Towards two dimensional synthetic lattice of momentum states

We describe progress towards an experimental platform for engineering two dimensional synthetic lattices based on laser coupled atomic momentum states of potassium-39 atoms. This technique allows for the local and time-dependent control over nearly all system parameters, including tunneling phases, which makes it suitable for studying a range of novel transport phenomena in two-dimensional lattices. We describe how an arrangement of three equally separated in-plane Bragg lasers can be used as a versatile setup for realizing triangular lattices, honeycomb lattices, Kagome lattices, and Hofstadter model. The ability to augment these various two-dimensional lattices with disorder or other forms of parameter variation promises to allow for the exploration of a broad range of lattice physics. We additionally describe the experimental progress towards creating Bose-Einstein condensates of potassium-39 atoms, the control of atomic interactions by a Feshbach resonance, and the implementation of two-dimensional momentum state synthetic lattices.