  Heat-Bath Algorithmic cooling (HBAC) techniques provide ways to selectively
enhance the polarization of target quantum subsystems. However, the cooling in
these techniques are bounded. Here we report the first experimental observation
of the HBAC cooling bound. We use HBAC to hyperpolarize nuclear spins in
diamond. Using two carbon nuclear spins as the source of polarization (reset)
and the 14N nuclear spin as the computation bit, we demonstrate that repeating
a single cooling step increases the polarization beyond the initial reset
polarization and reaches the cooling limit of HBAC. We benchmark the
performance of our experiment over a range of variable reset polarization. With
the ability to polarize the reset spins to different initial polarizations, we
envisage that the proposed model could serve as a test bed for studies on
Quantum Thermodynamics.
