Efficient Three-Dimensional Sub-Doppler Cooling of $^{40}$Ca$^+$ in a Penning Trap

TL;DR

This paper demonstrates a highly efficient three-dimensional sub-Doppler laser cooling method for $^{40}$Ca$^+$ ions in a Penning trap, achieving near ground-state cooling using a novel two-photon dark resonance technique.

Contribution

It introduces a new sub-Doppler cooling approach in a Penning trap that uses a single laser beam configuration and a parametric drive to cool all three motional modes effectively.

Findings

Achieved cooling of axial mode from 72 to 1.5 quanta.

Cooling time constant of approximately 108 microseconds.

Good agreement with a semiclassical theoretical model.

Abstract

We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a $^{40}$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(8) $\mu$s, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in 800 $\mu$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 kHz, which places the motion well outside of 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.