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Physical Review A

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

Published Jul 17, 2000• 48 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.62.022504

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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 ${\mathrm{Rb}}_{2}$ and ${\mathrm{Cs}}_{2}{0}_{u}^{+}{(ns+np}^{2}{P}_{3/2})$ spectra, where $n=5,6.$ 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 ${}^{87}{\mathrm{Rb}}_{2}$ is reproduced. A strong isotopic effect is found for the rubidium dimer, the lifetimes of ${}^{85}{\mathrm{Rb}}_{2}$ and ${}^{87}{\mathrm{Rb}}_{2}$ 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 ${P}_{1/2}$ dissociation limit. Excellent agreement is obtained with the numerical results, suggesting the possibility of fitting to experimental spectra.

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We report on new observations of the photoassociation spectroscopy of ultracold cesium molecules using a highly sensitive detection technique and a combined analysis with all observed electronic states. The technique is achieved by directly modulating the frequency of the trapping lasers of a magneto-optical trap. New observations of the Cs2 0g(-), 0u(+), and 1g states at the asymptotes 6S1/2 + 6P1/2 and 6S1/2 + 6P3/2 are reported. The spectral range is extended to the red detuning of 112 cm(-1) below the 6S1/2 + 6P3/2 dissociation limit. Dozens of vibrational levels of the ultracold Cs2 0g(-), 0u(+), and 1g states are observed for the first time. The available experimental binding energies of these states are analyzed simultaneously in a framework of the generalized LeRoy-Bernstein theory and the almost degenerate perturbation theory by Marinescu and Dalgarno [Phys. Rev. A: At., Mol., Opt. Phys. 52, 311 (1995)]. The unique atomic-related parameter c3 governing the dispersion forces of all the molecular states is estimated as (10.29 ± 0.05) a.u.

The Journal of Chemical Physics•Dec 28, 2014•23 citations
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.
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.
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.
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 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.
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.
We report on new observations of the photoassociation spectroscopy of ultracold cesium molecules using a highly sensitive detection technique and a combined analysis with all observed electronic states. The technique is achieved by directly modulating the frequency of the trapping lasers of a magneto-optical trap. New observations of the Cs2 0g(-), 0u(+), and 1g states at the asymptotes 6S1/2 + 6P1/2 and 6S1/2 + 6P3/2 are reported. The spectral range is extended to the red detuning of 112 cm(-1) below the 6S1/2 + 6P3/2 dissociation limit. Dozens of vibrational levels of the ultracold Cs2 0g(-), 0u(+), and 1g states are observed for the first time. The available experimental binding energies of these states are analyzed simultaneously in a framework of the generalized LeRoy-Bernstein theory and the almost degenerate perturbation theory by Marinescu and Dalgarno [Phys. Rev. A: At., Mol., Opt. Phys. 52, 311 (1995)]. The unique atomic-related parameter c3 governing the dispersion forces of all the molecular states is estimated as (10.29 ± 0.05) a.u.