This paper discusses the effects of small interactions like hyperfine structure or Zeeman effect on ultra-cold collisions. These interactions are usually neglected during collisions, but it is shown here that they may have large dynamical consequences in the particular case of collisions of ultra-cold atoms interacting through the resonance dipole-dipole terms (proportional to r -3 , where r is the internuclear distance). These collisions involving an excited atomic pair are responsible for most of the escape processes in laser traps and a very interesting prospect is to reduce the escape rate through the use of external fields.
This paper discusses the effects of small interactions like hyperfine structure or Zeeman effect on ultra-cold collisions. These interactions are usually neglected during collisions, but it is shown here that they may have large dynamical consequences in the particular case of collisions of ultra-cold atoms interacting through the resonance dipole-dipole terms (proportional to r -3 , where r is the internuclear distance). These collisions involving an excited atomic pair are responsible for most of the escape processes in laser traps and a very interesting prospect is to reduce the escape rate through the use of external fields.
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.
In this dissertation I present a variety of experiments on collisions between ultra-cold rubidium atoms. These collisions take place in light-force atom traps, where temperatures below 1 mK are reached. At these low temperatures weak, long-range interactions between the atoms are important, and collision times are long. Consequently, the absorption and spontaneous emission of photons plays an important role in determining the collision dynamics. The collisions studied in this dissertation involve excitation of the atoms to a state where the relatively strong dipole-dipole interaction with another atom results in attraction (or repulsion) after which spontaneous emission may take place. The resulting energy transfer in such a collision can eject the atoms from the trap. We have observed such collisions in both stable isotopes of rubidium. If the excitedstate is involved, the two isotopes behave quite di ff erently. This makes clear the importance of hyperfine interactions in the collision dynamics. In contrast, for the excited-state such di ff erences disappeare, because the hyperfine interaction is strong enough to eliminate hyperfine mixing of the potentials. Another collision process involved collisions with a repulsive dipole-dipole interaction. This experiment gives strong support for a Landau-Zener treatment of the excitation process. These collisions enabled the measurement of the trap depth. Finally, collisions between rubidium atoms that have undergone a two-step excitation by two near-infrared photons produce violet fluorescence as a signature of the collision. We have observed this e ff ect. The data shows unexpected features, which warrant further investigation. P3 2 ⁄
In this dissertation, I present ab initio theoretical results on cold and ultra-cold collision of atomic and molecular systems with magnetic and electric dipole moments. The collisions of different isotopes of maximally spin-polarized chromium atoms (52Cr and 53Cr), alkali-metal atom (Rb) - chromium atom, and magnetically trapped hydroxide (OH) with cold supersonic helium beam are considered in this thesis. Spin-changing cross sections and rate constants in Cr-Cr isotopic collision in the presence of a magnetic field are calculated by propagating a set of multichannel equations in the field. The coupling between dipole-dipole allowed and hyperfine channels are included. The short range electrostatic interactions between atoms and atom-molecule are represented with highly-accurate Born-Oppenheimer (BO) potential energy curves. Due to the large spin multiplicity in Cr-Cr and Rb-Cr interactions, more than the usual singlet and triplet channels are obtained. The long-range van der Waals (vdW) interactions between atoms are calculated, for Cr, by including accurate transition frequencies, discrete dipole matrix elements, and photoionization continuum oscillator strengths, and for Rb, using published dynamic polarizabilities. The vdW coefficients for Cr-Cr and Rb-Cr are obtained. In the cold collision regime, I investigate the influence of angular momentum shape resonances on the elastic and inelastic (loss channel) rate coefficients, and when the Zeeman relaxation, resulting in the loss of atoms from the trap, dominates elastic collision. Dipolar collisions are crucial to achieving quantum degeneracy. Magnetically tuned Fano-Feshbach closed-channel resonances are used to obtain zero-energy scattering lengths in comparison with observation of trap loss. In bosonic chromium collisions, resonances appear due only to dipolar interaction. The interplay between hyperfine and dipolar resonances in mixed-species Cr-Cr and Rb-Cr collisions is studied. In Rb-Cr, it is found that the molecule has broken symmetry and therefore contains a large permanent electric dipole moment in the ground state. A recent collisional experiment at JILA of a supersonic helium beam with a magnetically trapped OH radical found the onset of a quantum threshold in the total OH loss rate. Using ab initio BO energy surfaces, I calculated the spin-changing collisions which removed OH from the trap. Only after including the effect of the trapping potential on the collision dynamics, some agreement with observation was found. ^
Measurements of the temperature dependence of trap loss collisions of laser-cooled rubidium atoms are presented. A significant suppression of the rate of collisions between ground- and excited-state atoms is observed for temperatures below $\\sim$70 muK. In such inelastic collisions, the atomic excitation takes place at long range and must survive against spontaneous decay to short range. Our results are consistent with recent predictions for the low temperature suppression of these collisions due to reduced survival of atomic excitation at low collision velocities.^ We report on measurements of trap loss collisions between ultracold Rb atoms which are confined in a magneto-optical trap. Both isotopes sp85Rb and sp87Rb have been studied over wide range of trap laser intensities and detunings. The trap loss collision rates exhibit variations over 3 orders of magnitude. We observe significant differences between the isotopes. At large detunings the ability of the trap to recapture products of the hyperfine-changing collisions is significantly diminished. This finding is supported by our numerical simulations of the recapture process. The trap loss rates due to collisions with room temperature background gas have also been measured.^ Using laser light tuned to a repulsive molecular potential, we have been able to suppress inelastic ground-state hyperfine changing collisions between ultracold sp87Rb atoms. Adiabatic excitation to the repulsive curve alters the atomic trajectories and prevents the atoms from approaching close enough for the hyperfine change to occur. Experimental results show suppressions up to $\\sim$50% and are in reasonable agreement with a simple Landau-Zener model.^ Finally, we have observed a significant cooperative effect in ultracold trap loss collisions induced by two separate lasers. One laser, tuned close to the atomic resonance, excites the atom pair to an attractive potential at long range. The resulting acceleration and deflection give rise to an enhancement in the collisional flux of ground-state atoms reaching short range, as probed by a second laser. Enhancements up to a factor of $\\sim$3 have been observed. ^
This tutorial chapter provides an introduction to the vibrant field of cold molecular collisions in the presence of external electromagnetic fields. The kinetic energy of molecules confined in electromagnetic traps is small compared to their interactions with external fields, so the influence of molecule -field interactions on molecular collisions at ultralow temperatures can no longer be neglected or treated perturbatively. The intricate topology of spin-dependent, multidimensional intermolecular interactions makes it necessary to use accurate, non-perturbative quantum scattering techniques for solving the Schrodinger equation for molecules colliding in the presence of external fields. The primary goal of this chapter is to provide an overview of multichannel quantum scattering theory of molecular collisions in external fields, with a focus on rigorous coupled-channel methodology applied to molecules of current experimental interest. We also present an overview of the mechanisms for controlling elastic and inelastic molecular collisions with external magnetic fields.
The binary collision dynamics of 2Dg,3/2 ground state scandium atoms is studied from first principles. We employ 30 coupled diabatic ab initio potentials in a coupled-channels study of the scattering dynamics of cold and ultracold scandium atoms in external magnetic fields. Due to the long-ranged magnetic dipolar interaction, the field dependence of the cross section does not follow the threshold laws derived by Volpi and Bohn [Phys. Rev. A 65, 052712 (2002)]. In the field-free case, the near-threshold cross section is independent of the collision energy, and hence the cross section does not follow the well-established Wigner threshold laws. The observed threshold behavior is explained in the Born approximation. For energies above $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, inelastic collisions are driven by the anisotropic nonrelativistic electronic interaction. For energies below $100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, the ratio of elastic-to-inelastic collisions is likely to be favorable for evaporative cooling. Both anisotropy in the long-range interaction and in the short-range potential contribute to large cross sections for inelastic collisions at higher energies and lead to a small ratio of elastic-to-inelastic collisions. This is in agreement with the large rates for Zeeman relaxation of submerged-shell atoms observed experimentally. The effect of the uncertainty in the ab initio potential is sampled by scaling the reduced mass and is found to have little influence on the conclusions drawn from this work.