Correlation of strontium anharmonicity with charge-lattice dynamics of the apical oxygens and their coupling to cuprate superconductivity

X-ray absorption spectra of both $YSr_2Cu_{2.75}Mo_{0.25}O_{7.54}$ and $Sr_2CuO_{3.3}$ show a remarkably strong, three-way correlation between: a) their Cu-apical-O pair distributions that constitute the Internal Quantum Tunneling Polaron (IQTP) component of their dynamic structures; b) their Cu-Sr pair distributions; and c) their superconductivity. Application of Kuramoto's synchronization technique to exact diagonalization calculations of a pair of IQTPs bridged by Sr and a planar O atom shows a first order phase transition to a synchronized state in which a fraction of the hole originally confined to the apical O atoms of the cluster is transferred onto the planar O. The resulting entanglement of the conducting and dielectric layers in combination with the $\ell = 2$ angular momentum of the synchronized IQTP dynamic network could be a critical component of the mechanism for d-wave pairing and condensation. This combination of experimental results and theory demonstrates the Sr-apical O dielectric layer of cuprates plays an important role in high temperature superconductivity via the collective charge dynamics of their IQTPs.