  High resolution resonant inelastic x-ray scattering has been performed to
reveal the role of lattice-coupling in a family of quasi-1D insulating
cuprates, Ca$_{2+5x}$Y$_{2-5x}$Cu$_5$O$_{10}$. Site-dependent low energy
excitations arising from progressive emissions of a 70 meV lattice vibrational
mode are resolved for the first time, providing a direct measurement of
electron-lattice coupling strength. We show that such electron-lattice coupling
causes doping-dependent distortions of the Cu-O-Cu bond angle, which sets the
intra-chain spin exchange interactions. Our results indicate that the lattice
degrees of freedom are fully integrated into the electronic behavior in low
dimensional systems.
