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Spectroscopic studies of the (4)1Σ+ state of RbCs and modeling of the optical cycle for ultracold X 1Σ+(v=0,J=0) molecule production

Valdis Zuters, O. Docenko, M. Tamanis +4 more

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 ${}^{85}$Rb${\phantom{\rule{0.16em}{0ex}}}^{133}$Cs and ${}^{87}$Rb${\phantom{\rule{0.16em}{0ex}}}^{133}$Cs 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 ${}^{85}$Rb${\phantom{\rule{0.16em}{0ex}}}^{133}$Cs as well as ${v}^{\ensuremath{'}}=59$ and 61 for ${}^{87}$Rb${\phantom{\rule{0.16em}{0ex}}}^{133}$Cs 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.

Physical Review AFeb 13, 201311 citations

Deperturbation treatment of the AΣ+1–bΠ3 complex of NaRb and prospects for ultracold molecule formation in XΣ+1(v=0;J=0)

O. Docenko, M. Tamanis, R. Ferber +6 more

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 ${\mathrm{Na}}^{85}\mathrm{Rb}$ and ${\mathrm{Na}}^{87}\mathrm{Rb}$ 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 $(>360)$ of the predominantly triplet $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0,1}$ sublevels. The direct deperturbation analysis of the singlet-triplet $A--b$ complex was performed by means of the inverted channel-coupling approach with Hund's coupling case $\mathbf{a}$ 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) $A--b$ 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 $J$ 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 $A--b$ 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 $A--b--a$, $X$ 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 ${v}_{X}=0$; ${J}_{X}=0$.

Physical Review AApr 13, 200751 citations

Radiative transition probabilities, lifetimes and dipole moments for the vibrational levels of the X 1Σ+ ground state of K8539Rb

Warren T. Zemke, William C. Stwalley

Using a potential energy curve (based primarily on the RKR potential of Amiot and Verges [J. Chem. Phys. 112, 7068 (2000)]) and a dipole moment function (based primarily on ab initio calculations of Park et al. [Chem. Phys. 257, 135 (2000)]), we have calculated radiative transition probabilities (Einstein A coefficients), radiative lifetimes, and dipole moment expectation values involving all vibrational levels (for several rotational quantum numbers) of the X1Sigma+ ground state of 39K85Rb. We observe that the radiative lifetimes of vibrationally excited levels, in particular, are approximately 10(3)-10(6) seconds, far too long to be significant in most ultracold experiments involving 39K85Rb or its isotopomers. Comparison with other molecules (LiH and HF) suggests that simple scaling (A approximately mu2nu3 approximately tau(-1)) will predict similarly long lifetimes for many other heteronuclear molecules, e.g., RbCs.

The Journal of Chemical PhysicsDec 22, 200332 citations

Formation of ultracold SrYb molecules in an optical lattice by photoassociation spectroscopy: theoretical prospects

Michał Tomza, Filip Pawłowski, Małgorzata Jeziorska +2 more

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the electronic ground state and the first fifteen excited singlet and triplet states. All the excited state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles and doubles framework and large basis-sets, while the ground state potential was computed using the coupled cluster method with single, double, and noniterative triple excitations. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. The electronic structure data were employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed b(3)Σ(+), a(3)Π, A(1)Π, and C(1)Π states with subsequent efficient stabilization into the v'' = 1 vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from v'' = 1 to v'' = 0. Alternatively, photoassociation and stabilization to v'' = 0 can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.

arXiv:1104.3015Physical Chemistry Chemical PhysicsJan 1, 201141 citations

Formation of deeply bound ultracold Sr 2 molecules by photoassociation near the 1S+3P1 intercombination line

Wojciech Skomorowski, Robert Moszyński, Christiane P. Koch

We predict feasibility of the photoassociative formation of Sr${}_{2}$ molecules in arbitrary vibrational levels of the electronic ground state based on state-of-the-art ab initio calculations. Key is the strong spin-orbit interaction between the $c\phantom{\rule{0.16em}{0ex}}$${}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Pi}}_{u}$, $A\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}$, and $B\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}$ states. It creates not only an effective dipole moment allowing free-to-bound transitions near the ${}^{1}\phantom{\rule{-0.16em}{0ex}}S+{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ intercombination line but also facilitates bound-to-bound transitions via resonantly coupled excited-state levels to deeply bound levels of the ground $X\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{g}^{+}$ potential, with ${v}^{\ensuremath{'}\ensuremath{'}}$ as low as ${v}^{\ensuremath{'}\ensuremath{'}}=6$. The spin-orbit interaction is responsible for both optical pathways. Therefore, those excited-state levels that have the largest bound-to-bound transition moments to deeply bound ground-state levels also exhibit a sufficient photoassociation probability, comparable to that of the lowest weakly bound excited-state level previously observed by Zelevinsky et al. [Phys. Rev. Lett. 96, 203201 (2006)]. Our study paves the way for an efficient photoassociative production of Sr${}_{2}$ molecules in ground-state levels suitable for experiments testing the electron-to-proton mass ratio.

arXiv:1203.4552Physical Review AApr 17, 201228 citations

Long-range coupling of X1Σ+ and a3Σ+ states of the atom pair K+Cs

R. Ferber, О. Nikolayeva, M. Tamanis +2 more

The K and Cs atom pair and its $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ electronic molecular states are studied by Fourier-transform spectroscopy with special emphasis on bound states close to the ground state asymptote $(4s)\text{K}+(6s)\text{Cs}$. Significant vibrational mixing due to hyperfine coupling was observed leading to improved potential energy curves for both states. The observed intensity pattern of the hyperfine structure for the last vibrational levels of $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ reveals deep insight into the multicomponent wave function of such levels with its influence for modeling the asymptotic behavior of the excited electronic states involved in the reported observations. Examples of derived properties of cold collisions are given and the importance of the present results for efficient production schemes for ultracold KCs is discussed.

Physical Review AJul 23, 201323 citations

Modeling of the X 1Σ+ , a 3Σ+→ E(4) 1Σ+→X 1Σ+(v=0,J=0) optical cycle for ultracold KCs molecule production

Abstract

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Modeling of the X 1Σ+ , a 3Σ+→ E(4) 1Σ+→X 1Σ+(v=0,J=0) optical cycle for ultracold KCs molecule production

Abstract

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