Two elementary models of molecular structure are used to investigate inelastic collisions in cold trapped dipolar gases. A two-state model of a polar molecule (such as one with a Λ-doublet) permits analytic description of the inelastic collision process at energies considerably higher than the gap energy, predicting rate constants and cross sections given by elementary formulae. Alternatively, a three-state model of a rotor molecule in an electric field is investigated, with resultant rate constants and cross sections scaling simply with molecular mass, rotational constant, dipole moment and polarizing field strength. Semiclassical inelastic collision cross sections and rate constants are demonstrated to depend strongly on the model used, especially as regards their dependence on the polarizing field. Inelastic cross sections among doublet dipoles decrease with increasing field strength, while they increase in proportion to the square of the field strength for collisions between rotor dipoles.
Two elementary models of molecular structure are used to investigate inelastic collisions in cold trapped dipolar gases. A two-state model of a polar molecule (such as one with a Λ-doublet) permits analytic description of the inelastic collision process at energies considerably higher than the gap energy, predicting rate constants and cross sections given by elementary formulae. Alternatively, a three-state model of a rotor molecule in an electric field is investigated, with resultant rate constants and cross sections scaling simply with molecular mass, rotational constant, dipole moment and polarizing field strength. Semiclassical inelastic collision cross sections and rate constants are demonstrated to depend strongly on the model used, especially as regards their dependence on the polarizing field. Inelastic cross sections among doublet dipoles decrease with increasing field strength, while they increase in proportion to the square of the field strength for collisions between rotor dipoles.
Inelastic collisions between dipolar molecules, assumed to be trapped in a static electric field at cold (> 10−3K) temperatures, are investigated and compared with elastic collisions. For molecules with a Λ-doublet energy-level structure, a dipole moment arises because of the existence of two nearly degenerate states of opposite parity, and the collision of two such dipoles can be solved entirely analytically in the energy range of interest. Cross sections and rate constants are found to satisfy simple, universal formulas. In contrast, for molecules in a Σ electronic ground state, the static electric field induces a dipole moment in one of three rotational sublevels. Collisions between two rotor dipoles are calculated numerically; the results scale simply with molecule mass, rotational constant, dipole moment, and field strength. It might be expected that any particles interacting only under the influence of the dipole-dipole interaction would show similar behavior; however, the most important and general result of this research is that at cold temperatures inelastic rate constants and cross sections for dipoles depend strongly upon the internal structure of the molecules. The most prominent difference between the Λ-doublet and rotor molecules is variation of the inelastic cross section with applied field strength. For Λ-doublet dipoles, cross sections decrease with increasing field strength. For rotor dipoles, cross sections increase proportionally with the square of field strength. Furthermore, the rate constants of the two types of molecules depend very differently on the angular orientations of the dipoles in the electric field.
The collisional stability of ultracold polar molecules in electrostatic traps is considered. Rate constants for collisions that drive molecules from weak-electric-field-seeking to strong-field-seeking states are estimated using a simple model that emphasizes long-range dipolar forces. The rate constants for collisional losses are found to vary substantially as a function of molecular parameters used in the model, such as dipole moment, mass, and the splitting of the molecular $\ensuremath{\Lambda}$ doublet. Varying these parameters over physically reasonable ranges yields rate constants as low as ${10}^{\ensuremath{-}20} {\mathrm{cm}}^{3}/\mathrm{sec}$ and as high as ${10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{sec}.$ Nevertheless, the loss rates rise dramatically in the presence of the externally applied trapping electric field. For this reason it is argued that electrostatic traps are likely to be less stable against collisional losses than their magnetic counterparts.
Collisions of polar $^{1}\ensuremath{\Sigma}$ state molecules at ultralow energies are considered, within a model that accounts for long-range dipole-dipole interactions, plus rotation of the molecules. We predict a substantial suppression of dipole-driven inelastic collisions at high values of the applied electric field, namely, field values of several times ${B}_{0}∕\ensuremath{\mu}$. Here B0 is the rotational constant, and $\ensuremath{\mu}$ is the electric dipole moment of molecules. The sudden large drop in the inelastic cross section is attributed to the onset of degeneracy between molecular rotational levels, which dramatically alters the scattering Hamiltonian. This capability could, in principle, be used to stabilize ultracold gases against collisional losses.
Cold molecules promise to reveal a rich set of novel collision dynamics in the low-energy regime. By combining for the first time the techniques of Stark deceleration, magnetic trapping, and cryogenic buffer gas cooling, we present the first experimental observation of cold collisions between two different species of state-selected neutral polar molecules. This has enabled an absolute measurement of the total trap loss cross sections between OH and ND(3) at a mean collision energy of 3.6 cm(-1) (5 K). Due to the dipolar interaction, the total cross section increases upon application of an external polarizing electric field. Cross sections computed from ab initio potential energy surfaces are in agreement with the measured value at zero external electric field. The theory presented here represents the first such analysis of collisions between a (2)Π radical and a closed-shell polyatomic molecule.
We investigate the ultracold collisions of rotationally excited dipolar molecules in free-space, taking the hetero-nuclear bi-alkali molecule of KRb as an example. We show that we can sharply tune the elastic, inelastic and reactive rate coefficients of lossy molecular collisions when a second rotationally excited colliding channel crosses the threshold of the initial colliding channel, with the help of an applied electric field, as found by Avdeenkov et al for non-lossy molecules ( Phys. Rev. A 73 022707 ). We can increase or decrease the inelastic and reactive processes whether the second channel is above or below the initial channel. This is seen for both bosonic and fermionic molecules. Additionally, we include the electric quadrupole and octopole moment to the dipole moment in the expression of the long-range multipole–multipole interaction. We found that for processes mediated by the incident channel, such as elastic and reactive collisions, the inclusion of quadrupole and octopole moments is not important at ultralow energies. The moments are important for processes mediated by state-to-state transitions like inelastic collisions.
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. ^