Search for long-range anomalous spin dependent forces using a K-$^{3}$He co-magnetometer

Various theories propose new long-range forces. We test the existence of long range spin dependent forces between neutrons. We use a K-$^{3}$He co-magnetometer with a sensitivity of 1 fT/Hz$^{1/2}$ and a spin-source of hyperpolarized $^{3}$He gas with about 10$^{22}$ polarized spins. The co-magnetometer is insensitive to ordinary magnetic fields but sensitive to interactions with anomalous coupling to electronic or nuclear spin. Nuclear spin polarization of a 12 amagat $^{3}$He cell is achieved through spin exchange optical pumping. The separation of the spin-source from the co-magnetometer is approximately 50 cm. The $^{3}$He spin polarization is reversed using Adiabatic Fast Passage every 10 sec with losses of about 2$\times $10$^{-5}$ per flip. We look for a signal in the co-magnetometer correlated with the modulation of the spin source. Present sensitivity of the experiment to the neutron spin coupling constant (g$_{n}^{2}$/4$\pi )$ for light pseudoscalar particles is in the range of 10$^{-9}$, about an order of magnitude better than existing limits from gravitational weak equivalence principle and inverse square law tests, with further improvement anticipated.