  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.

Atomic Physics