Sub-Doppler cooling of a trapped ion in a phase-stable polarization gradient

Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing more tailorable light-matter interactions in general. In this paper, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of $2\pi\cdot1.45~ \rm MHz$ we achieve $\langle n \rangle = 1.3 \pm 1.1$ in $500~\mu \rm s$ and cooling rates of ${\sim}0.3 \, \rm quanta/\mu s$. We examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a simple model. Cooling is fast and power-efficient, with improved performance compared to simulated operation under the corresponding running wave configuration.