Spin-orbit coupling in a strontium optical lattice clock

Synthetic gauge fields are a promising tool for creating complex Hamiltonians with ultracold neutral atoms that may mimic the fractional Quantum Hall effect and other topological states. A promising approach is to use spin-orbit coupling to treat an internal degree of freedom as an effective `synthetic' spatial dimension. Here, this synthetic dimension is comprised by the internal ground and excited states used for high-precision clock spectroscopy in a fermionic strontium optical lattice clock. We report on our progress towards this goal in a system where atoms tunnel through a 1D optical lattice during clock interrogation. We present measurements of the lattice band structure under varying Lamb-Dicke parameters and in a regime where s-wave collisions are expected to contribute density dependent frequency shifts.