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  • Open Access

Solving the inverse parametric problem

Michele Cortinovis, Fabio Lingua*, and David B. Haviland

  • *Contact author: lingua@kth.se
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Phys. Rev. Applied 26, 014007 – Published 6 July, 2026

DOI: https://doi.org/10.1103/1bdh-lcxq

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 frequency 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 nonreciprocal 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 multimodal Gaussian states.

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Phys. Rev. Applied 26, 014007– Published 6 July, 2026
  • Received 17 December 2025
  • Revised 15 March 2026
  • Accepted 29 May 2026
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