Absolute numbering of asymptotic vibrational levels of diatomic molecules from cold physics experiments

We present a simple method for determination of absolute vibrational numbering of isolated near dissociation levels in diatomic molecules, usually observed in cold physics experiments. The method is based on the isotope shift and works even when energies of only two levels from one isotopologue and one level from another isotopologue have been measured. It is demonstrated on data from recently reported precise measurements of binding energies of levels lying close to the dissociation limits in ultracold Yb2, CsYb, RbSr and RbYb molecules. Its predictions agree with these of much more elaborate multi-isotope potential curve fitting. PACS numbers: 31.50.Bc, 33.20.Kf, 33.20.Vq, 33.50.D

Quantum Theory of Complex Ultracold Collisions

This thesis reports on a variety of calculations on cold and ultracold scattering, with a broad theme of how best to consider and understand complex systems in simple ways. Firstly, we investigate quantum defect theory. We demonstrate that it is not only an excellent model for simple systems, but can also provide simple predictions of the \emph{range} of possible behaviours for complex systems, in particular for a model of collisional losses. These predictions agree well with expensive coupled-channels calculations in cases where the full calculations also predict only the range of possible behaviours. Secondly, we consider effects relating to thermalisation of cold and ultracold gases. We show that considering the correct transport cross section, $\sigma_\eta^{(1)}$, is important for determination of scattering lengths and their signs by interspecies thermalisation. This cross section is also important to the understanding of high-quality simulations of sympathetic cooling in a microwave trap, which suggest Rb is likely to be a good coolant for CaF. We also correct an error in the interpretation of previous results for sympathetic cooling in a magnetic trap, showing this may work from over 100 mK for Li+CaF and many Kelvin when using atomic hydrogen as a coolant. Thirdly, we study quantum chaos in ultracold collisions. We find very clear and strong signs of chaos in Li+CaH. We also show that a more strongly coupled system, Li+CaF, is \emph{not} fully chaotic and that there is unexpected structure in the levels of chaos as the CaF rotational constant is varied. We also show that signatures of chaos can emerge in a very simple atom-atom system, Yb(${}^1S_0$)+Yb(${}^3P_2$), which interacts on only two Born-Oppenheimer potentials. Finally, we examine the idea that metastable states in 2-body scattering greatly enhance 3-body recombination at ultracold temperatures. We attempt to put it on a more rigorous theoretical grounding by considering Smith's collision lifetime and related quantities, but those are shown to lack clear interpretations in the ultracold regime. We therefore consider 3-body scattering theory and arrive at some general conclusions about how we expect such 2-body features to appear in 3-body scattering and suggest possible ways forward

Ultracold Mixtures of Rubidium and Ytterbium for Open Quantum System Engineering

Exquisite experimental control of quantum systems has led to sharp growth of basic quantum research in recent years. Controlling dissipation has been crucial in producing ultracold, trapped atomic samples. Recent theoretical work has suggested dissipation can be a useful tool for quantum state preparation. Controlling not only how a system interacts with a reservoir, but the ability to engineer the reservoir itself would be a powerful platform for open quantum system research. Toward this end, we have constructed an apparatus to study ultracold mixtures of rubidium (Rb) and ytterbium (Yb). We have developed a Rb-blind optical lattice at 423.018(7) nm, which will enable us to immerse a lattice of Yb atoms (the system) into a Rb BEC (superfluid reservoir). We have produced Bose-Einstein condensates of 170-Yb and 174-Yb, two of the five bosonic isotopes of Yb, which also has two fermionic isotopes. Flexible optical trapping of Rb and Yb was achieved with a two-color dipole trap of 532 and 1064 nm, and we observed thermalization in ultracold mixtures of Rb and Yb. Using the Rb-blind optical lattice, we measured very small light shifts of 87-Rb BECs near the light shift zero-wavelengths adjacent the 6p electronic states, through a coherent series of lattice pulses. The positions of the zero-wavelengths are sensitive to the electric dipole matrix elements between the 5s and 6p states, and we made the first experimental measurement of their strength. By measuring a light shift, we were not sensitive to excited state branching ratios, and we achieved a precision better than 0.3%

Magnetic Feshbach resonances between atoms in 2^2S and 3^3P0_0 states: mechanisms and dependence on atomic properties

Magnetically tunable Feshbach resonances exist in ultracold collisions between atoms in 2 S and 3 P 0 states, such as an alkali-metal atom colliding with Yb or Sr in a clock state. We investigate the mechanisms of these resonances and identify the terms in the collision Hamiltonian responsible for them. They involve indirect coupling between the open and closed channels, via intermediate channels involving atoms in 3 P 1 states. The resonance widths are generally proportional to the square of the magnetic field and are strongly enhanced when the magnitude of the background scattering length is large. For any given pair of atoms, the scattering length can be tuned discretely by choosing different isotopes of the 3 P 0 atom. For each combination of an alkali-metal atom and either Yb or Sr, we consider the prospects of finding an isotopic combination that has both a large background scattering length and resonances at a high but experimentally accessible field. We conclude that 87 Rb + Yb , Cs + Yb , and 85 Rb + Sr are particularly promising combinations

Strengths of near-threshold optical Feshbach resonances

Optical Feshbach resonances allow one to control cold atomic scattering, produce ultracold molecules and study atomic interactions via photoassociation spectroscopy. Here we give practical analytic expressions for the strength parameter, the optical length, of Feshbach resonances due to near-threshold bound states of an excited molecular state dominated by either a resonant-dipole or van der Waals interaction. For example, for a laser intensity $I$, binding energy $E_b$, $s$-wave scattering length $a$, and Condon point $R_C$, the optical length for a very weakly bound resonant-dipole state is $l_{\rm opt} \propto I (a-R_C)^2/\sqrt{-E_b}$. We also extend the utility of the optical length to associative STIRAP in 3D optical lattices by showing the free-bound Rabi frequency to be proportional to $\Omega_{\rm FB} \propto \sqrt{l_{\rm opt}} \omega_{\rm trap}^{3/4}$ for a trapping frequency $\omega_{\rm trap}$.Comment: 8 pages, 4 figures, plenty handy formula

Degenerate mixtures of rubidium and ytterbium for engineering open quantum systems

In the last two decades, experimental progress in controlling cold atoms and ions now allows us to manipulate fragile quantum systems with an unprecedented degree of precision. This has been made possible by the ability to isolate small ensembles of atoms and ions from noisy environments, creating truly closed quantum systems which decouple from dissipative channels. However in recent years, several proposals have considered the possibility of harnessing dissipation in open systems, not only to cool degenerate gases to currently unattainable temperatures, but also to engineer a variety of interesting many-body states. This thesis will describe progress made towards building a degenerate gas apparatus that will soon be capable of realizing these proposals. An ultracold gas of ytterbium atoms, trapped by a species-selective lattice will be immersed into a Bose-Einstein condensate (BEC) of rubidium atoms which will act as a bath. Here we describe the challenges encountered in making a degenerate mixture of rubidium and ytterbium atoms and present two experiments performed on the path to creating a controllable open quantum system. The first experiment will describe the measurement of a tune-out wavelength where the light shift of \Rb{87} vanishes. This wavelength was used to create a species-selective trap for ytterbium atoms. Furthermore, the measurement of this wavelength allowed us to extract the dipole matrix element of the $5s \rightarrow 6p$ transition in \Rb{87} with an extraordinary degree of precision. Our method to extract matrix elements has found use in atomic clocks where precise knowledge of transition strengths is necessary to account for minute blackbody radiation shifts. The second experiment will present the first realization of a degenerate Bose-Fermi mixture of rubidium and ytterbium atoms. Using a three-color optical dipole trap (ODT), we were able to create a highly-tunable, species-selective potential for rubidium and ytterbium atoms which allowed us to use \Rb{87} to sympathetically cool \Yb{171} to degeneracy with minimal loss. This mixture is the first milestone creating the lattice-bath system and will soon be used to implement novel cooling schemes and explore the rich physics of dissipation