  Using a Bang-Bang optimal control (BB) technique, we transfer polarization
from abundant high-$\gamma$ nuclei directly to singlet order. This approach is
analogous to algorithmic cooling (AC) procedure used in quantum state
purification. Specifically, we apply this method for enhancing the singlet
order in a natural abundant $^{13}$C-$^{13}$C spin pair using a set of nine
equivalent protons of an 11-spin system. Compared to the standard method not
involving polarization transfer, we find an enhancement of singlet order by
about three times. In addition, since the singlet magnetization is contributed
by the faster relaxing protons, the recycle delay is halved. Thus effectively
we observe a sensitivity enhancement by 4.2 times or a reduction in the overall
experimental time by a factor of 18. We also discuss a possible extension of
AC, known as heat-bath algorithmic cooling (HBAC).
