lu-Fano plots of computed bound levels below the P1/2{P}_{1/2}P1/2​ dissociation limit. Excellent agreement is obtained with the numerical results, suggesting the possibility of fitting to experimental spectra.
We have observed short-range photoassociation of 7Li85Rb^{7}\mathrm{Li}^{85}\mathrm{Rb}7Li85Rb to the two lowest vibrational states of the $d{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}}$ potential. We have also observed several ${a}^{3}\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Sigma}}}^{+}$ vibrational levels with generation rates between $\ensuremath{\sim}{10}^{2}$ and $\ensuremath{\sim}{10}^{3}$ molecules per second, resulting from the spontaneous decay of these $d{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}}$ molecules. We observe an alternation of the peak heights in the rotational photoassociation spectrum that depends on the parity of the excited molecular state. Franck-Condon overlap calculations predict that photoassociation to higher vibrational levels of the $d{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}}$ potential, in particular, the sixth vibrational level, should populate the lowest vibrational level of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state at a rate as high as 104{10}^{4}104 molecules per second. This work also motivates an experimental search for short-range photoassociation to other bound molecular states, such as $c{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}^{+}$ or $b{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}}$, as prospects for preparing ground-state molecules.
This thesis is concerned with long range behavior of the interaction potential of two neutral atoms.Two aspects are of special interest: First, how the long range behavior changes if one of the atoms is replaced by another isotope.Second, how to model the influence of a laser field on long range interaction.Several high precision spectroscopy experiments on particle beams are carried out.The transition frequencies of the D lines of 39,40,41 K are measured with frequency comb generated by a self-referenced femtosecond laser, which is locked to a Cs-clock.Discrepancies in the literature are removed and new values for the hyperfine structures of the 4p 1/2 and 4p 3/2 state and the isotope shift of both D lines are derive.On a beam of potassium dimers the A 1 Σ + u state of K 2 is studied up to the dissociation limit complementing and extending photoassociation spectroscopy of ultracold ensembles.Local perturbation due to the spin-orbit coupling with the b 3 Π u state are identified.Molecular hyperfine structure of levels close to the asymptote is observed and modeled by atomic parameter only.Improved values of the atomic radiative lifetime of the states 4p 1/2 and 4p 3/2 are derived from the long range parameter C 3 of the molecule.Also, an improved value for the dissociation energy of the X 1 Σ + g ground state is obtained and recipes for the investigation of cold collision via spectroscopy of the molecular structure at the ground state asymptotes are derived.For the first time asymptotic levels of two isotopomers of K 2 are studied and a comparison of asymptotic spectra of two isotopomers 39 K 2 and 39 K 41 K shows that corrections to the Born-Oppenheimer potential are needed.Optical coupling between asymptotic ground state levels and long range levels of an excited state has been suggested as tool for influencing cold collisions.Here, we model lineshapes for an experiment which investigates such a coupling systematically in Na 2 by laser spectroscopy in a beam.A fit program for the lineshape is used to compare experimental and theoretical values and to check the validity of the applied model from multichannel quantum defect theory.The dependency on the detuning of the coupling laser is reproduced but other details failed.To allow similar studies are reported for alkali metals on the simpler quantum system from alkali earth elements the development of an oven for a continuous beam of Ca 2 for Doppler-free spectroscopy is discussed including a major change of design and first experiences are reported.The heating of the oven is, unlike those for the beams applied above, outside the vacuum tank because of the high temperatures needed for the oven.
Numerical calculations of vibrational levels of alkali dimers close to the dissociation limit are developed in the framework of a Fourier Grid Hamiltonian method. The aim is to interpret photoassociation experiments in cold atom samples. In order to avoid the implementation of very large grids we propose a mapping procedure adapted to the asymptotic R−n behavior of the long-range potentials. On a single electronic potential, this allows us to determine vibrational wave functions extending up to 500a0 using a minimal number of grid points. Calculations with two electronic states, A 1Σu+ and b 3Πu states, both correlated to the Rb(5s)+Rb(5p) dissociation limit, coupled by fine structure are presented. We predict strong perturbation effects in the Rb2(0u+) spectrum, manifested under the 5s, 5p 2P1/2 dissociation limit by an oscillatory behavior of the rotational constants.