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Complex physical systems provide a fertile ground for exploring various phenomena owing to the quantum nature inherent in their structure. Atoms and molecules not only serve as realistic systems for experimental investigation, but also exhibit a complexity stemming from their many-body interactions which is of significant theoretical interest. This thesis delves into the domain of ultracold collisions between different interacting species (where temperature T < 1mK), and introduces novel applications for probing such systems, particularly focusing on molecular formation via photoassociation. Molecular interactions, in comparison to their atomic counterparts, present heightened complexity. The interplay of electrostatic forces among electrons and nuclei intricately couples all degrees of freedom within a single molecule. Historically, the exploration of quantum dynamics between molecules was pioneered by Born and Oppenheimer. Their seminal work involved solving Schrödinger’s equation in two steps. First step is addressing a portion of the molecular Hamiltonian where the nuclei are clamped in space (adiabatic). This adiabatic solution yields effective potentials between nuclei, encapsulating the integrated influence of the surrounding electronic cloud. The second step is to solve for the nuclear degrees of freedom in the vicinity of the effective potentials. The validity of the Born-Oppenheimer approximation stems from the substantial mass disparity between electrons and nuclei, enabling a quasi-separation of the electronic and nuclear Hamiltonians. The first order Born-Oppenheimer approximation assumes a partial separation of the molecular wave function Ψmolecule ≈ ΞvibrationYrotationalΦelectronic. A comprehensive treatment is provided for systems with numerous degrees of freedom, elucidating how the Born-Oppenheimer approximation manifests when applied to molecules. This chapter also encapsulates the principal findings from collision theory and photoassociation spectroscopy, as well as foundational techniques underpinning this thesis. Spectroscopic investigations encompass four relevant transition types: boundbound (Rabi oscillations), bound-free (photoionization), free-free (elastic scattering), and free-bound (photoassociation) transitions. Photoassociation (PA) spectroscopy probes laserinduced processes where the reactants interact through a channel |i〉, and can absorb one or more photons causing a transition to a bound state in an excited channel |f〉. The excited complex usually decays with a high probability to the ground state of the formed molecule. The same process can be utilized experimentally to prepare a cold molecule in its vibrational ground state. Diatomic PA has been of great theoretical and experimental interest in recent years. Herein, we present a theoretical inquiry into photoassociation within triatomic systems, with a particular focus on alkali atom-dimer systems, and introduce a method for calculating PA rates.Moreover, this thesis presents different methods for shielding polar molecules from their short-range interactions where inelastic collisions and chemical reactions can occur with high probability. Shielding polar molecules has been shown to suppress inelastic collisions substantially between two molecules. A technique to shield two polar molecules in their ground state is studied and applied to model collisions in a gas of ground state (NaCs) molecules at temperatures T ≈ 100nK. The results show a region of interactions between two polar molecules that has an extremely long-range nature and is well isolated from the short-range losses, allowing for long-range spectroscopic studies. A new long-range regime of molecular physics arises in the study of shielded molecules where long-range vibrational tetramer states form. Different tetramer formation pathways are studied within a range of different shielding parameters. In fact, microwave shielding provides a region to study collisions between polar molecules, and controls their dynamics without worrying about shortrange losses. It has also been applied in the observation of a Bose gas of polar molecules. |
