# Quantum dynamics of a few-photon parametric oscillator

## TL;DR

This paper demonstrates a microwave quantum parametric oscillator operating with few photons, capable of generating nonclassical superposition states, and develops techniques for characterizing its quantum states, advancing quantum information processing.

## Contribution

It introduces a quantum parametric oscillator at microwave frequencies with the ability to produce and analyze nonclassical states, including Schrödinger's cat states, in a nonlinear resonator.

## Key findings

- Oscillator operates with only a few photons.
- System can generate superpositions of phases, creating Schrödinger's cat states.
- Developed quantum state tomography for nonlinear resonators.

## Abstract

Modulating the frequency of a harmonic oscillator at nearly twice its natural frequency leads to amplification and self-oscillation. Above the oscillation threshold, the field settles into a coherent oscillating state with a well-defined phase of either $0$ or $\pi$. We demonstrate a quantum parametric oscillator operating at microwave frequencies and drive it into oscillating states containing only a few photons. The small number of photons present in the system and the coherent nature of the nonlinearity prevents the environment from learning the randomly chosen phase of the oscillator. This allows the system to oscillate briefly in a quantum superposition of both phases at once - effectively generating a nonclassical Schr\"{o}dinger's cat state. We characterize the dynamics and states of the system by analyzing the output field emitted by the oscillator and implementing quantum state tomography suited for nonlinear resonators. By demonstrating a quantum parametric oscillator and the requisite techniques for characterizing its quantum state, we set the groundwork for new schemes of quantum and classical information processing and extend the reach of these ubiquitous devices deep into the quantum regime.