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Physical Review A

Photoassociation of cold calcium atoms through the AΣu+1(1D1+1S1),cΠu3(1P3+1S1) , and aΣu+3(1P3+1S1) states: Anab initiononadiabatic treatment

Béatrice Bussery‐Honvault, Jean–Michel Launay, Robert Moszyński

Published Jul 1, 2005• 16 citations
Publisher

Abstract

A nonadiabatic theory of photoassociation spectra and spontaneous emission processes in diatomic molecules is presented. This theory was applied in nearly exact nonadiabatic calculations of the photoassociation intensities to the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$, and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$ manifold of states for two colliding calcium atoms at ultralow temperatures and of the spontaneous emission coefficients to the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ electronic state. The calculations were based on most recent state-of-the-art ab initio results for the potential energy curves for the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ and excited $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$, and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$ states, for the spin-orbit and nonadiabatic coupling matrix elements, and for the transition dipole moment governing the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}\ensuremath{\leftarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ transitions. The computed photoassociation spectrum shows several transitions in the detuning frequency range up to $\ensuremath{-}3000\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. This frequency range corresponds to vibrational levels of the ${J}^{\ensuremath{'}}=1$ state of ${\mathrm{Ca}}_{2}$ that can mostly be assigned to the $c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}$ state. The two by far most intense lines at a detuning frequency around $\ensuremath{-}800\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ correspond to the last two bound rovibrational levels lying below the $1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S$ asymptote which are heavily mixed and can partly be assigned to the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ state. The corresponding lifetimes and Franck-Condon factors suggest that these levels can be detected experimentally and should show a relatively efficient spontaneous emission to the ground state. An analysis of the branching ratios describing the probability of the decay from these two levels to bound vibrational levels of the ground electronic state shows that the decay will end in the levels with the vibrational quantum number between 10 and 16 with a total probability well over 90%.

DOI
10.1103/physreva.72.012702

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Photoassociation spectroscopy

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Cambridge University Press eBooks•Dec 4, 2003•0 citations
A nonadiabatic theory of photoassociation spectra and spontaneous emission processes in diatomic molecules is presented. This theory was applied in nearly exact nonadiabatic calculations of the photoassociation intensities to the A1\ensuremathΣu+(11S+11D),c3\ensuremathΠu(13P+11S)A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)A1\ensuremathΣu+​(11S+11D),c3\ensuremathΠu​(13P+11S), and a3\ensuremathΣu+(13P+11S)a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)a3\ensuremathΣu+​(13P+11S) manifold of states for two colliding calcium atoms at ultralow temperatures and of the spontaneous emission coefficients to the ground X1\ensuremathΣg+X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}X1\ensuremathΣg+​ electronic state. The calculations were based on most recent state-of-the-art ab initio results for the potential energy curves for the ground X1\ensuremathΣg+X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}X1\ensuremathΣg+​ and excited A1\ensuremathΣu+(11S+11D),c3\ensuremathΠu(13P+11S)A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)A1\ensuremathΣu+​(11S+11D),c3\ensuremathΠu​(13P+11S), and a3\ensuremathΣu+(13P+11S)a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)a3\ensuremathΣu+​(13P+11S) states, for the spin-orbit and nonadiabatic coupling matrix elements, and for the transition dipole moment governing the A1\ensuremathΣu+\ensuremath←X1\ensuremathΣg+A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}\ensuremath{\leftarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}A1\ensuremathΣu+​\ensuremath←X1\ensuremathΣg+​ transitions. The computed photoassociation spectrum shows several transitions in the detuning frequency range up to \ensuremath−3000GHz\ensuremath{-}3000\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}\ensuremath−3000GHz. This frequency range corresponds to vibrational levels of the J\ensuremath′=1{J}^{\ensuremath{'}}=1J\ensuremath′=1 state of Ca2{\mathrm{Ca}}_{2}Ca2​ that can mostly be assigned to the c3\ensuremathΠuc\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}c3\ensuremathΠu​ state. The two by far most intense lines at a detuning frequency around \ensuremath−800GHz\ensuremath{-}800\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}\ensuremath−800GHz correspond to the last two bound rovibrational levels lying below the 13P+11S1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S13P+11S asymptote which are heavily mixed and can partly be assigned to the A1\ensuremathΣu+A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}A1\ensuremathΣu+​ state. The corresponding lifetimes and Franck-Condon factors suggest that these levels can be detected experimentally and should show a relatively efficient spontaneous emission to the ground state. An analysis of the branching ratios describing the probability of the decay from these two levels to bound vibrational levels of the ground electronic state shows that the decay will end in the levels with the vibrational quantum number between 10 and 16 with a total probability well over 90%.
State-of-the-art ab initio techniques have been applied to compute the potential-energy curves for the ground $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and excited ${}^{1}{\ensuremath{\Pi}}_{g}(4s3d)$ states of the calcium dimer in the Born-Oppenheimer approximation. The weakly bound ground state was calculated by symmetry-adapted perturbation theory, while the strongly bound excited state was computed using a combination of the linear-response theory within the coupled-cluster singles and doubles framework for the core-valence electronic correlation and of the full configuration interaction for the valence-valence correlation. The ground-state potential has been corrected by considering the relativistic terms resulting from the first-order many-electron Breit theory, and the retardation corrections. The magnetic electronic transition dipole moment governing the ${}^{1}{\ensuremath{\Pi}}_{g}{\ensuremath{\leftarrow}}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ transitions has been obtained as the first residue of the polarization propagator computed with the coupled-cluster method restricted to single and double excitations. The computed energies and transition moments have been analytically fitted and used in the dynamical calculations of the rovibrational energy levels, ground-state scattering length, photoassociation intensities at ultralow temperatures, and spontaneous emission coefficients from the ${}^{1}{\ensuremath{\Pi}}_{g}(4s3d)$ to the $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ state. The spectroscopic constants of the theoretical ground-state potential are in a good agreement with the experimental values derived from the Fourier-transform spectra [O. Allard et al., Eur. Phys. J. D (to be published)]. The theoretical s-wave scattering length for the ground state is a=44bohrs,a=44\mathrm{bohrs},a=44bohrs, suggesting that it should be possible to obtain a stable Bose-Einstein condensate of calcium atoms. Finally, the computed photoassociation intensities and spontaneous emission coefficients suggest that it should be possible to obtain cold calcium molecules by photoassociation of cold atoms to the first ${}^{1}{\ensuremath{\Pi}}_{g}$ state followed by a spontaneous emission to the ground state.
The properties of photoassociation (PA) spectra near the intercombination line (the weak transition between and states) of group II atoms are theoretically investigated. As an example, we have carried out a calculation for calcium atoms colliding at ultralow temperatures of , , and . Unlike in most current photoassociation spectroscopy, the Doppler effect can significantly affect the shape of the investigated lines. Spectra are obtained using and short-range potentials and long-range van der Waals and resonance dipole potentials. The similar van der Waals coefficients of ground and excited states cause the PA to differ greatly from those of strong, allowed transitions with resonant dipole interactions. The density of spectral lines is lower, the Condon points are at relatively short range, the reflection approximation for the Franck-Condon factors is not applicable, and the spontaneous decay to bound ground-state molecules is efficient. Finally, the possibility of efficient production of cold molecules is discussed.
In this work, a comprehensive theoretical investigation is carried out to explore the electronic and spectroscopic properties of selected diatomic molecular ions MgRb+ and SrRb+. Using high-level ab initio calculations based on a pseudopotential approach, along with large Gaussian basis sets and full valence configuration interaction (FCI), we accurately determine adiabatic potential energy curves, spectroscopic constants, transition dipole moments (TDMs), and permanent electric dipole moments (PDMs). To deepen our understanding of these systems, we calculate radiative lifetimes for vibrational levels in both ground and low-lying excited electronic states. This includes evaluating spontaneous and stimulated emission rates, as well as the effects of blackbody radiation. We also compute Franck–Condon factors and analyze photoassociation processes for both ions. Furthermore, to explore low-energy collisional dynamics, we investigate elastic scattering in the first excited states (21Σ+) describing the collision between the Ra atom and Mg+ or Sr+ ions. Our findings provide detailed insights into the theoretical electronic structure of these molecular ions, paving the way for future experimental studies in the field of cold and ultracold molecular ion physics.
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.
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.
Introduction If, while approaching on an unbound ground-state potential, two atoms absorb a photon and couple to an excited bound molecular state, they are said to undergo photoassociation. Figure 5.1 illustrates the process. At long range electrostatic dispersion forces give rise to the ground-state molecular potential varying as C 6 / R 6 . If the two atoms are homonuclear, then a resonant dipole–dipole interaction sets up ± C 3 / R 3 excited-state repulsive and attractive potentials. Figure 5.2 shows the actual long-range excited potential curves for the sodium dimer, originating from the 2 S ½ + 2 P 3/2 and 2 S ½ + 2 P ½ separated atom states. For cold and ultracold photoassociation processes the long-range attractive potentials play the key role; the repulsive potentials figure importantly in optical shielding and suppression, the subject of Chapter 6. In the presence of a photon with frequency ω p the colliding pair with kinetic energy k B T couples from the ground-state to the attractive molecular state in a free–bound transition near the Condon point R C , the point at which the difference potential just matches ћω p . Scanning the probe laser ω p excites population of vibration–rotation states in the excited bound potential and generates a free–bound spectrum. This general class of measurements is called photoassociative spectroscopy (PAS) and can be observed in several different ways. The observation may consist of bound-state decay by spontaneous emission, most probably as the nuclei move slowly around the outer turning point, to some distribution of continuum states on the ground potential controlled by bound–free nuclear Franck–Condon overlap factors.