We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a ${}^{40}\mathrm{Ca}^{+}$ ion confined in a compact Penning trap operating with a magnetic field of 0.91 T. Using the same set of laser beams as required for the initial Doppler laser cooling operation, we detune the laser frequencies to produce a narrow two-photon dark resonance. The process achieves a $1/e$ cooling time constant of $108\left(8\right)\mu \text{s}$, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in $800\mu \mathrm{s}$ as measured by resonantly probing an electric quadrupole transition near 729 nm. A parametric drive is applied to the trap electrodes, which coherently exchanges the axial mode occupation with that of each radial mode, allowing for three-dimensional sub-Doppler cooling using only the axially propagating laser beams. This sub-Doppler cooling is achieved for an axial oscillation frequency of ${\omega }_z=2\pi \times 221\mathrm{kHz}$, which places the motion well outside the Lamb-Dicke confinement regime at the Doppler laser cooling limit. Our measured cooling rate and final mode occupation are in good agreement with a semiclassical model which combines a Lindblad master equation solution for ion-photon interactions with classical harmonic-oscillator motion of the trapped ion.

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• Permanent magnets
• Trapped ions
• Atom & ion cooling
• Cooling & trapping
• Lindblad equation
• Penning traps