Quantum Mie scattering and metrology with a Fabry-Perot interferometer and quantum states of light

We present a model for quantum Mie scattering in one dimension, and show that quantum states of light, such as Fock states, exhibit the same transmission functions as coherent states for an ordinary intensity measurement. If a number-resolving measurement is carried out instead, we observe narrower transmission functions than for the classical case. We discuss applications of this effect for high-precision length measurements in interferometry.