Magic Wavelengths and Dipole-Dipole Interactions in Ultracold RbCs Molecules

Ultracold polar molecules have become the subject of burgeoning fields of research in recent years owing to their prospects in quantum simulation, quantum computation and precision measurement. Their relatively large ground state dipole moment, coupled with a complex internal structure forms an incredibly powerful toolbox in which to perform quantum science experiments. Unfortunately, spatial confinement using light, which is necessary for many of the aforementioned applications, causes differential ac Stark shifts between quantum states, limiting coherence times and stifling their applicability. By accessing a so-called magic condition, this effect can be eliminated. This thesis presents work towards producing a quantum simulator based on a bulk gas of 87Rb133Cs molecules. We develop a magic wavelength trap by exploring nominally forbidden transitions from the X1Σ + ground state to b 3Π0 states. By tuning our trapping laser between transitions to different vibrational states of b3Π0, we can arbitrarily tune the difference in polarisability between pairs of rotational states and engineer second-scale coherence times. When we trap our molecules in a superposition of rotational states that exhibit a dipole moment in the laboratory frame, we observe the effects of long-range dipole-dipole interactions between molecules. These dipole-dipole interactions form the basis for quantum simulation and computation applications, observations of which marks an important milestone for realising a quantum simulator using 87Rb133Cs. We then demonstrate a route to ground state 87Rb133Cs molecules that is compatible with a protocol for loading Feshbach molecules into an optical lattice, developed by researchers at the University of Innsbruck. This method can be combined with a magic wavelength trap to produce a sample of 87Rb133Cs molecules in a magic lattice. Finally, we engineer synthetic dimensions that simulate simple single-particle Hamiltonians by coupling multiple rotational states in 87Rb133Cs. This forms the foundations for utilising rotational states of diatomic molecules as a platform for exploring synthetic dimensions