Limits on new long range nuclear spin-dependent forces set with a K-3He co-magnetometer

A magnetometer using spin-polarized K and ${}^3$He atoms occupying the same volume is used to search for anomalous nuclear spin-dependent forces generated by a separate ${}^3$He spin source. We measure changes in the ${}^3$He spin precession frequency with a resolution of 18 pHz and constrain anomalous spin forces between neutrons to be less than $2\times {10}^{-8}$ of their magnetic or less than $2\times {10}^{-3}$ of their gravitational interactions on a length scale of 50 cm. We present new limits on neutron coupling to light pseudoscalar and vector particles, including torsion, and constraints on recently proposed models involving unparticles and spontaneous breaking of Lorentz symmetry.