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Physical Review A

Spectroscopic data, spin-orbit functions, and revised analysis of strong perturbative interactions for the A 1Σ+ and b 3Π states of RbCs

O. Docenko, M. Tamanis, R. Ferber, T. H. Bergeman, Svetlana Kotochigova, A. V. Stolyarov, Andreia F. Nogueira, Carlos Eduardo Fellows

Published Apr 16, 2010• 50 citations
Publisher

Abstract

The current interest in producing ultracold RbCs molecules by optical excitation from weakly bound Feshbach resonances and stimulated decay to the absolute ground state requires detailed analyses of the intermediate excited states. In this study, we present two sets of experimental Fourier-transform spectroscopic data of the $A{ }^{1}{\ensuremath{\Sigma}}^{+}$-$b{ }^{3}\ensuremath{\Pi}$ complex. The $A$-$b$ mixed vibrational levels are the most likely candidates to be intermediates in the molecular formation. The more recent and more accurate data set is from mixed $A$-$b\ensuremath{\rightarrow}X$ transitions, while the second is derived in large part from $(4){ }^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}A$-$b$ emission and extends to higher $A$-$b$ energy levels. From a detailed analysis of the spectroscopic data we obtain term values which allow one to construct potentials and spin-orbit functions. Vibrational numbering of the $A$ state has been raised by one quantum over a previous report [T. Bergeman et al., Phys. Rev. A 67, 050501 (2003)] while the numbering of the $b$ state is established with a considerable degree of certainty with help of data on the $^{85}\mathrm{Rb}$$^{133}\mathrm{Cs}$ and $^{87}\mathrm{Rb}$$^{133}\mathrm{Cs}$ isotopomers. In addition, we have performed calculations of spin-orbit functions by two distinct methods. The fitted spin-orbit coupling matrix element between the two ${\ensuremath{\Omega}}^{p}={0}^{+}$ states, $A{ }^{1}{\ensuremath{\Sigma}}^{+}$ and $b{ }^{3}{\ensuremath{\Pi}}_{0+}$, happens to agree rather well with the results from both of these methods, while for the diagonal $b{ }^{3}\ensuremath{\Pi}$ state spin-orbit function, the fitted function agrees fairly well with that obtained by the other method.

DOI
10.1103/physreva.81.042511

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A comprehensive study of the electronic states at the $4s+5s$ asymptote in $\mathrm{KRb}$ is presented. Abundant spectroscopic data on the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state were collected by Fourier-transform spectroscopy, which allows one to determine an accurate experimental potential energy curve up to $14.8\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. The existing data set [C. Amiot et al., J. Chem. Phys. 112, 7068 (2000)] on the ground state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ was extended by several additional levels lying close to the atomic asymptote. In a coupled channels fitting routine complete molecular potentials for both electronic states were fitted. Along with the line frequencies of the molecular transitions, recently published positions of Feshbach resonances in $^{40}\mathrm{K}$ and $^{87}\mathrm{Rb}$ mixtures [F. Ferlaino et al., Phys. Rev. A 74, 039903 (2006)] were included in the fit. This makes the derived potential curves capable for an accurate description of observed cold collision features so far. Predictions of scattering lengths and Feshbach resonances in other isotopic combinations are reported.

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Production and State-Selective Detection of Ultracold RbCs Molecules

Andrew J. Kerman, Jeremy Sage, Sunil Sainis +2 more

Using resonance-enhanced two-photon ionization, we detect ultracold, metastable RbCs molecules formed in their lowest triplet state $a\text{ }^{3}\ensuremath{\Sigma}^{+}$ via photoassociation in a laser-cooled mixture of $^{85}\mathrm{Rb}$ and $^{133}\mathrm{Cs}$ atoms. We obtain extensive bound-bound excitation spectra of these molecules, which provide detailed information about their vibrational distribution, as well as spectroscopic data on several RbCs molecular states including $a\text{ }^{3}\ensuremath{\Sigma}^{+}$, $(2)\text{ }^{3}\ensuremath{\Sigma}^{+}$, and $(1)\text{ }^{1}\ensuremath{\Pi}$. Analysis of this data allows us to predict strong transitions from observed levels to the absolute vibronic ground state of RbCs, potentially allowing the production of stable, ultracold polar molecules at rates in excess of ${10}^{6}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$.

arXiv:physics/0402116•Physical Review Letters•Apr 12, 2004•192 citations
The current interest in producing ultracold RbCs molecules by optical excitation from weakly bound Feshbach resonances and stimulated decay to the absolute ground state requires detailed analyses of the intermediate excited states. In this study, we present two sets of experimental Fourier-transform spectroscopic data of the A1\ensuremathΣ+A{ }^{1}{\ensuremath{\Sigma}}^{+}A1\ensuremathΣ+-b3\ensuremathΠb{ }^{3}\ensuremath{\Pi}b3\ensuremathΠ complex. The AAA-bbb mixed vibrational levels are the most likely candidates to be intermediates in the molecular formation. The more recent and more accurate data set is from mixed AAA-b\ensuremath→Xb\ensuremath{\rightarrow}Xb\ensuremath→X transitions, while the second is derived in large part from (4)1\ensuremathΣ+\ensuremath→A(4){ }^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}A(4)1\ensuremathΣ+\ensuremath→A-bbb emission and extends to higher AAA-bbb energy levels. From a detailed analysis of the spectroscopic data we obtain term values which allow one to construct potentials and spin-orbit functions. Vibrational numbering of the AAA state has been raised by one quantum over a previous report [T. Bergeman et al., Phys. Rev. A 67, 050501 (2003)] while the numbering of the bbb state is established with a considerable degree of certainty with help of data on the ^{85}\mathrm{Rb}$$^{133}\mathrm{Cs} and ^{87}\mathrm{Rb}$$^{133}\mathrm{Cs} isotopomers. In addition, we have performed calculations of spin-orbit functions by two distinct methods. The fitted spin-orbit coupling matrix element between the two \ensuremathΩp=0+{\ensuremath{\Omega}}^{p}={0}^{+}\ensuremathΩp=0+ states, A1\ensuremathΣ+A{ }^{1}{\ensuremath{\Sigma}}^{+}A1\ensuremathΣ+ and b3\ensuremathΠ0+b{ }^{3}{\ensuremath{\Pi}}_{0+}b3\ensuremathΠ0+​, happens to agree rather well with the results from both of these methods, while for the diagonal b3\ensuremathΠb{ }^{3}\ensuremath{\Pi}b3\ensuremathΠ state spin-orbit function, the fitted function agrees fairly well with that obtained by the other method.
The article presents a study of the strongly spin-orbit coupled singlet A(1)Σ(+) and triplet b(3)Π states of the RbCs molecule, which provide an efficient optical path to transfer ultracold molecules to their rovibrational ground state. Fourier-transform A(1)Σ(+) - b(3)Π → X(1)Σ(+) and (4)(1)Σ(+) → A(1)Σ(+) - b(3)Π laser-induced fluorescence (LIF) spectra were recorded for the natural mixture of the (85)Rb(133)Cs and (87)Rb(133)Cs isotopologues produced in a heat pipe oven. Overall 8730 rovibronic term values of A(1)Σ(+) and b(3)Π states were determined with an uncertainty of 0.01 cm(-1) in the energy range [9012, 14087] cm(-1), covering rotational quantum numbers J ∈ [6, 324]. An energy-based deperturbation analysis performed in the framework of the four A(1)Σ(+) - b(3)Π(Ω = 0, 1, 2) coupled-channels approach reproduces 97% of the experimental term values of both isotopologues with a standard deviation of 0.0036 cm(-1). The reliability of the deperturbed mass-invariant potentials and spin-orbit coupling functions of the interacting A(1)Σ(+) and b(3)Π states is additionally proved by a good reproduction of the A - b → X and (4)(1)Σ(+) → A - b relative intensity distributions. The achieved accuracy of the A - b complex description allowed us to use the latter to assign the observed (5)(1)Σ(+) → A - b and (3)(1)Π → A - b transitions. As is demonstrated, LIF to the A - b complex becomes as informative as to the ground X(1)Σ(+) state, which is confirmed by comparing the results of (4)(1)Σ(+) state analysis based on (4)(1)Σ(+) → A - b LIF with the data from V. Zuters et al. [Phys. Rev. A 87, 022504 (2013)] based on (4)(1)Σ(+) → X LIF.
We spectroscopically investigate the hyperfine, rotational, and Zeeman structure of the vibrational levels ${v}^{\ensuremath{'}}=0,7,13$ within the electronically excited $c{\phantom{\rule{0.222222em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ state of 87Rb2^{87}\mathrm{Rb}_{2}87Rb2​ for magnetic fields of up to 1000G1000\phantom{\rule{0.28em}{0ex}}\text{G}1000G. As spectroscopic methods we use short-range photoassociation of ultracold Rb atoms as well as photoexcitation of ultracold molecules which have been previously prepared in several well-defined quantum states of the $a{\phantom{\rule{0.222222em}{0ex}}}^{3}\mathrm{\ensuremath{\Sigma}}{}_{u}^{+}$ potential. As a by-product, we present optical two-photon transfer of weakly bound Feshbach molecules into $a{\phantom{\rule{0.222222em}{0ex}}}^{3}\mathrm{\ensuremath{\Sigma}}{}_{u}^{+}$, v=0v=0v=0 levels featuring different nuclear spin quantum numbers. A simple model reproduces well the molecular level structures of the $c{\phantom{\rule{0.222222em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ vibrational states and provides a consistent assignment of the measured resonance lines. Furthermore, the model can be used to predict the relative transition strengths of the lines. From fits to the data we extract for each vibrational level the rotational constant, the effective spin-spin interaction constant, as well as the Fermi contact parameter and the anisotropic hyperfine constant. In an alternative approach, we perform coupled-channel calculations where we fit the relevant potential energy curves, spin-orbit interactions, and hyperfine functions. The calculations reproduce the measured hyperfine level term frequencies with an average uncertainty of $\ifmmode\pm\else\textpm\fi{}9\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, similar as for the simple model. From these fits we obtain a section of the potential energy curve for the $c{\phantom{\rule{0.222222em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ state which can be used for predicting the level structure for the vibrational manifold ${v}^{\ensuremath{'}}=0$ to 13 of this electronic state.
We performed high-resolution Fourier-transform spectroscopy measurements and direct-potential-fit of the shelflike RbCs $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ state. Overall, 2317 rovibronic ${v}^{\ensuremath{'}},{J}^{\ensuremath{'}}$ term values with ${v}^{\ensuremath{'}}\ensuremath{\in}[3,88]$, ${J}^{\ensuremath{'}}\ensuremath{\in}[7,276]$ were obtained with accuracy 0.01 cm${}^{\ensuremath{-}1}$ from the $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+},a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ laser-induced fluorescence (LIF) spectra. The mass-invariant potential energy curve constructed by means of the Chebyshev polynomial expansion reproduced the experimental term values of both 85{}^{85}85Rb133{\phantom{\rule{0.16em}{0ex}}}^{133}133Cs and 87{}^{87}87Rb133{\phantom{\rule{0.16em}{0ex}}}^{133}133Cs isotopologues with a standard deviation of 0.005 cm${}^{\ensuremath{-}1}$. We simulated the optical cycle $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+},a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}\ensuremath{'}},{J}^{\ensuremath{'}\ensuremath{'}}=0)\ensuremath{\rightarrow}(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}},{J}^{\ensuremath{'}}=1)\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}\ensuremath{'}}=0,{J}^{\ensuremath{'}\ensuremath{'}}=0)$ appropriate to transfer translationally ultracold RbCs molecules into their absolute ground state from the weakly bound rovibronic levels of both singlet $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and triplet $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ ground states. The optimal transfer via the intermediate $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ state with ${v}^{\ensuremath{'}}=58,60$, and 61 for 85{}^{85}85Rb133{\phantom{\rule{0.16em}{0ex}}}^{133}133Cs as well as ${v}^{\ensuremath{'}}=59$ and 61 for 87{}^{87}87Rb133{\phantom{\rule{0.16em}{0ex}}}^{133}133Cs was predicted. The required spin-allowed $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{-}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and spin-forbidden $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{-}a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ dipole transition moments were obtained within the framework of ab initio quasirelativistic calculations. The predicted $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+},a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ transition probabilities were consistent with the experimental relative intensity distributions for several $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}})\ensuremath{\rightarrow}X,a({v}^{\ensuremath{'}\ensuremath{'}})$ LIF progressions.
High resolution Fourier transform spectra (FTS) of laser induced fluorescence (LIF) of $C\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+};D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}\ensuremath{\rightarrow}A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ and $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ transitions in Na85Rb{\mathrm{Na}}^{85}\mathrm{Rb}Na85Rb and Na87Rb{\mathrm{Na}}^{87}\mathrm{Rb}Na87Rb were obtained. An analysis of the direct LIF spectra together with the rotational relaxation satellites provided highly accurate rovibronic term values for $(4\ensuremath{\leqslant}J\ensuremath{\leqslant}163)$ of the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ complex, covering about 1950 mostly singlet levels $0\ensuremath{\leqslant}{v}_{A}\ensuremath{\leqslant}49$ and a considerable number (>360)(>360)(>360) of the predominantly triplet $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0,1}$ sublevels. The direct deperturbation analysis of the singlet-triplet A−−bA--bA−−b complex was performed by means of the inverted channel-coupling approach with Hund's coupling case a\mathbf{a}a basis functions. The electronic matrix elements of the model $4\ifmmode\times\else\texttimes\fi{}4$ Hamiltonian were defined as piecewise analytical functions of the internuclear distance. Besides the Born-Oppenheimer potential energy curves of the mutually perturbed states and the off-diagonal spin-orbit (SO) A−−bA--bA−−b coupling function, the SO splitting of the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ state was determined due to the pronounced electronic-rotation interaction between the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0}$ and $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{1}$ components observed for high JJJ levels. Overall, 24 mass-invariant fitting parameters have been required to reproduce about 2300 experimental term values of both isotopomers with a standard deviation of $0.012\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is consistent with the uncertainty of the FTS experiment. An analytical mapping procedure based on a reduced variable representation of the radial coordinate was used to diminish the computational effort for the uniform finite-difference grid solution of the coupled-channel equations. The derived nonadiabatic A−−bA--bA−−b wave functions were used to evaluate the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}--D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$, $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$, $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ rovibronic transition probabilities. The relative intensity distributions predicted for the $D\ensuremath{\rightarrow}A--b$ and $A--b\ensuremath{\rightarrow}X$ LIF progressions agree with their experimental counterparts within the accuracy of the measurements. The calculated A−−b−−aA--b--aA−−b−−a, XXX transition probabilities were applied for simulation of the stimulated Raman $a\ensuremath{\rightarrow}A--b\ensuremath{\rightarrow}X$ processes, which can lead to efficient formation of ultracold NaRb molecules in the ground level vX=0{v}_{X}=0vX​=0; JX=0{J}_{X}=0JX​=0.
A comprehensive study of the electronic states at the 4s+5s4s+5s4s+5s asymptote in KRb\mathrm{KRb}KRb is presented. Abundant spectroscopic data on the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state were collected by Fourier-transform spectroscopy, which allows one to determine an accurate experimental potential energy curve up to 14.8A˚14.8\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}14.8A˚. The existing data set [C. Amiot et al., J. Chem. Phys. 112, 7068 (2000)] on the ground state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ was extended by several additional levels lying close to the atomic asymptote. In a coupled channels fitting routine complete molecular potentials for both electronic states were fitted. Along with the line frequencies of the molecular transitions, recently published positions of Feshbach resonances in 40K^{40}\mathrm{K}40K and 87Rb^{87}\mathrm{Rb}87Rb mixtures [F. Ferlaino et al., Phys. Rev. A 74, 039903 (2006)] were included in the fit. This makes the derived potential curves capable for an accurate description of observed cold collision features so far. Predictions of scattering lengths and Feshbach resonances in other isotopic combinations are reported.
Using resonance-enhanced two-photon ionization, we detect ultracold, metastable RbCs molecules formed in their lowest triplet state $a\text{ }^{3}\ensuremath{\Sigma}^{+}$ via photoassociation in a laser-cooled mixture of 85Rb^{85}\mathrm{Rb}85Rb and 133Cs^{133}\mathrm{Cs}133Cs atoms. We obtain extensive bound-bound excitation spectra of these molecules, which provide detailed information about their vibrational distribution, as well as spectroscopic data on several RbCs molecular states including $a\text{ }^{3}\ensuremath{\Sigma}^{+}$, $(2)\text{ }^{3}\ensuremath{\Sigma}^{+}$, and $(1)\text{ }^{1}\ensuremath{\Pi}$. Analysis of this data allows us to predict strong transitions from observed levels to the absolute vibronic ground state of RbCs, potentially allowing the production of stable, ultracold polar molecules at rates in excess of ${10}^{6}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$.