  Algorithmic cooling methods manipulate an open quantum system in order to
lower its temperature below that of the environment. We show that significant
cooling is achieved on an ensemble of spin-pair systems by exploiting the
long-lived nuclear singlet state, which is an antisymmetric quantum
superposition of the "up" and "down" qubit states. The effect is demonstrated
by nuclear magnetic resonance (NMR) experiments on a molecular system
containing a coupled pair of near-equivalent 13C nuclei. The populations of the
system are subjected to a repeating sequence of cyclic permutations separated
by relaxation intervals. The long-lived nuclear singlet order is pumped well
beyond the unitary limit, and the nuclear magnetization is enhanced by 21%
relative to its thermal equilibrium value. To our knowledge this is the first
demonstration of algorithmic cooling using a quantum superposition state and
without making a distinction between rapidly and slowly relaxing qubits.
