The achievable bounds of cooling quantum systems, and the possibility to violate them is not well-explored experimentally. For example, among the common methods to enhance spin polarization (cooling), one utilizes the low temperature and high-magnetic field condition or employs a resonant exchange with highly polarized spins. The achievable polarization, in such cases, is bounded either by Boltzmann distribution or by energy conservation. Heat-bath algorithmic cooling schemes (HBAC), on the other hand, have shown the possibility to surpass the physical limit set by the energy conservation and achieve a higher saturation limit in spin cooling. Despite, the huge theoretical progress, and few principle demonstrations, neither the existence of the limit nor its application in cooling quantum systems towards the maximum achievable limit have been experimentally verified. Here, we show the experimental saturation of the HBAC limit for single nuclear spins, beyond any available polarization in solid-state spin system, the Nitrogen-Vacancy centers in diamond. We benchmark the performance of our experiment over a range of variable reset polarizations (bath temperatures), and discuss the role of quantum coherence in HBAC.

冷却量子系统的可实现界限以及违反它们的可能性尚未通过实验进行充分探索。例如，在增强自旋极化（冷却）的常用方法中，有一种利用低温和高磁场条件或采用具有高极化自旋的共振交换。在这种情况下，可实现的极化受玻尔兹曼分布或能量守恒的限制。另一方面，热浴算法冷却方案 (HBAC) 已显示出超越能量守恒设定的物理极限并在自旋冷却中实现更高饱和极限的可能性。尽管有巨大的理论进步和很少的原理论证，极限的存在及其在冷却量子系统中向最大可实现极限的应用都没有经过实验验证。在这里，我们展示了单核自旋的 HBAC 极限的实验饱和，超出了固态自旋系统中任何可用的极化，金刚石中的氮空位中心。我们在一系列可变复位极化（浴温）上对我们的实验性能进行了基准测试，并讨论了量子相干性在 HBAC 中的作用。