AC-Josephson Effect and Sub-Comb Mode-Locking in a Kerr-Induced Synchronized Cavity Soliton

TL;DR

This paper explores AC-driven Kerr-induced synchronization in microresonator solitons, demonstrating Shapiro steps and sub-comb mode-locking, with experimental validation and implications for tunable frequency combs.

Contribution

It introduces an AC version of Kerr-induced synchronization, showing fractional Shapiro steps and sub-comb mode-locking in microresonator solitons, supported by theoretical and experimental analysis.

Findings

Observation of integer and fractional Shapiro steps.

Experimental demonstration of sub-comb mode-locking.

Validation of Adler and Lugiato-Lefever models in this context.

Abstract

Kerr-induced synchronization (KIS) [1] involves the capture of a dissipative Kerr soliton (DKS) microcomb [2] tooth by a reference laser injected into the DKS resonator. This phase-locking behavior is described by an Adler equation whose analogous form describes numerous other physical systems [3], such as Josephson junctions [4]. We present an AC version of KIS whose behavior is similar to microwave-driven Josephson junctions, where periodic synchronization occurs as so-called Shapiro steps. We demonstrate consistent results in the AC-KIS dynamics predicted by the Adler model, Lugiato-Lefever equation, and experimental data from a chip-integrated microresonator system. The (integer) Shapiro steps in KIS can simply be explained as the sideband created through the reference laser phase modulation triggering the synchronization. Notably, our optical system allows for easy tuning of the Adler damping parameter, enabling the further observation of fractional-Shapiro steps, where the synchronization happens at a fraction of the driving microwave frequency. Here, we show that the comb tooth is indirectly captured thanks to a four-wave mixing Bragg-scattering process, leading to sub-comb mode-locking, and we demonstrate this experimentally through noise considerations. Our work opens the door to the study of synchronization phenomena in the context of microresonator frequency combs, synthesis of condensed-matter state analogues with DKSs, and the use of the fractional Shapiro steps for flexible and tunable access to the KIS regime.