Abstract
In this thesis, we present experimental methods and results for direct measurements of the photoassociation of two individual ultra-cold rubidium-85 atoms, each prepared in the |F = 2,m_F = −2⟩ ground state. From there two individual rubidium-85 atoms are loaded into separate far-off resonance optical tweezers which are near-deterministically prepared into |F = 2,m_F = −2⟩. The two optical tweezers are then merged and the atoms are exposed to photoassociation light. To ensure the correct frequency of photoassociation light is used a dual cavity locking scheme, capable of generating frequencies with a stability of ±425.7 kHz over a large wavelength range for use in photoassociation spectroscopy, was developed. From there, a light modulation technique is implemented to isolate the photoassociation event from unwanted far-off resonance trap effects, such as the AC Stark shift. By controlling the intensity, frequency, and duration parameters of the photoassociation pulses applied to the rubidium atoms, frequency-dependent, and time-dependent atom loss is observed for a single band of the 0^{+}_{u} series; located at 377.00067±0.00006 THz. The resonance and linewidth data exhibits the same behaviour as photoassociation performed on large atom ensembles within the many-body regime. However, two distinct fast and slow photoassociation rates are observed in contrast to the many-body regime where only a single photoassociation rate constant, K_{PA}, has been reported. This marks a novel physical process which heretofore has not been reported in the field of atomic or molecular physics.