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arXiv:1006.5314 · Physical Review A

Photoassociation of a cold-atom–molecule pair: Long-range quadrupole-quadrupole interactions

Maxence Lepers, Olivier Dulieu, Viatcheslav Kokoouline

Published Oct 21, 2010• 16 citations
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Abstract

The general formalism of the multipolar expansion of electrostatic interactions is applied to the calculation of the potential energy between an excited atom (without fine structure) and a ground-state diatomic molecule at large mutual separations. Both partners exhibit a permanent quadrupole moment so that their mutual long-range interaction is dominated by a quadrupole-quadrupole term, which is attractive enough to bind trimers. Numerical results are given for an excited Cs($6{}^{2}P$) atom and a ground-state ${\mathrm{Cs}}_{2}$ molecule. The prospects for achieving photoassociation of a cold-atom--dimer pair are thus discussed and found promising. The formalism can be generalized to the long-range interaction between molecules to investigate the formation of cold tetramers.

DOI
10.1103/physreva.82.042711

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The general formalism of the multipolar expansion of electrostatic interactions is applied to the calculation of the potential energy between an excited atom (without fine structure) and a ground-state diatomic molecule at large mutual separations. Both partners exhibit a permanent quadrupole moment so that their mutual long-range interaction is dominated by a quadrupole-quadrupole term, which is attractive enough to bind trimers. Numerical results are given for an excited Cs(62P6{}^{2}P62P) atom and a ground-state Cs2{\mathrm{Cs}}_{2}Cs2​ molecule. The prospects for achieving photoassociation of a cold-atom--dimer pair are thus discussed and found promising. The formalism can be generalized to the long-range interaction between molecules to investigate the formation of cold tetramers.
The electrostatic interaction between an excited atom and a diatomic ground-state molecule in an arbitrary rovibrational level at large mutual separations is investigated with a general second-order perturbation theory, in the perspective of modeling the photoassociation between cold atoms and molecules. We find that the combination of quadrupole-quadrupole and van der Waals interactions competes with the rotational energy of the dimer, limiting the range of validity of the perturbative approach to distances larger than 100 Bohr radii. Numerical results are given for the long-range interaction between Cs and Cs2{}_{2}2​, showing that the photoassociation is probably efficient for any Cs2{}_{2}2​ rotational energy.
Ultracold collisions of neutral atoms and molecules have been of great interest since experimental advances enabled the cooling and trapping of such species. This study develops a simplified theoretical treatment of a low-energy collision between an alkali atom and a diatomic molecule accompanied by absorption of a photon from an external electromagnetic field. The long-range interaction between the two species is treated, including the atomic spin–orbit interaction. The long-range potential energy curves for the triatomic complex are calculated in realistic detail, while effects of the short-range behavior are mimicked by applying different boundary conditions at the van der Waals length. For neutral colliding species, the leading interaction term is the dipole–dipole interaction. In the case of nonpolar dimers like Cs 2, the second leading term is the quadrupole–quadrupole interaction. However, there is also a strong dipole–quadrupole interaction for dimers with a large permanent dipole moment such as NaCs, making the dipole–quadrupole interaction the second leading term for an atom colliding with a polar dimer. Our applications of the simplified treatment show a higher density of trimer states for a polar dimer compared to the case of a nonpolar dimer like Cs 2 . This is a consequence of the strong quadrupole–dipole coupling between the atom and the dimer dipole moment.
Abstract Using the multipolar expansion of electrostatic and magnetostatic potential energies, we characterize the long-range interactions between two weakly-bound diatomic molecules, taking as an example the paramagnetic Er 2 Feshbach molecules which were produced recently. Since inside each molecule individual atoms conserve their identity, the intermolecular potential energy can be expanded as the sum of pairwise atomic potential energies. In the case of Er 2 Feshbach molecules, we show that the interaction between atomic magnetic dipoles gives rise to the usual term of the multipolar expansion, where R is the intermolecular distance, but also to additional terms scaling as and so on. Those terms are due to the interaction between effective molecular multipole moments, and are strongly anisotropic with respect to the orientation of the molecules. Similarly, the atomic pairwise van der Waals interaction results in ... terms in the intermolecular potential energy. By calculating the reduced electric-quadrupole moment of erbium ground level a.u., we also demonstrate that the electric–quadrupole interaction energy is negligible with respect to the magnetic dipole and van der Waals interaction energies. The general formalism presented in this article can be applied to calculate the long-range potential energy between arbitrary charge distributions composed of almost free subsystems.
The term "long-range interactions" refers to electrostatic and magnetostatic potential energies between atoms and molecules with mutual distances ranging from a few tens to a few hundreds Bohr radii. The involved energies are much smaller than the usual chemical bond energies. However, they are comparable with the typical kinetic energies of particles in an ultracold gas (T≪1KT\ll 1KT≪1K), so that the long-range interactions play a central role in its dynamics. The progress of research devoted to ultracold gases shed a new light on the well-established topic of long-range interactions, because: (i) the interacting atoms and molecules can be prepared in a well-defined quantum (electronic, vibrational, rotational, fine or hyper-fine), ground or excited level; and (ii) long-range interactions can be tailored at will using external electromagnetic fields. In this chapter, we present the essential concepts and mathematical relations to calculate long-range potential energies. We start with deriving the multipolar expansion of the electrostatic interaction energy between classical charge distributions, both in Cartesian coordinates for pedagogical purpose, and in spherical coordinates for practical use. Then we combine multipolar expansion and quantum perturbation theory, to obtain the general first- and second-order energy corrections, including the well-known van der Waals energy. We consider two central examples in the current context of ultracold gases: (i) a pair of alkali-metal atoms and (ii) a pair of alkali-metal heteronuclear diatomic molecules submitted to an electric field. We highlight the key role of the total angular momenta of the interacting particles and of the complex, irrespective of their electronic or nuclear, orbital or spin nature.
We investigate theoretically the long-range electrostatic interactions between a ground-state homonuclear alkali-metal dimer and an excited alkali-metal atom taking into account its fine-structure. The interaction involves the combination of first-order quadrupole-quadrupole and second-order dipole-dipole effects. Depending on the considered species, the atomic spin-orbit may be comparable to the atom-molecule electrostatic energy and to the dimer rotational structure. Here we extend our general description in the framework of the second-order degenerate perturbation theory [M. Lepers and O. Dulieu, Eur. Phys. J. D, 2011] to various regimes induced by the magnitude of the atomic spin-orbit. A complex dynamics of the atom-molecule may take place at large distances, which may have consequences for the search for an universal model of ultracold inelastic collisions as proposed for instance in the study of Z. Idziaszek and P. S. Julienne [Phys. Rev. Lett.104, 2010, 113202].
In the molecular photoassociation process, two free cold atoms absorb one photon by a resonant way, to create an excited molecule in a well defined ro-vibrational state. The photoassociative spectroscopy of alkaline dimers yields accurate determinations for the long-range parts of molecular potential curves correlated to the first s + p asymptote. In contrast to atoms, laser cooling of molecules is very difficult because of the lack of a closed two-level scheme for recycling the population. The molecular photoassociation of cold atoms opens also a promising alternative for the formation of cold ground state molecules. Photoassociation of cold cesium atoms has permitted the first observation of translationally cold ground state molecules. The case of the cesium atom is very favorable because the 0 g - and 1 u purely long-range states below the dissociation limit 6s 1/2 +6p 3/2 present Condon points at intermediate distances. Such configurations offer rather efficient channels for the creation of singlet or triplet ground state Cs 2 molecules after spontaneous decay.