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arXiv:1608.00225 · Physical Review A

Twofold diabatization of the KRb (1–2)Π1 complex in the framework ofab initioand deperturbation approaches

S. V. Kozlov, E. A. Pazyuk, A. V. Stolyarov

Published Oct 14, 2016• 9 citations
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Abstract

We performed a diabatization of the mutually perturbed $1^{1}\mathrm{\ensuremath{\Pi}}$ and $2^{1}\mathrm{\ensuremath{\Pi}}$ states of KRb based on both electronic structure calculation and direct coupled-channel deperturbation analysis of experimental energies. The potential energy curves (PECs) of the diabatic states and their scalar coupling were constructed from the ab initio adiabatic PECs by analytically integrating the radial $\ensuremath{\langle}{\ensuremath{\psi}}_{1}^{ad}|\ensuremath{\partial}/\ensuremath{\partial}R|{\ensuremath{\psi}}_{2}^{ad}\ensuremath{\rangle}$ matrix element obtained by a finite-difference method. The diabatic potentials and electronic coupling function were refined by the least squares fitting of the rovibronic term values of the $1{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}\ensuremath{\sim}2{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ complex. The empirical PECs combined with the coupling function as well as the diabatized spin-orbit coupling and transition dipole matrix elements are crucial to discovering efficient photoassociation pathways for production of ultracold ground-state KRb molecules.

DOI
10.1103/physreva.94.042510

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We performed a diabatization of the mutually perturbed 11\ensuremathΠ1^{1}\mathrm{\ensuremath{\Pi}}11\ensuremathΠ and 21\ensuremathΠ2^{1}\mathrm{\ensuremath{\Pi}}21\ensuremathΠ states of KRb based on both electronic structure calculation and direct coupled-channel deperturbation analysis of experimental energies. The potential energy curves (PECs) of the diabatic states and their scalar coupling were constructed from the ab initio adiabatic PECs by analytically integrating the radial \ensuremath⟨\ensuremathψ1ad∣\ensuremath∂/\ensuremath∂R∣\ensuremathψ2ad\ensuremath⟩\ensuremath{\langle}{\ensuremath{\psi}}_{1}^{ad}|\ensuremath{\partial}/\ensuremath{\partial}R|{\ensuremath{\psi}}_{2}^{ad}\ensuremath{\rangle}\ensuremath⟨\ensuremathψ1ad​∣\ensuremath∂/\ensuremath∂R∣\ensuremathψ2ad​\ensuremath⟩ matrix element obtained by a finite-difference method. The diabatic potentials and electronic coupling function were refined by the least squares fitting of the rovibronic term values of the 11\ensuremathΠ\ensuremath∼21\ensuremathΠ1{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}\ensuremath{\sim}2{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}11\ensuremathΠ\ensuremath∼21\ensuremathΠ complex. The empirical PECs combined with the coupling function as well as the diabatized spin-orbit coupling and transition dipole matrix elements are crucial to discovering efficient photoassociation pathways for production of ultracold ground-state KRb molecules.
We present a deperturbation analysis of the spin-orbit-coupled $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ and $b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{{0}^{+}}$ states of LiRb based on the rovibrational energy levels observed previously by photoassociation spectroscopy in the bosonic 7Li85Rb^{7}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}^{85}\mathrm{Rb}7Li85Rb molecule. Using the genetic algorithm (GA), we optimize the pointwise ab initio potential energy curves of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state and the $b{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}}$ state based on spectroscopic data. Then we fit the pointwise potentials obtained by the GA and the ab initio spin-orbit-coupling term with the expanded Morse oscillator (EMO) function. Finally, we optimize the parameters of the EMO function using the sequential least-squares quadratic programming algorithm with the guidance of the experimental data and pointwise potentials obtained by the GA. From the fitted results, we calculate the transition dipole moment matrix elements for transitions from the rovibrational levels of the coupled $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}\text{--}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{{0}^{+}}$ state to the Feshbach state and the absolute rovibrational ground state for the fermionic 6Li87Rb^{6}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}^{87}\mathrm{Rb}6Li87Rb molecule. Based on the calculated transition dipole moment matrix elements, several levels of the coupled $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}\text{--}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{{0}^{+}}$ state are predicted to be suitable as the intermediate state for stimulated Raman adiabatic passage transfer from the Feshbach state to the absolute rovibrational ground state. In addition, we also provide a similar estimation for the $B{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}\text{--}c{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{1}^{+}\text{--}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{1}$ state based on available ab initio interaction potentials.
In response to the need to investigate and create a reliable dataset of spin-orbit coupling matrix elements, we have extended our recent work in which we presented results for the potential energy curves and permanent and transition dipole moments in KRb. This paper presents 190 allowed spin-orbit couplings between 30 singlet and triplet Σ + , Π , and Δ electronic states of the KRb molecule. These results are crucial for accurately interpreting spectroscopic data, especially for the deperturbation analysis challenges. 23 tables and 21 graphs present the L S X , L S Y , and L S Z components of reported spin-orbit couplings. Using the MOLPRO code, we performed MRCI calculations using the large-core pseudopotentials and core polarization potentials with reoptimized cutoff parameters. The spin-orbit parameters of the potassium pseudopotential were deduced and optimized from scratch. The Gaussian basis sets used in our calculations were appropriately selected, augmented, and optimized. We compare some of our data with available theoretical and experimental results.
Numerical simulation of the effect of intramolecular electrostatic interactions on redistribution of relative intensities in the vibrational structure of (1 ~ 2) 1 Π–X 1 Σ + rotationally resolved transitions of the KRb molecule is performed within the precision nonadiabatic model of coupled vibrational channels. It is established that mutual perturbation of electronically excited states modifies in a nontrivial way a nodal structure of nonadiabatic wavefunction of the (1 ~ 2) 1 Π complex, which is possible to use for rising efficiency of twostep laser synthesis and stabilization of ultracold ensembles of KRb molecules in the ground electronic state.
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.
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