Sideband cooling of small ion Coulomb crystals in a Penning trap

Abstract

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.

14 pages, 8 figures