Precision Franck-Condon spectroscopy from highly-excited vibrational states

As per the Franck-Condon principle, absorption spectroscopy reveals changes in nuclear geometry in molecules or solids upon electronic excitation. It is often assumed these changes cannot be resolved beyond the ground vibrational wavefunction width ($\sqrt{\hbar/m\omega}$). Here, we show this resolution dramatically improves with highly-excited vibrational initial states (with occupation number $\langle n\rangle$). These states magnify changes in geometry by $2\langle n\rangle +1$, a possibly counterintuitive result given the spatial uncertainty of Fock states grows with $n$. We also discuss generalizations of this result to multimode systems. Our result is relevant to optical spectroscopy, polariton condensates, and quantum simulators ($\textit{e.g.}$, boson samplers).