# Tunable and nonlinearity-enhanced dispersive-plus-dissipative coupling in photon-pressure circuits

## TL;DR

This paper presents a new photon-pressure circuit platform that combines tunable dispersive and dissipative coupling, enhancing nonlinear interactions and enabling new quantum control possibilities.

## Contribution

The work introduces a nonlinearity-enhanced combination of dispersive and dissipative coupling in photon-pressure circuits with tunable parameters.

## Key findings

- The coupling rates scale stronger with pump photon number than the usual square root dependence.
- A Fano-like response is observed in photon-pressure induced transparency due to coupling interference.
- Dynamical backaction is modified, including a parametric instability from a red-detuned pump tone.

## Abstract

Photon-pressure circuits are the circuit implementation of the cavity optomechanical Hamiltonian and discussed for qubit readout, low-frequency quantum photonics and dark matter axion detection. Due to the enormous design flexibility of superconducting circuits, photon-pressure systems provide fascinating possibilities to explore unusual parameter regimes of the optomechanical Hamiltonian. Here, we report the realization of a photon-pressure platform, in which a GHz circuit interacts with a MHz circuit via a magnetic-flux-tunable combination of dispersive and dissipative photon-pressure. In addition, both coupling rates are considerably enhanced by nonlinearities of the GHz-mode, which leads to the multi-photon coupling rates scaling stronger with the pump photon number nc than the usual \documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{{n}_{\mathrm{c}}}$$\end{document}nc dependence. We demonstrate that interference of the two interaction paths leads to a Fano-like response in photon-pressure induced transparency, and that the dynamical backaction is considerably modified compared to the dispersive case, including a parametric instability caused by a red-detuned pump tone.

This work demonstrates a nonlinearity-enhanced combination of dispersive and dissipative coupling in photon-pressure circuits, a circuit-QED analog of optomechanics, and reveals how transparency and backaction are modified by coupling-interference. The results hold relevance for radiation-pressure systems, (quantum) control protocols and Hamiltonian simulation.