G. Stutter

We have recently demonstrated the laser cooling of a single $^{40}$Ca$^+$ ion to the motional ground state in a Penning trap using the resolved-sideband cooling technique on the electric quadrupole transition S$_{1/2} \leftrightarrow$ D$_{5/2}$. Here we report on the extension of this technique to small ion Coulomb crystals made of two or three $^{40}$Ca$^+$ ions. Efficient cooling of the axial motion is achieved outside the Lamb-Dicke regime on a two-ion string along the magnetic field axis as well as on two- and three-ion planar crystals. Complex sideband cooling sequences are required in order to cool both axial degrees of freedom simultaneously. We measure a mean excitation after cooling of $\bar n_\text{COM}=0.30(4)$ for the centre of mass mode and $\bar n_\text{B}=0.07(3)$ for the breathing mode of the two-ion string with corresponding heating rates of 11(2) s$^{-1}$ and 1(1) s$^{-1}$ at a trap frequency of 162 kHz. The ground state occupation of the axial modes is above 75% for the two-ion planar crystal and the associated heating rates 0.8(5) s$^{-1}$ at a trap frequency of 355 kHz.

We report the laser cooling of a single $^{40}\text{Ca}^+$ ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole $S_{1/2}\leftrightarrow D_{5/2}$ transition, broadened by a quench laser coupling the $D_{5/2}$ and $P_{3/2}$ levels. We find the final ground state occupation to be $98\pm1\%$. We measure the heating rate of the trap to be very low with $\dot{\bar{n}}\approx 0.3\pm0.2\textrm{s}^{-1}$ for trap frequencies from $150-400\textrm{kHz}$, consistent with the large ion-electrode distance.