Theoretical Studies of Ultracold Dipolar Molecules

Strongly interacting ultracold dipolar molecules are a rich platform for quantum information and quantum simulation of phenomena relevant to condensed matter systems. This dissertation presents novel theoretical and computational studies of ultracold dipolar molecules relevant to these areas in three broad categories./nFirst, the path integral ground state quantum Monte Carlo method is extended to simulations with both translational and rotational degrees of freedom, including the development of a novel estimator of the elementary excitation energies of a system with these degrees of freedom based on the well known Feynman-Bijl approximation. This is then used to study dipolar molecular ensembles confined to one-dimensional optical lattices. The ground state phase diagram is characterized with both a mean-field method and the aforementioned quantum Monte Carlo method. A quantum phase transition is found for very short optical lattice spacings or very large dipole moments. The prospects for experimentally realizing a system which exhibits this phase transition are discussed./nSecond, the path integral ground state quantum Monte Carlo method is utilized to study the ground state of dipole molecules confined to two-dimensional optical lattices. On square lattices a crossover from a weakly interacting disordered phase to a strongly interacting striped phase is found for short lattice spacings or large dipole moments. On triangular lattices a crossover between a disordered phase and a completely polarized phase is found, also for short lattice spacings or large dipole moments. The relevance of such simulations to self-assembled dipolar crystals in two dimensions is discussed and simulation results of these systems are presented. Simulations of polarized and harmonically confined molecular systems in two dimensions with translations and rotations are also presented and a realistic interaction potential using highly accurate ab initio quantum chemistry techniques is calculated for LiH--LiH interactions as a preliminary step toward developing a high quality trial wave function for the simulation of systems possessing both translational and rotational degrees of freedom./nFinally, several novel applications for dipolar molecules confined to optical lattices are proposed. An experimental realization of a topological phase using $^2\Sigma$ ground state molecules with applied near resonant microwave fields and transverse magnetic fields is proposed. A method to create an array of dipole-coupled two-level molecules exhibiting superradiance and possessing novel spectroscopic properties using $^1\Sigma$ ground state molecules in the combination of a far off-resonant laser field and a moderate magnetic field is proposed. Additionally, a method to create entangled pairs of molecules using closed-shell dipolar molecules immersed in an intense far off-resonant laser field is reviewed and an extension in which parallel optical lattices are merged and molecules are allowed to collide in the presence of a far off-resonant laser field is proposed. Simulation results are presented indicating that a significant amount of entanglement may be generated in such a way in realistic molecular systems.

Advisor: Whaley, K. Birgitta