The inverse parametric problem

TL;DR

This paper introduces a method to calculate and control frequency components in a parametric oscillator, enabling complex mode scattering and routing, with applications in quantum information processing.

Contribution

It presents a novel computational approach for mode scattering control and demonstrates its effectiveness through experiments and numerical analysis.

Findings

Successfully realized complex mode scattering at microwave frequencies

Demonstrated non-reciprocal mode circulation

Developed a rapid mode routing technique

Abstract

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.