Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Lu-Fano plot for interpretation of the photoassociation spectra

Viatcheslav Kokoouline, Cyril Drag, P. Pillet, Françoise Masnou-Seeuws

Published Jun 7, 2002• 14 citations
Publisher

Abstract

Recently, the method of Lu-Fano plots was extended to potentials with general ${R}^{\ensuremath{-}n}$ asymptotic behavior. The aim of this paper is to discuss the efficiency of this method for the interpretation of experimental vibrational spectra of long-range diatomic molecules when two channels are coupled. A Lu-Fano analysis is implemented on experimental data for the ${\mathrm{Cs}}_{2}{0}_{u}^{+}{(6S+6P}_{1/2,3/2})$ photoassociation spectra below the ${6S+P}_{1/2}$ and ${6S+P}_{3/2}$ dissociation limits. The parameters are fitted on level energies and predissociation widths, giving information about the asymptotic coefficients ${C}_{3}$ for both channels and about a coupling parameter which determines the variation of predissociation widths as a function of detuning. This parameter can be extrapolated above the ${6S+P}_{3/2}$ threshold to yield the fine-structure transition cross section between the two channels. The probability for such a transition in a model where hyperfine structure effects are neglected is found to be 0.54.

DOI
10.1103/physreva.65.062710

Related papers

Photoassociation spectroscopy of Rb287(5s1∕2+5p1∕2)0u+ long-range molecular states: Coupling with the (5s1∕2+5p3∕2)0u+ series analyzed using the Lu-Fano approach

Haikel Jelassi, B. Viaris de Lesegno, Laurence Pruvost

We report on photoassociation of cold $^{87}\mathrm{Rb}$ atoms providing the spectroscopy of $(5{s}_{1∕2}+5{p}_{1∕2}){0}_{u}^{+}$ long-range molecular states, in the energy range of [$\ensuremath{-}12.5$, $\ensuremath{-}0.7\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$] below the dissociation limit. A Lu-Fano approach coupled to the LeRoy-Bernstein formula is used to analyze the data. The Lu-Fano graph exhibits the coupling of the molecular series with the $(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}$ one, which is due to spin effects in the molecule. A two-channel model involving an improved LeRoy-Bernstein formula allows us to characterize the molecular series, to localize $(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}$ levels, to evaluate the coupling, and to predict the energy and width of the first predissociated level of $(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}$ series. An experimental spectrum confirms the prediction.

Physical Review A•Jul 28, 2006•22 citations

Theoretical treatment of channel mixing in excited Rb2 and Cs2 ultracold molecules: Perturbations in 0u+ photoassociation and fluorescence spectra

Viatcheslav Kokoouline, Olivier Dulieu, Françoise Masnou-Seeuws

The mapped Fourier grid method, using a coordinate adapted to the local de Broglie wavelength associated to the vibrational motion in a molecule, and recently developed by Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)], is used to compute the perturbed binding energies and rotational constants of the ${\mathrm{Cs}}_{2}{0}_{u}^{+}(6s+6p{}^{2}{P}_{1/2,3/2})$ photoassociation spectrum below the lower dissociation limit. The results are shown to be very sensitive to the molecular potential curves and spin-orbit coupling. In the case of ${\mathrm{Rb}}_{2}{0}_{u}^{+}(5s+5p{}^{2}{P}_{1/2,3/2}),$ a strong isotopic effect is also predicted. The results can be interpreted in the framework of generalized two-channel quantum defect theory, and generalized Lu-Fano plots are presented. This work suggests that parameters could easily be fitted to experimental spectra, eliminating the difficulties caused by limitations in the accuracy of the short-range molecular potentials.

Physical Review A•Jul 17, 2000•48 citations

Mapped Fourier methods for long-range molecules: Application to perturbations in the Rb2(0u+) photoassociation spectrum

Viatcheslav Kokoouline, Olivier Dulieu, Ronnie Kosloff +1 more

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.

The Journal of Chemical Physics•May 22, 1999•237 citations

Photoassociation spectroscopy of Rb287 (5s1∕2+5p1∕2)0g− long-range molecular states: Analysis by Lu-Fano graph and improved LeRoy-Bernstein formula

Haikel Jelassi, B. Viaris de Lesegno, Laurence Pruvost

We report on cold atom photoassociation of $^{87}\mathrm{Rb}$ giving spectroscopy data of the $(5{s}_{1∕2}+5{p}_{1∕2}){0}_{g}^{\ensuremath{-}}$ long-range molecular states in the asymptotic range of [$\ensuremath{-}12.5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, $\ensuremath{-}1.5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$] below the dissociation limit. Using a Lu-Fano approach to analyze the data, we show that an improved LeRoy-Bernstein model has to be applied. This approach lets us determine the phase shift of the wave function at the dissociation limit of the ${0}_{g}^{\ensuremath{-}}$ series.

Physical Review A•Mar 2, 2006•35 citations

Formation of ultracold molecules by photoassociation: theoretical developments

Olivier Dulieu, Françoise Masnou-Seeuws

In recent years several groups of researchers have succeeded in making samples of cold molecules, at temperatures below 1 K, and of ultracold molecules, at temperatures below 1 mK. We concentrate on the formation of Cs2 dimers. Starting with laser-cooled atoms, photoassociation forms molecules in an excited electronic state. Various mechanisms are presented for stabilizing these molecules by spontaneous emission into a bound level of the ground electronic state. The design of new formation schemes requires precise knowledge of molecular potential curves that is well beyond the accuracy of ab initio calculations. We show that analytical long-range potentials can be fitted on photoassociation spectra and yield, through the determination of the C3 long-range coefficient, a value of the radiative lifetime of the 6P3/2 cesium level with an unprecedented accuracy. For short-range potentials it is possible to avoid explicit calculations by using asymptotic methods that generalize to long-range molecules the quantum-defect concepts developed for Rydberg atoms. Considering two coupled channels, we show how generalized Lu–Fano plots can extract precise information from experimental spectra.

Journal of the Optical Society of America B•May 1, 2003•18 citations

Reanalysis of the photoassociation spectrum of133Cs2(6P3/2) 1gstate

Jie Ma, Yuqing Li, Jizhou Wu +5 more

Reanalysis of the photoassociation spectrum of the weakly binding (6S1/2 + 6P3/2) 1g133Cs2 levels, reported in the previous study [J. Mol. Spectro. 255 (2009) 106], is performed by using a Lu—Fano graph coupled to the improved LeRoy—Bernstein formula including two additional modified terms. A more accurate coefficient (c3) is obtained for the leading long-range potential (−c3/R3) of a diatomic molecule.

Chinese Physics B•Aug 1, 2013•0 citations
Recently, the method of Lu-Fano plots was extended to potentials with general R\ensuremath−n{R}^{\ensuremath{-}n}R\ensuremath−n asymptotic behavior. The aim of this paper is to discuss the efficiency of this method for the interpretation of experimental vibrational spectra of long-range diatomic molecules when two channels are coupled. A Lu-Fano analysis is implemented on experimental data for the Cs20u+(6S+6P1/2,3/2){\mathrm{Cs}}_{2}{0}_{u}^{+}{(6S+6P}_{1/2,3/2})Cs2​0u+​(6S+6P1/2,3/2​) photoassociation spectra below the 6S+P1/2{6S+P}_{1/2}6S+P1/2​ and 6S+P3/2{6S+P}_{3/2}6S+P3/2​ dissociation limits. The parameters are fitted on level energies and predissociation widths, giving information about the asymptotic coefficients C3{C}_{3}C3​ for both channels and about a coupling parameter which determines the variation of predissociation widths as a function of detuning. This parameter can be extrapolated above the 6S+P3/2{6S+P}_{3/2}6S+P3/2​ threshold to yield the fine-structure transition cross section between the two channels. The probability for such a transition in a model where hyperfine structure effects are neglected is found to be 0.54.
We report on photoassociation of cold 87Rb^{87}\mathrm{Rb}87Rb atoms providing the spectroscopy of (5s1∕2+5p1∕2)0u+(5{s}_{1∕2}+5{p}_{1∕2}){0}_{u}^{+}(5s1∕2​+5p1∕2​)0u+​ long-range molecular states, in the energy range of [$\ensuremath{-}12.5$, $\ensuremath{-}0.7\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$] below the dissociation limit. A Lu-Fano approach coupled to the LeRoy-Bernstein formula is used to analyze the data. The Lu-Fano graph exhibits the coupling of the molecular series with the (5s1∕2+5p3∕2)0u+(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}(5s1∕2​+5p3∕2​)0u+​ one, which is due to spin effects in the molecule. A two-channel model involving an improved LeRoy-Bernstein formula allows us to characterize the molecular series, to localize (5s1∕2+5p3∕2)0u+(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}(5s1∕2​+5p3∕2​)0u+​ levels, to evaluate the coupling, and to predict the energy and width of the first predissociated level of (5s1∕2+5p3∕2)0u+(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}(5s1∕2​+5p3∕2​)0u+​ series. An experimental spectrum confirms the prediction.
The mapped Fourier grid method, using a coordinate adapted to the local de Broglie wavelength associated to the vibrational motion in a molecule, and recently developed by Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)], is used to compute the perturbed binding energies and rotational constants of the Cs20u+(6s+6p2P1/2,3/2){\mathrm{Cs}}_{2}{0}_{u}^{+}(6s+6p{}^{2}{P}_{1/2,3/2})Cs2​0u+​(6s+6p2P1/2,3/2​) photoassociation spectrum below the lower dissociation limit. The results are shown to be very sensitive to the molecular potential curves and spin-orbit coupling. In the case of Rb20u+(5s+5p2P1/2,3/2),{\mathrm{Rb}}_{2}{0}_{u}^{+}(5s+5p{}^{2}{P}_{1/2,3/2}),Rb2​0u+​(5s+5p2P1/2,3/2​), a strong isotopic effect is also predicted. The results can be interpreted in the framework of generalized two-channel quantum defect theory, and generalized Lu-Fano plots are presented. This work suggests that parameters could easily be fitted to experimental spectra, eliminating the difficulties caused by limitations in the accuracy of the short-range molecular potentials.
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.
We report on cold atom photoassociation of 87Rb^{87}\mathrm{Rb}87Rb giving spectroscopy data of the $(5{s}_{1∕2}+5{p}_{1∕2}){0}_{g}^{\ensuremath{-}}$ long-range molecular states in the asymptotic range of [$\ensuremath{-}12.5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, $\ensuremath{-}1.5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$] below the dissociation limit. Using a Lu-Fano approach to analyze the data, we show that an improved LeRoy-Bernstein model has to be applied. This approach lets us determine the phase shift of the wave function at the dissociation limit of the ${0}_{g}^{\ensuremath{-}}$ series.
In recent years several groups of researchers have succeeded in making samples of cold molecules, at temperatures below 1 K, and of ultracold molecules, at temperatures below 1 mK. We concentrate on the formation of Cs2 dimers. Starting with laser-cooled atoms, photoassociation forms molecules in an excited electronic state. Various mechanisms are presented for stabilizing these molecules by spontaneous emission into a bound level of the ground electronic state. The design of new formation schemes requires precise knowledge of molecular potential curves that is well beyond the accuracy of ab initio calculations. We show that analytical long-range potentials can be fitted on photoassociation spectra and yield, through the determination of the C3 long-range coefficient, a value of the radiative lifetime of the 6P3/2 cesium level with an unprecedented accuracy. For short-range potentials it is possible to avoid explicit calculations by using asymptotic methods that generalize to long-range molecules the quantum-defect concepts developed for Rydberg atoms. Considering two coupled channels, we show how generalized Lu–Fano plots can extract precise information from experimental spectra.