Sensing weak forces and electric fields with trapped ion crystals*

When cooled to near the Doppler limit, ion plasmas confined in a Penning trap form two and three-dimensional crystals, which provide a useful platform for quantum simulation and sensing experiments. This talk will focus on recent experiments to measure small displacements, and hence weak forces and electric fields, using single-plane crystals consisting of several hundred Be$^{+}$ ions. By coupling the spin and motional degrees of freedom of the ions through the application of a spin-dependent optical dipole force, displacements of $50\,$pm ($40\times$ smaller than the ground-state wavefunction) are measured with a single measurement signal-to-noise ratio of 1. This displacement sensitivity is calibrated by driving the axial motion of the crystal far from the center-of-mass mode frequency, and implies $12\,\mathrm{yN}/\sqrt{\mathrm{Hz}}$ and $77\,(\mathrm{uV/m})/\sqrt{\mathrm{Hz}}$ sensitivities to forces and electric fields, respectively. When driving on-resonance with the center-of-mass mode, the sensitivity to weak forces and electric fields is greatly improved, but new limitations arise from frequency fluctuations of this mode.