# Injection locking and parametric locking in a superconducting circuit

## TL;DR

This paper demonstrates injection and parametric locking in a superconducting circuit using a Josephson mixer, revealing new insights into frequency locking mechanisms relevant for quantum information technologies.

## Contribution

It introduces two locking schemes in a superconducting circuit and compares their behaviors, linking laser physics with superconducting quantum circuits.

## Key findings

- Locking range depends on pump and signal power.
- Both locking schemes successfully stabilize emission frequencies.
- Results align with Adler's laser theory.

## Abstract

When a signal is injected in a parametric oscillator close enough to its resonance, the oscillator frequency and phase get locked to those of the injected signal. Here, we demonstrate two frequency locking schemes using a Josephson mixer in the parametric down-conversion regime, pumped beyond the parametric oscillation threshold. The circuit then emits radiation out of two spectraly and spatially separated resonators at frequencies determined by the locking schemes that we choose. When we inject the signal close to a resonance, it locks the oscillator emission to the signal frequency by injection locking. When we inject the signal close to the difference of resonances, it locks the oscillator emission by parametric locking. We compare both schemes and investigate the dependence of the parametric locking range on the pump and the injection signal power. Our results can be interpreted using Adler's theory for lasers, which makes a new link between laser physics and superconducting circuits that could enable better understanding of pumped circuits for quantum information applications such as error correction, circulators and photon number detectors.