Franck-Condon spectroscopy for precision measurements

In molecular and solid-state spectroscopy, the displaced harmonic oscillator is a standard paradigm. In this work, we present features of this simple model that were previously overlooked and outline potential applications in precision measurements. Contrary to standard practice, we choose initial states that are not the vibrational ground state. Specifically, we look at Fock states and coherent states. Using this, we propose a measurement scheme for displacement based on Franck-Condon spectroscopy. Furthermore, we identify length scales associated with vibrational Fock states that determine the precision of these measurements. Notably, our proposed scheme does not surpass the standard quantum limit, therefore, coherent states achieve similar levels of precision as Fock states. Our measurement scheme may also be implemented within boson sampling and opens new avenues for precision measurements in molecular systems using spectroscopy.