Kuramoto synchronization of quantum tunneling polarons for describing the dynamic structure in cuprate superconductors

A major open topic in cuprates is the interplay between the lattice and electronic dynamics and the importance of their coupling to the mechanism of high-temperature superconductivity (HTSC). As evidenced by Extended X-ray Absorption Fine Structure experiments (EXAFS), anharmonic structural effects are correlated with the charge dynamics and the transition to a superconducting phase in different HTSC compounds. Here we describe how structural anharmonic effects can be coupled to electronic and lattice dynamics in cuprate systems by performing the exact diagonalization of a prototype anharmonic many-body Hamiltonian on a relevant six-atom cluster and show that the EXAFS results can be understood as a Kuramoto synchronization between coupled internal quantum tunneling polarons associated with the two-site distribution of the copper-apical-oxygen ($Cu-O_{ap}$) pair in the dynamic structure. Furthermore, we find that this first order, anti-phase synchronization transition can be fine tuned by temperature and anharmonicity of the lattice vibrations, and promotes the pumping of charge, initially stored at the apical oxygen reservoirs, into the copper-oxide planes. Simultaneously, the internal quantum tunneling polaron extends to the copper-planar-oxygen ($Cu-O_{pl}$) pair. All these findings support an interpretation of the EXAFS data in terms of an effective, quantum mechanical triple-well-potential, which accurately represents the anti-phase synchronization of apical oxygens displacements and lattice-assisted charge transfer to the $CuO_2$ plane.