Multiphoton Scattering Tomography with Coherent States

We have proposed an experimental procedure to reconstruct the scattering matrix of an unknown quantum system interacting with propagating photons. Our method requires coherent state laser or microwave inputs and homodyne detection at the scatterer's output, and provides simultaneous information about multiple ---elastic and inelastic--- segments of the scattering matrix. The method is resilient to detector noise and its errors can be made arbitrarily small by combining experiments at various laser powers. Finally, we show that the tomography of scattering has to be performed using pulsed lasers to efficiently gather information about the nonlinear processes in the scatterer. The techniques in this work are general, allowing a full characterization of how a small quantum system interacts with the environment, and it is particularly well suited for working with superconducting circuits. This work has been published in Tomás Ramos, Juan José García-Ripoll, Phys. Rev. Lett. 119, 153601 (2017).