Theory of cooling and imaging an atom in an optical tweezer

For any quantum simulation experiment using tweezers, the first essential step is to achieve motional ground state population by cooling the single atom at each site using single photon or two photon processes. Despite the established understanding of sub-Doppler cooling techniques like Polarization Gradient (PG) and Gray Molasses (GM) cooling in free space, their efficacy in tight traps and the quantum descriptions of these processes remain less explored. This is especially relevant to the case of neutral atoms, where it is not uncommon for the ground and excited states to have different polarizabilities. For instance, what are the coldest temperatures you can achieve using these methods and what are their theoretical limits? What is the mechanism behind GM cooling that results in significantly colder temperatures compared to PG cooling? While choosing among various cooling techniques in the tweezers, which method should be preferred to achieve the highest ground state population? Why does Raman sideband (RSB) cooling work far better than any other process and is there a way to circumvent this experimentally tedious technique while still reaching comparable ground state population? During this presentation, I will address all these questions and discuss simulations that support the theoretical framework for Rubidium (Rb) and Lithium (Li) under realistic experimental conditions. Our model will also provide a unified framework to compare all sub-Doppler cooling methods used for a single atom in a tweezer and present a criterion to get the highest possible ground state population via each route.