# Parametric effects in circuit quantum electrodynamics

## TL;DR

This paper reviews recent progress in quantum parametric phenomena in superconducting circuits, focusing on theoretical foundations, experimental advances, and applications in quantum amplification, frequency conversion, and entanglement.

## Contribution

It provides a comprehensive overview of physical processes, theoretical models, and experimental results in quantum parametric effects within circuit quantum electrodynamics.

## Key findings

- Development of quantum limited parametric amplifiers
- Observation of quantum noise squeezing and photon entanglement
- Experimental demonstration of nonlinear down-conversion and oscillations

## Abstract

We review recent advances in the research on quantum parametric phenomena in superconducting circuits with Josephson junctions. We discuss physical processes in parametrically driven tunable cavity and outline theoretical foundations for their description. Amplification and frequency conversion are discussed in detail for degenerate and non-degenerate parametric resonance, including quantum noise squeezing and photon entanglement. Experimental advances in this area played decisive role in successful development of quantum limited parametric amplifiers for superconducting quantum information technology. We also discuss nonlinear down-conversion processes and experiments on self-sustained parametric and subharmonic oscillations.