A Generalized Theory for Optical Cooling of a Trapped Atom with Spin

Cooling atoms to the ground-state of optical tweezers is becoming increasingly important for high-fidelity imaging, cooling, and molecular assembly. While extensive theoretical work has been conducted on cooling in free space, fewer studies have focused on cooling in bound states. In this work, we present a unified formalism for optical cooling mechanisms in neutral atom tweezers, including resolved and unresolved sideband cooling with different trapping potentials, polarization gradient cooling, gray molasses cooling, \(\Lambda\)-enhanced gray molasses cooling, and Raman sideband cooling. We perform simulations and demonstrate good agreement with a simplified spin model. We derive and discuss the fundamental limits of each cooling mechanism and propose new strategies for achieving ground-state cooling in optical tweezers. Our findings provide valuable insights into optimizing cooling schemes for neutral atoms in optical tweezers, paving the way for minimizing thermal decoherence in Rydberg and molecular gates and improving efficiencies of molecular assembly.