  The ability to detect extremely small forces is vital for a variety of
disciplines including precision spin-resonance imaging, microscopy, and tests
of fundamental physical phenomena. Current force-detection sensitivity limits
have surpassed 1 $aN/\sqrt{Hz}$ (atto $=10^{-18}$) through coupling of micro or
nanofabricated mechanical resonators to a variety of physical systems including
single-electron transistors, superconducting microwave cavities, and individual
spins. These experiments have allowed for probing studies of a variety of
phenomena, but sensitivity requirements are ever-increasing as new regimes of
physical interactions are considered. Here we show that trapped atomic ions are
exquisitely sensitive force detectors, with a measured sensitivity more than
three orders of magnitude better than existing reports. We demonstrate
detection of forces as small as 174 $yN$ (yocto $=10^{-24}$), with a
sensitivity 390$\pm150$ $yN/\sqrt{Hz}$ using crystals of $n=60$ $^{9}$Be$^{+}$
ions in a Penning trap. Our technique is based on the excitation of normal
motional modes in an ion trap by externally applied electric fields, detection
via and phase-coherent Doppler velocimetry, which allows for the discrimination
of ion motion with amplitudes on the scale of nanometers. These experimental
results and extracted force-detection sensitivities in the single-ion limit
validate proposals suggesting that trapped atomic ions are capable of detecting
of forces with sensitivity approaching 1 $yN/\sqrt{Hz}$. We anticipate that
this demonstration will be strongly motivational for the development of a new
class of deployable trapped-ion-based sensors, and will permit scientists to
access new regimes in materials science.
