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

Abstract

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 ≪ 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.A m ′ C

Accurate Determination of the Dynamical Polarizability of Dysprosium

“…[19] and 193 a.u. [22], being consistent with both of them within the corresponding er an ror estimates of a few percent [41,42]. For the small tensorial part, our result is consistent with the theoretical value of 1.34 a.u.…”

Sticky collisions of ultracold RbCs molecules

“…The necessary matrix elements can be found in, for example, Ref. [65]. The result for the rotational ground state, C 6,rot = µ 4 elec /6B, is well known.…”

Modeling Photoassociative Spectra of Ultracold NaK + K

“…The calculated long-range PES can be fitted to the standard multipolar expansion expressed in atomic units of distance and energy where E ∞ ( r ) is the r -dependent energy of the K···NaK complex for R → ∞, thus identical to b PEC of NaK (see the Supporting Information). The dominant term characterized by the C 6 van der Waals coefficient results from the cumulative effect of the Debye (or induction) interaction of a permanent dipole inducing an instantaneous dipole on a non-polar particle, and of the London (dispersion) interaction between the dipoles induced on each partner. − The parameters in eq are obtained via a two-step procedure: (i) by fitting V ( R , r , θ) between R = 60 a.u. and R = 160 a.u.…”