  Spin bath polarization is the key to enhancing the sensitivity of quantum
sensing and information processing. Significant effort has been invested in
identifying the consequences of quantumness and its control for spin-bath
polarization. Here, by contrast, we focus on the adverse role of quantum
correlations (entanglement) in a spin bath that can impede its cooling in many
realistic scenarios. We propose to remove this impediment by modified cooling
schemes, incorporating probe-induced disentanglement via alternating,
non-commuting probe-bath interactions, so as to suppress the buildup of quantum
correlations in the bath. The resulting bath polarization is thereby
exponentially enhanced. The underlying thermodynamic principles have
far-reaching implications for quantum technological applications
