# Phase-slip oscillator: few-photon non-linearities

## TL;DR

This paper introduces a superconducting oscillator with phase-slip non-linearities that oscillate with photon number, enabling new quantum effects and potential experimental verification of coherent phase-slips.

## Contribution

It demonstrates that phase-slip induced non-linearities oscillate with photon number, unlike previous featureless non-linearities, opening new avenues for quantum applications.

## Key findings

- Non-linearities oscillate with photon number N.
- Multiple metastable states with few photons.
- Oscillatory responses of the resonator.

## Abstract

Non-linear effects on driven oscillations are important in many fields of physics, ranging from applied mechanics to optics. They are instrumental for quantum applications. A limitation is that the non-linearities known up to now are featureless functions of the number of photons N in the oscillator. Here we show that the non-linearities found in an oscillator where superconducting inductance is subject to coherent phase-slips, are more interesting. They oscillate as a function of number of photons N with a period of the order of square root of N, which is the spread of the coherent state. We prove that such non-linearities result in multiple metastable states encompassing few photons and study oscillatory dependence of various responses of the resonator. The experimental realization of our proposal can deliver an unambiguous verification of coherent quantum phase-slips.