We apply a simplified description to weakly bound states and cold-collision continuum states of pairs of ground-state alkali-metal atoms, which complements the usual more elaborate coupled-channel treatment. It is based on a diabatic treatment of the transition region between the exchange-dominated interatomic distance range at small $r$ and the hyperfine-dominated range at large $r$. The models contain the degenerate internal states approximation for H atoms as a special case.
We apply a simplified description to weakly bound states and cold-collision continuum states of pairs of ground-state alkali-metal atoms, which complements the usual more elaborate coupled-channel treatment. It is based on a diabatic treatment of the transition region between the exchange-dominated interatomic distance range at small r and the hyperfine-dominated range at large r. The models contain the degenerate internal states approximation for H atoms as a special case.
From a theoretical point of view, one of the appealing features of clouds of alkali atom vapours is that particle separations, which are typically of order 10 2 nm, are large compared with the scattering length a which characterizes the strength of interactions. Scattering lengths for alkali atoms are of the order of 100 a 0 , where a 0 , is the Bohr radius, and therefore alkali atom vapours are dilute, in the sense that the dominant effects of interaction are due to two-body encounters. It is therefore possible to calculate properties of the gas reliably from a knowledge of two-body scattering at low energies, which implies that information about atomic scattering is a key ingredient in work on Bose–Einstein condensates. An alkali atom in its electronic ground state has several different hyperfine states, as we have seen in Secs. 3.1 and 3.2. Interatomic interactions give rise to transitions between these states and, as we described in Sec. 4.6, such processes are a major mechanism for loss of trapped atoms. In a scattering process, the internal states of the particles in the initial or final states are described by a set of quantum numbers, such as those for the spin, the atomic species, and their state of excitation. We shall refer to a possible choice of these quantum numbers as a channel.1 At the temperatures of interest for Bose-Einstein condensation, atoms are in their electronic ground states, and the only relevant internal states are therefore the hyperfine states. Because of the existence of several hyperfine states for a single atom, the scattering of cold alkali atoms is a multi-channel problem.
We present ab initio potentials for ground state lithium, sodium, potassium and rubidium atoms interacting with ground state chromium atoms via the 6 Σ + and 8 Σ + states of the corresponding dimers. Each potential is matched to the leading van der Waals dispersion energy − C 6 / R 6 − C 8 / R 8 and an exchange energy; we list the values of C 6 , C 8 and the exchange fitting parameters. We present calculated values from quantal and semi-classical approximations for the s-wave scattering length and effective range and the p-wave scattering volume for collisions of each of the alkali-metal atoms lithium, sodium, potassium and rubidium with 52 chromium atoms and comment on s-wave scattering by 53 chromium atoms.
An important feature of cold atomic vapours is that particle separations, which are typically of order 10 2 nm, are usually an order of magnitude larger than the length scales associated with the atom–atom interaction. Consequently, the two-body interaction between atoms dominates, and three-and higher-body interactions are unimportant. Moreover, since the atoms have low velocities, many properties of these systems may be calculated in terms of a single parameter, the scattering length. An alkali atom in its electronic ground state has several different hyperfine states, as we have seen in Secs. 3.1 and 3.2. Interatomic interactions give rise to transitions between these states and, as we described in Sec. 4.6, such processes are a major mechanism for loss of trapped atoms. In a scattering process, the internal states of the particles in the initial or final states are described by a set of quantum numbers, such as those for the spin, the atomic species, and their state of excitation. We shall refer to a possible choice of these quantum numbers as a channel . At the temperatures of interest for Bose–Einstein condensation, atoms are in their electronic ground states, and the only relevant internal states are therefore the hyperfine states. Because of the existence of several hyperfine states for a single atom, the scattering of cold alkali atoms is a multi-channel problem.
The interaction of alkali K and Rb atoms that reside in the ground state is considered in the range of collision energies E = 10−4 to 10−2 au. The singlet (X 1Σ+) and triplet (a 3Σ+) interaction potentials available in the literature are analyzed and modified. For the KRb dimer in the range of interatomic distances 15–21a 0, we chose analytical representations of the singlet and triplet potentials that more accurately describe the interaction of alkali Rb and K atoms in the ground state. Complex cross sections of the spin exchange are calculated for the first time that permit one to calculate the processes of polarization transfer and relaxation times, as well as shifts in the magnetic resonance frequencies caused by K-Rb spin exchange collisions.
Research on ultracold molecules has seen a growing interest recently in the context of high-resolution spectroscopy and quantum computation. After forming weakly bound molecules from atoms in cold collisions, the preparation of molecules in low vibrational levels of the ground state is experimentally challenging, and typically achieved by population transfer using excited electronic states. Accurate potential energy surfaces are needed for a correct description of processes such as the coherent de-excitation from the highest and therefore weakly bound vibrational levels in the electronic ground state via couplings to electronically excited states. This paper is dedicated to the vibrational analysis of potentially relevant electronically excited states in the alkali-metal (Li, Na, K, Rb)-- alkaline-earth metal (Ca,Sr) diatomic series. Graphical maps of Frank-Condon overlap integrals are presented for all molecules of the group. By comparison to overlap graphics produced for idealized potential surfaces, we judge the usability of the selected states for future experiments on laser-enhanced molecular formation from mixtures of quantum degenerate gases.
Introduction Interactions between separated atoms are complicated by the large number of degrees of freedom of a many-atom system, and are very difficult to describe quantitatively. Although the Hamiltonian for such systems can be written down easily, finding the eigenfunctions requires a sophisticated effort and large computer resources. This area of quantum chemistry, with all its intricacies, is a complex subfield of science that cannot be adequately described in a single book chapter. Therefore the student is referred to specialized books in this field for further reading [165, 170]. In the 1990s a new field of chemistry emerged that considered such interactions between atoms at ultra-cold temperatures. The field focuses strongly on atomic interactions at large internuclear distances where the atoms are well separated and their electronic clouds do not strongly overlap. In such circumstances the interactions are dominated by the properties of the states of the atoms and they can be understood from an atomic point of view. In this chapter the basic features of this field will be described. The interaction energy (electronic potential energy) between two colliding partners separated by a large distance is called the dissociation limit. Light interactions with the particles can occur with the total energy above or below this limit. The relative kinetic energy does not contribute because it is so very small at such low temperatures. In the presence of a light field tuned below this limit for a pair that has one of the atoms in an excited state, two unbound atoms can be associated into a bound molecular state (for example, an S–P collision of two alkali atoms). Such photo-association is more likely at a large interatomic separation because there is good radial overlap between the incoming, low-energy scattering state and the outer turning point of the bound excited state, so it usually produces a molecule in a high vibrational state. Studying these states provides important information about interatomic interactions near the dissociation limit. The long-range part of the potential is dominated by atomic parameters and in Sec. 18.2 it is shown how these potentials can be constructed. The LeRoy–Bernstein method, which was developed long before the advent of cold-atom photo-association, is described in Sec. 18.3 and can be used to extract these parameters from measurements of the bound states.