Efficient Sub-Doppler Cooling of ⁴⁰Ca⁺ in a Permanent Magnet Penning Trap in the Weak-Confinement Regime

Penning trap arrays of single ions are identified as a potential quantum computing QCCD architecture. Doppler cooled ion temperatures in the weak confinement regime will prevent the highest fidelity operations. In Penning traps, sub-Doppler cooling with sideband excitation techniques typically requires >20 ms per mode. Instead, we demonstrate axial mode cooling from 73(23) to 1.5(3) in 800 us via a dark resonance cooling scheme. In order to cool each radial mode, we first cool the axial mode and then apply a parametric drive which exchanges the axial mode occupation with a radial mode occupation. Repeating this procedure for each radial mode achieves three-dimensional sub-Doppler cooling despite being well outside the Lamb Dicke confinement regime at the Doppler cooling limit. After 800 us of dark resonance cooling and 3 ms of sideband cooling per mode, we measure final mode occupations of 21(4), 15(2), and 0.12(6) for the magnetron (f_-=96 kHz), modified cyclotron (f₊=254 kHz), and axial modes (f_z = 221 kHz), respectively. The ion’s final radial mode occupations are limited to > 10 by the recoil heating of the ion during dark resonance and sideband cooling.  The measured cooling rate and final mode occupations are in good agreement with a semiclassical model describing the process.