There is at present great interest in the properties of ultracold molecules. Molecules are created in traps in excited rovibrational states and any vibrational relaxation results in the trap loss. This thesis provides a theoretical study of interactions and collisions in the spin-polarized lithium -b lithium dimer system at ultralow energies. Potential energy surface of the electronic quartet ground state of lithium trimer is generated ab initio using the CCSD(T) method and represented by an IMLS/Shepard fit. Long-range nonadditive interactions are modelled using a symmetric global form with coefficients taken from a fit to the atom-molecule dispersion coefficients. The surface allows barrierless atom-exchange reactions. It has a global minimum of ≈ 4000 cm(^-1) at equilateral geometries with r(_e) = 3.1 Å. The nonadditive interactions are very strong near equilibrium. They increase the well depth by a factor of 4 and reduce the interatomic distance by ≈ 1 Å. Another surface of À symmetry in C(_s) meets the ground state surface at linear geometries at short range. Part of the seam, near D(_ooh) geometries, is in an energetically accessible region for cold collisions. Inside the seam, the lowest À surface correlates with (^4)II rather than (^4)Σ state. Inelastic and reactive collisions are investigated using a quantum mechanical coupled channel method in hyperspherical coordinates. Bosonic and fermionic systems in the spin-stretched states are considered. The inelastic rate coefficients from the rovibrationally excited states of dimer at ultralow collision energies are large, often above 10-(^-10) cm(^3)s(^-1) The elastic cross sections are ≈ 3 orders of magnitude lower at 1 nK. Atom-molecule mixtures, at the densities found in Bose-Einstein condensates of alkali metal atoms that were recently produced, would last only a fraction of a second. Classical Langevin model describes semi-quantitatively the energy dependence of inelastic cross sections above ≈ 50 mK. No systematic differences between the bosonic and fermionic systems were found. Sensitivity of the results on potential was investigated. Reactions in isotopic mixtures of lithium may be exothermic even from the molecular ground state. The reactive rate coefficients are 1 - 2 orders of magnitude smaller than those in systems involving an initially vibrationally excited dimer.
Cold atoms can adsorb to a surface with the emission of a single phonon when the binding energy is sufficiently small. The effects of phonon damping and adsorbent size on the adsorption rate in this quantum regime are studied using the multimode Rabi model. It is demonstrated that the adsorption rate can be either enhanced or suppressed relative to the Fermi golden rule rate, in analogy to cavity effects in the spontaneous emission rate in QED. A mesoscopic-sized adsorbent behaves as an acoustic cavity that enhances the adsorption rate when tuned to the adsorption transition frequency and suppresses the rate when detuned. This acoustic cavity effect occurs in the regime where the frequency spacing between vibrational modes exceeds the phonon linewidth.
Using the Dirac–Frenkel variational principle, a time-dependent description of the dynamics of a two-level system coupled to a bosonic bath is formulated. The method is applied to the case of a gas of cold atoms adsorbing to an elastic membrane at a finite temperature via phonon creation. The time-dependence of the system state is analytically calculated using Laplace transform methods, and a closed-form expression for the transition rate is obtained. Atoms in the gas transition to the adsorbed state through a resonance that has contributions from a distribution of vibrational modes of the membrane. The resonance can decay with the creation of a phonon to complete the adsorption process. The adsorption rate at low membrane temperatures agrees with the golden rule estimate to the lowest order in the coupling constant for values greater than a critical coupling strength. Below this critical coupling strength, the adsorption rate is exponentially suppressed by a phonon reduction factor whose exponent diverges with increasing adsorbent size. The rate changes discontinuously with coupling strength for low temperature membranes, and the magnitude of the discontinuity decreases with increasing temperature. These variational results suggest the quantum adsorption model may contain a first-order quantum phase transition.
We study a submonolayer
4He adsorbed on fluorographene (GF) and on hexagonal boron nitride (hBN) at low coverage. The adsorption potentials have been computed ab initio with a suitable density functional theory including dispersion forces. The properties of the adsorbed
4He atoms have been computed at finite temperature with path integral Monte Carlo and at
T=0K with variational path integral. From both methods we find that the lowest energy state of
4He on GF is a superfluid. Due to the very large corrugation of the adsorption potential this superfluid has a very strong spatial anisotropy, the ratio between the largest and smallest areal density being about 6, the superfluid fraction at the lowest
T is about 55%, and the temperature of the transition to the normal state is in the range 0.5--1 K. Thus, GF offers a platform for studying the properties of a strongly interacting highly anisotropic bosonic superfluid. At a larger coverage
4He has a transition to an ordered commensurate state with occupation of 1/6 of the adsorption sites. This phase is stable up to a transition temperature located between 0.5 and 1 K. The system has a triangular order similar to that of
4He on graphite but each
4He atom is not confined to a single adsorption site and the atom visits also the nearest neighboring sites giving rise to a novel three-lobed density distribution. The lowest energy state of
4He on hBN is an ordered commensurate state with occupation of 1/3 of the adsorption sites and triangular symmetry. A disordered state is present at lower coverage as a metastable state. In the presence of an electric field the corrugation of the adsorption potential is slightly increased but up to a magnitude of 1 V/\AA{} the effect is small and does not change the stability of the phases of
4He on GF and hBN. We have verified that also in the case of graphene such electric field does not modify the stability of the commensurate $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}R{30}^{\ensuremath{\circ}}$ phase.