Revealing Correlated Electron-Nuclear Dynamics in Molecules with Energy-Resolved Population Image

We explore a new fashion, named energy-resolved population image (EPI), to represent on an equal footing the temporary electronic transition and nuclear motion during laser-molecular interaction. By using the EPI we have intuitively demonstrated the population transfer in vibrational H$_2^+$ exposed to extreme ultraviolet pulses, revealing the energy sharing rule for the correlated electron and nuclei. We further show that the EPI can be extended to uncover the origins of the distinct energy sharing mechanisms in multi-photon and tunneling regimes. The present study has clarified a long-standing issue about the dissociative ionization of H$_2^+$ and paves the way to identify instantaneous molecular dynamics in strong fields.