Solving the inverse parametric problem

We present a method to calculate the frequency components of a pump waveform driving a parametric oscillator, which realizes a desired frequency mixing or scattering between modes.

The method is validated by numerical analysis and we study its sensitivity to added Gaussian noise.

A series of experiments apply the method and demonstrate its ability to realize complex scattering processes involving many modes at microwave frequencies, including non-reciprocal mode circulation.

We also present an approximate method to dynamically control mode scattering, capable of rapidly routing signals between modes in a prescribed manner.

These methods are useful tools for encoding and manipulating continuous variable quantum information with multi-modal Gaussian states.