Two-tone Doppler cooling of radial two-dimensional crystals in a radio-frequency ion trap

We study the Doppler-cooling of radial two-dimensional (2D) Coulomb crystals trapped barium ions in a radiofrequency trap. Ions 2D experience micromotion an amplitude that increases linearly with distance from trap center, leading to position-dependent frequency modulation laser light each ion's rest frame. use two tones separated by approximately 100 MHz efficiently cool distinct regions differing amplitudes micromotion. This technique allows us and more than 50 populating four shells crystal, where single tone Doppler cooling we are limited 30 three shells. also individually characterize all within this information locate center determine Matthieu parameters ${q}_{x}$ ${q}_{y}$.