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arXiv:1305.5769 · Physical Review A

Long-range interactions between polar alkali-metal diatoms in external electric fields

Maxence Lepers, Romain Véxiau, M Aymar, Nadia Bouloufa-Maafa, Olivier Dulieu

Published Sep 26, 2013• 40 citations
arXivHTMLPDF

Abstract

We computed the long-range interactions between two identical polar bialkali molecules in their rovibronic ground level for all ten species involving Li, Na, K, Rb, and Cs, using accurate quantum chemistry results combined with available spectroscopic data. A huge van der Waals interaction is found for eight species in free space. The competition of the van der Waals interaction with the dipole-dipole interaction induced by an external electric field parallel or perpendicular to the intermolecular axis is investigated by varying the electric-field magnitude and the intermolecular distance. Our calculations predict a regime with the mutual orientation of the two molecules but with no preferential direction in the laboratory frame. A mechanism for the stimulated one-photon radiative association of a pair of ultracold polar molecules into ultracold tetramers is proposed, which would open the way towards the optical manipulation of ultracold polyatomic molecules.

DOI
10.1103/physreva.88.032709

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CHAPTER 4. Long-range Interactions Between Ultracold Atoms and Molecules

Maxence Lepers, Olivier Dulieu

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 of Bohr radii. The energies involved 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 ≪ 1 K), so that the long-range interactions play a central role in its dynamics. The progress of research devoted to ultracold gases sheds 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 hyperfine), 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 by 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 in the presence of 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.

RSC theoretical and computational chemistry series•Jan 1, 2017•4 citations
We computed the long-range interactions between two identical polar bialkali molecules in their rovibronic ground level for all ten species involving Li, Na, K, Rb, and Cs, using accurate quantum chemistry results combined with available spectroscopic data. A huge van der Waals interaction is found for eight species in free space. The competition of the van der Waals interaction with the dipole-dipole interaction induced by an external electric field parallel or perpendicular to the intermolecular axis is investigated by varying the electric-field magnitude and the intermolecular distance. Our calculations predict a regime with the mutual orientation of the two molecules but with no preferential direction in the laboratory frame. A mechanism for the stimulated one-photon radiative association of a pair of ultracold polar molecules into ultracold tetramers is proposed, which would open the way towards the optical manipulation of ultracold polyatomic molecules.
Long-range electrostatic, induction, and dispersion coefficients including terms of order ${R}^{\ensuremath{-}8}$ have been calculated by the sum over states method using time-dependent density-functional theory. We also computed electrostatic moments and static polarizabilities of the individual diatoms up to the octopole order using coupled-cluster and density-functional theory. The laboratory-frame transformed electrostatic moments and van der Waals coefficients corresponding to the alignment of the diatomic molecules were found. We use this transformation to obtain the coupling induced by an external dc electric field and present values for all XYXYXY combinations of like polar alkali-metal diatomic molecules with atoms from Li to Cs. Analytic solutions to the dressed-state laboratory-frame electrostatic moments and long-range intermolecular potentials are also given for the dc low-field limit.
We have calculated the isotropic C6 coefficients characterizing the long-range van der Waals interaction between two identical heteronuclear alkali-metal diatomic molecules in the same arbitrary vibrational level of their ground electronic state X(1)Σ(+). We consider the ten species made up of (7)Li, (23)Na, (39)K, (87)Rb, and (133)Cs. Following our previous work [Lepers et al., Phys. Rev. A 88, 032709 (2013)], we use the sum-over-state formula inherent to the second-order perturbation theory, composed of the contributions from the transitions within the ground state levels, from the transition between ground-state and excited state levels, and from a crossed term. These calculations involve a combination of experimental and quantum-chemical data for potential energy curves and transition dipole moments. We also investigate the case where the two molecules are in different vibrational levels and we show that the Moelwyn-Hughes approximation is valid provided that it is applied for each of the three contributions to the sum-over-state formula. Our results are particularly relevant in the context of inelastic and reactive collisions between ultracold bialkali molecules in deeply bound or in Feshbach levels.
The dynamics of ultracold quantum gases composed of atoms or molecules with extremely low translational energy E t /k B << 1 millikelvin is dominated by the long-range mutual interactions between particles. Such studies require a detailed modelling of the atom-molecule or molecule-molecule long-range interactions inside the quantum gas with or without the presence of external fields. This paper focuses on two particular aspects relevant to ultracold chemistry: (i) The calculation of rates for photoassociation of a cold atom and a cold molecule to create ultracold excited trimers, based on the knowledge of the long-range interaction between the two species, showing that such rates are encouraging under the density and temperature conditions of a nearly degenerate quantum gas; (ii) The determination of the long-range interactions between two identical polar bialkali molecules in their rovibronic ground level in the presence of an electric field, showing the possibility for the formation of ultracold polar tetramers by stimulated emission.
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.
The calculation of non-covalent interactions of highly polarizable molecules is an outstanding problem in chemistry and physics. Difficulties arise both in accurate treatments of dispersion interactions between molecules and in the evaluation of surfaces of sufficient size for use in further computations. While ``gold-standard" calculations using coupled cluster theory with singles, doubles and perturbative triples provides a reliable method for evaluating interactions the computational cost involved in calculating more than a few points of an interaction surface becomes prohibitive for even medium sized molecules. Expanding the long range interaction into a van der Waals series reduces the cost of evaluating a surface to the computation of a few parameters. We describe here the implementation of a new computer program for calculating van der Waals coefficients for arbitrary molecules using the sum over states method. The laboratory-frame transformation of the computed van der Waals surface and the inclusion of rotational state dressing on the surface is derived. Analytic approximations for the interactions of two linear molecules in the presence of a small DC electric field are also derived. Recent achievements in the formation and manipulation of ultracold polar molecules have opened the door to exciting new studies in cold chemical reactions. To characterize the energetics and reaction pathways of trimer and tetramer formation and reactions, we have computed the structure and thermochemistry of the model trimer Li3_33​ and every X2_22​Y2_22​ alkali tetramer through Cs. Related interest in the control of molecular ion reactions is also investigated with recent theoretical results for the rubidium hydroxide reaction presented here.
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 of Bohr radii. The energies involved 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 ≪ 1 K), so that the long-range interactions play a central role in its dynamics. The progress of research devoted to ultracold gases sheds 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 hyperfine), 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 by 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 in the presence of 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.