A single-atom 3D sub-attonewton force sensor

All physical interactions are mediated by forces. Ultra-sensitive force measurements are therefore a crucial tool for investigating the fundamental physics of magnetic, atomic, quantum, and surface phenomena. Laser cooled trapped atomic ions are a well controlled quantum system and a standard platform for precision metrology. Their low mass, strong Coulomb interaction, and readily detectable fluorescence signal make trapped ions favourable for performing high-sensitivity force measurements. Here we demonstrate a three-dimensional sub-attonewton sensitivity force sensor based on super-resolution imaging of the fluorescence from a single laser cooled $^{174}$Yb$^+$ ion in a Paul trap. The force is detected by measuring the net ion displacement with nanometer precision, and does not rely on mechanical oscillation. Observed sensitivities were 372$\pm$9$_\mbox{stat}$, 347$\pm$12$_\mbox{sys}\pm$14$_\mbox{stat}$, and 808$\pm$29$_\mbox{sys}\pm$42$_\mbox{stat}$ zN/$\sqrt{\mbox{Hz}}$ in the three dimensions, corresponding to 24x, 87x, and 21x of the quantum limit. We independently verified the accuracy of this apparatus by measuring a light pressure force of 95 zN on the ion, an important systematic effect in any optically based force sensor. This technique can be applied for sensing DC or low frequency forces external to the trap or internally from a co-trapped biomolecule or nanoparticle.