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Using a Bang-Bang optimal control (BB) technique, we transfer polarizationfrom abundant high-$\gamma$ nuclei directly to singlet order. This approach isanalogous to algorithmic cooling (AC) procedure used in quantum statepurification. Specifically, we apply this method for enhancing the singletorder in a natural abundant $^{13}$C-$^{13}$C spin pair using a set of nineequivalent protons of an 11-spin system. Compared to the standard method notinvolving polarization transfer, we find an enhancement of singlet order byabout three times. In addition, since the singlet magnetization is contributedby the faster relaxing protons, the recycle delay is halved. Thus effectivelywe observe a sensitivity enhancement by 4.2 times or a reduction in the overallexperimental time by a factor of 18. We also discuss a possible extension ofAC, known as heat-bath algorithmic cooling (HBAC).

Bang-Bang Optimal Control of Large Spin Systems: Enhancement of $^{13}$C-$^{13}$C Singlet-Order at Natural Abundance