  Achieving high energy resolution in spin systems is important for fundamental
physics research and precision measurements, with alkali-noble-gas
comagnetometers being among the best available sensors. We found a new
relaxation mechanism in such devices, the gradient of the
Fermi-contact-interaction field that dominates the relaxation of hyperpolarized
nuclear spins. We report on precise control over spin distribution,
demonstrating a tenfold increase of nuclear spin hyperpolarization and
transverse coherence time with optimal hybrid optical pumping. Operating in the
self-compensation regime, our $^{21}$Ne-Rb-K comagnetometer achieves an
ultrahigh inertial rotation sensitivity of $3\times10^{-8}$\,rad/s/Hz$^{1/2}$
in the frequency range from 0.2 to 1.0 Hz, which is equivalent to the energy
resolution of $3.1\times 10^{-23}$\,eV/Hz$^{1/2}$. We propose to use this
comagnetometer to search for exotic spin-dependent interactions involving
proton and neutron spins. The projected sensitivity surpasses the previous
experimental and astrophysical limits by more than four orders of magnitude.
